LMFDB - Embedded newform 1350.2.j.c.1099.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [1350,2,Mod(199,1350)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(1350, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([2, 3])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("1350.199"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 1350 = 2 \cdot 3^{3} \cdot 5^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1350.j (of order $6$, degree $2$, not minimal)

Newform invariants

comment:select newform

sage:traces = [4,0,0,2,0,0,0,0,0,0,6,0,0,-8,0,-2,0,0,-20] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(19)] == traces)

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

Self dual:	no
Analytic conductor:	$10.7798042729$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(\zeta_{6})$
Coefficient field:	$\Q(\zeta_{12})$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{2} + 1 $ x^4 - x^2 + 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 90)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			1099.1
Root			$0.866025 + 0.500000i$ of defining polynomial
Character	$\chi$	$=$	1350.1099
Dual form			1350.2.j.c.199.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.866025 - 0.500000i) q^{2} +(0.500000 + 0.866025i) q^{4} +(3.46410 + 2.00000i) q^{7} -1.00000i q^{8} +(1.50000 - 2.59808i) q^{11} +(3.46410 - 2.00000i) q^{13} +(-2.00000 - 3.46410i) q^{14} +(-0.500000 + 0.866025i) q^{16} -3.00000i q^{17} -5.00000 q^{19} +(-2.59808 + 1.50000i) q^{22} +(5.19615 - 3.00000i) q^{23} -4.00000 q^{26} +4.00000i q^{28} +(-3.00000 + 5.19615i) q^{29} +(-1.00000 - 1.73205i) q^{31} +(0.866025 - 0.500000i) q^{32} +(-1.50000 + 2.59808i) q^{34} -4.00000i q^{37} +(4.33013 + 2.50000i) q^{38} +(-1.50000 - 2.59808i) q^{41} +(9.52628 + 5.50000i) q^{43} +3.00000 q^{44} -6.00000 q^{46} +(4.50000 + 7.79423i) q^{49} +(3.46410 + 2.00000i) q^{52} +6.00000i q^{53} +(2.00000 - 3.46410i) q^{56} +(5.19615 - 3.00000i) q^{58} +(1.50000 + 2.59808i) q^{59} +(5.00000 - 8.66025i) q^{61} +2.00000i q^{62} -1.00000 q^{64} +(4.33013 - 2.50000i) q^{67} +(2.59808 - 1.50000i) q^{68} -6.00000 q^{71} +7.00000i q^{73} +(-2.00000 + 3.46410i) q^{74} +(-2.50000 - 4.33013i) q^{76} +(10.3923 - 6.00000i) q^{77} +(7.00000 - 12.1244i) q^{79} +3.00000i q^{82} +(-10.3923 - 6.00000i) q^{83} +(-5.50000 - 9.52628i) q^{86} +(-2.59808 - 1.50000i) q^{88} +6.00000 q^{89} +16.0000 q^{91} +(5.19615 + 3.00000i) q^{92} +(-9.52628 - 5.50000i) q^{97} -9.00000i q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 2 q^{4} + 6 q^{11} - 8 q^{14} - 2 q^{16} - 20 q^{19} - 16 q^{26} - 12 q^{29} - 4 q^{31} - 6 q^{34} - 6 q^{41} + 12 q^{44} - 24 q^{46} + 18 q^{49} + 8 q^{56} + 6 q^{59} + 20 q^{61} - 4 q^{64} - 24 q^{71}+ \cdots + 64 q^{91}+O(q^{100}) $ 4 * q + 2 * q^4 + 6 * q^11 - 8 * q^14 - 2 * q^16 - 20 * q^19 - 16 * q^26 - 12 * q^29 - 4 * q^31 - 6 * q^34 - 6 * q^41 + 12 * q^44 - 24 * q^46 + 18 * q^49 + 8 * q^56 + 6 * q^59 + 20 * q^61 - 4 * q^64 - 24 * q^71 - 8 * q^74 - 10 * q^76 + 28 * q^79 - 22 * q^86 + 24 * q^89 + 64 * q^91

Character values

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

$n$	$1001$	$1027$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$-1$

Coefficient data

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

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

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

$2$	−0.866025	−	0.500000i	−0.612372	−	0.353553i
$2$	−0.866025	−	0.500000i	−0.612372	−	0.353553i
$3$		0			0
$3$		0			0
$4$	0.500000	+	0.866025i	0.250000	+	0.433013i
$5$		0			0
$5$		0			0
$6$		0			0
$7$	3.46410	+	2.00000i	1.30931	+	0.755929i	0.981981	−	0.188982i	$-0.0605189\pi$
$7$	3.46410	+	2.00000i	1.30931	+	0.755929i	0.327327	+	0.944911i	$0.393852\pi$
$8$		−	1.00000i		−	0.353553i
$9$		0			0
$10$		0			0
$11$	1.50000	−	2.59808i	0.452267	−	0.783349i	−0.546259	−	0.837616i	$-0.683949\pi$
$11$	1.50000	−	2.59808i	0.452267	−	0.783349i	0.998526	+	0.0542666i	$0.0172821\pi$
$12$		0			0
$13$	3.46410	−	2.00000i	0.960769	−	0.554700i	0.0643593	−	0.997927i	$-0.479500\pi$
$13$	3.46410	−	2.00000i	0.960769	−	0.554700i	0.896410	+	0.443227i	$0.146166\pi$
$14$	−2.00000	−	3.46410i	−0.534522	−	0.925820i
$15$		0			0
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$		−	3.00000i		−	0.727607i	−0.931476	−	0.363803i	$-0.881478\pi$
$17$		−	3.00000i		−	0.727607i	0.931476	−	0.363803i	$-0.118522\pi$
$18$		0			0
$19$	−5.00000			−1.14708			−0.573539	−	0.819178i	$-0.694430\pi$
$19$	−5.00000			−1.14708			−0.573539	+	0.819178i	$0.694430\pi$
$20$		0			0
$21$		0			0
$22$	−2.59808	+	1.50000i	−0.553912	+	0.319801i
$23$	5.19615	−	3.00000i	1.08347	−	0.625543i	0.151642	−	0.988436i	$-0.451544\pi$
$23$	5.19615	−	3.00000i	1.08347	−	0.625543i	0.931831	+	0.362892i	$0.118211\pi$
$24$		0			0
$25$		0			0
$26$	−4.00000			−0.784465
$27$		0			0
$28$			4.00000i			0.755929i
$29$	−3.00000	+	5.19615i	−0.557086	+	0.964901i	0.440652	+	0.897678i	$0.354747\pi$
$29$	−3.00000	+	5.19615i	−0.557086	+	0.964901i	−0.997738	+	0.0672232i	$0.978586\pi$
$30$		0			0
$31$	−1.00000	−	1.73205i	−0.179605	−	0.311086i	0.762140	−	0.647412i	$-0.224149\pi$
$31$	−1.00000	−	1.73205i	−0.179605	−	0.311086i	−0.941745	+	0.336327i	$0.890815\pi$
$32$	0.866025	−	0.500000i	0.153093	−	0.0883883i
$33$		0			0
$34$	−1.50000	+	2.59808i	−0.257248	+	0.445566i
$35$		0			0
$36$		0			0
$37$		−	4.00000i		−	0.657596i	−0.944400	−	0.328798i	$-0.893356\pi$
$37$		−	4.00000i		−	0.657596i	0.944400	−	0.328798i	$-0.106644\pi$
$38$	4.33013	+	2.50000i	0.702439	+	0.405554i
$39$		0			0
$40$		0			0
$41$	−1.50000	−	2.59808i	−0.234261	−	0.405751i	0.724797	−	0.688963i	$-0.241934\pi$
$41$	−1.50000	−	2.59808i	−0.234261	−	0.405751i	−0.959058	+	0.283211i	$0.908600\pi$
$42$		0			0
$43$	9.52628	+	5.50000i	1.45274	+	0.838742i	0.998636	−	0.0522047i	$-0.0166248\pi$
$43$	9.52628	+	5.50000i	1.45274	+	0.838742i	0.454108	+	0.890947i	$0.349958\pi$
$44$	3.00000			0.452267
$45$		0			0
$46$	−6.00000			−0.884652
$47$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$47$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$48$		0			0
$49$	4.50000	+	7.79423i	0.642857	+	1.11346i
$50$		0			0
$51$		0			0
$52$	3.46410	+	2.00000i	0.480384	+	0.277350i
$53$			6.00000i			0.824163i	0.911147	+	0.412082i	$0.135198\pi$
$53$			6.00000i			0.824163i	−0.911147	+	0.412082i	$0.864802\pi$
$54$		0			0
$55$		0			0
$56$	2.00000	−	3.46410i	0.267261	−	0.462910i
$57$		0			0
$58$	5.19615	−	3.00000i	0.682288	−	0.393919i
$59$	1.50000	+	2.59808i	0.195283	+	0.338241i	0.946993	−	0.321253i	$-0.104104\pi$
$59$	1.50000	+	2.59808i	0.195283	+	0.338241i	−0.751710	+	0.659494i	$0.770771\pi$
$60$		0			0
$61$	5.00000	−	8.66025i	0.640184	−	1.10883i	−0.345207	−	0.938527i	$-0.612191\pi$
$61$	5.00000	−	8.66025i	0.640184	−	1.10883i	0.985391	−	0.170305i	$-0.0544754\pi$
$62$			2.00000i			0.254000i
$63$		0			0
$64$	−1.00000			−0.125000
$65$		0			0
$66$		0			0
$67$	4.33013	−	2.50000i	0.529009	−	0.305424i	−0.211604	−	0.977356i	$-0.567869\pi$
$67$	4.33013	−	2.50000i	0.529009	−	0.305424i	0.740613	+	0.671932i	$0.234535\pi$
$68$	2.59808	−	1.50000i	0.315063	−	0.181902i
$69$		0			0
$70$		0			0
$71$	−6.00000			−0.712069			−0.356034	−	0.934473i	$-0.615871\pi$
$71$	−6.00000			−0.712069			−0.356034	+	0.934473i	$0.615871\pi$
$72$		0			0
$73$			7.00000i			0.819288i	0.912245	+	0.409644i	$0.134347\pi$
$73$			7.00000i			0.819288i	−0.912245	+	0.409644i	$0.865653\pi$
$74$	−2.00000	+	3.46410i	−0.232495	+	0.402694i
$75$		0			0
$76$	−2.50000	−	4.33013i	−0.286770	−	0.496700i
$77$	10.3923	−	6.00000i	1.18431	−	0.683763i
$78$		0			0
$79$	7.00000	−	12.1244i	0.787562	−	1.36410i	−0.139895	−	0.990166i	$-0.544677\pi$
$79$	7.00000	−	12.1244i	0.787562	−	1.36410i	0.927457	−	0.373930i	$-0.121990\pi$
$80$		0			0
$81$		0			0
$82$			3.00000i			0.331295i
$83$	−10.3923	−	6.00000i	−1.14070	−	0.658586i	−0.194099	−	0.980982i	$-0.562178\pi$
$83$	−10.3923	−	6.00000i	−1.14070	−	0.658586i	−0.946605	+	0.322396i	$0.895512\pi$
$84$		0			0
$85$		0			0
$86$	−5.50000	−	9.52628i	−0.593080	−	1.02725i
$87$		0			0
$88$	−2.59808	−	1.50000i	−0.276956	−	0.159901i
$89$	6.00000			0.635999			0.317999	−	0.948091i	$-0.396989\pi$
$89$	6.00000			0.635999			0.317999	+	0.948091i	$0.396989\pi$
$90$		0			0
$91$	16.0000			1.67726
$92$	5.19615	+	3.00000i	0.541736	+	0.312772i
$93$		0			0
$94$		0			0
$95$		0			0
$96$		0			0
$97$	−9.52628	−	5.50000i	−0.967247	−	0.558440i	−0.0688512	−	0.997627i	$-0.521933\pi$
$97$	−9.52628	−	5.50000i	−0.967247	−	0.558440i	−0.898396	+	0.439187i	$0.855267\pi$
$98$		−	9.00000i		−	0.909137i
$99$		0			0
$100$		0			0
$101$	−6.00000	+	10.3923i	−0.597022	+	1.03407i	0.396236	+	0.918149i	$0.370316\pi$
$101$	−6.00000	+	10.3923i	−0.597022	+	1.03407i	−0.993258	+	0.115924i	$0.963017\pi$
$102$		0			0
$103$	3.46410	−	2.00000i	0.341328	−	0.197066i	−0.319531	−	0.947576i	$-0.603525\pi$
$103$	3.46410	−	2.00000i	0.341328	−	0.197066i	0.660859	+	0.750510i	$0.270192\pi$
$104$	−2.00000	−	3.46410i	−0.196116	−	0.339683i
$105$		0			0
$106$	3.00000	−	5.19615i	0.291386	−	0.504695i
$107$			9.00000i			0.870063i	0.900415	+	0.435031i	$0.143263\pi$
$107$			9.00000i			0.870063i	−0.900415	+	0.435031i	$0.856737\pi$
$108$		0			0
$109$	4.00000			0.383131			0.191565	−	0.981480i	$-0.438644\pi$
$109$	4.00000			0.383131			0.191565	+	0.981480i	$0.438644\pi$
$110$		0			0
$111$		0			0
$112$	−3.46410	+	2.00000i	−0.327327	+	0.188982i
$113$	15.5885	−	9.00000i	1.46644	−	0.846649i	0.467143	−	0.884182i	$-0.345283\pi$
$113$	15.5885	−	9.00000i	1.46644	−	0.846649i	0.999295	+	0.0375328i	$0.0119499\pi$
$114$		0			0
$115$		0			0
$116$	−6.00000			−0.557086
$117$		0			0
$118$		−	3.00000i		−	0.276172i
$119$	6.00000	−	10.3923i	0.550019	−	0.952661i
$120$		0			0
$121$	1.00000	+	1.73205i	0.0909091	+	0.157459i
$122$	−8.66025	+	5.00000i	−0.784063	+	0.452679i
$123$		0			0
$124$	1.00000	−	1.73205i	0.0898027	−	0.155543i
$125$		0			0
$126$		0			0
$127$			2.00000i			0.177471i	0.996055	+	0.0887357i	$0.0282826\pi$
$127$			2.00000i			0.177471i	−0.996055	+	0.0887357i	$0.971717\pi$
$128$	0.866025	+	0.500000i	0.0765466	+	0.0441942i
$129$		0			0
$130$		0			0
$131$	6.00000	+	10.3923i	0.524222	+	0.907980i	0.999602	+	0.0281993i	$0.00897729\pi$
$131$	6.00000	+	10.3923i	0.524222	+	0.907980i	−0.475380	+	0.879781i	$0.657689\pi$
$132$		0			0
$133$	−17.3205	−	10.0000i	−1.50188	−	0.867110i
$134$	−5.00000			−0.431934
$135$		0			0
$136$	−3.00000			−0.257248
$137$	−7.79423	−	4.50000i	−0.665906	−	0.384461i	0.128618	−	0.991694i	$-0.458946\pi$
$137$	−7.79423	−	4.50000i	−0.665906	−	0.384461i	−0.794524	+	0.607233i	$0.792279\pi$
$138$		0			0
$139$	−0.500000	−	0.866025i	−0.0424094	−	0.0734553i	0.844042	−	0.536278i	$-0.180170\pi$
$139$	−0.500000	−	0.866025i	−0.0424094	−	0.0734553i	−0.886451	+	0.462822i	$0.846837\pi$
$140$		0			0
$141$		0			0
$142$	5.19615	+	3.00000i	0.436051	+	0.251754i
$143$		−	12.0000i		−	1.00349i
$144$		0			0
$145$		0			0
$146$	3.50000	−	6.06218i	0.289662	−	0.501709i
$147$		0			0
$148$	3.46410	−	2.00000i	0.284747	−	0.164399i
$149$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$149$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$150$		0			0
$151$	5.00000	−	8.66025i	0.406894	−	0.704761i	−0.587646	−	0.809118i	$-0.699945\pi$
$151$	5.00000	−	8.66025i	0.406894	−	0.704761i	0.994540	+	0.104357i	$0.0332784\pi$
$152$			5.00000i			0.405554i
$153$		0			0
$154$	−12.0000			−0.966988
$155$		0			0
$156$		0			0
$157$	6.92820	−	4.00000i	0.552931	−	0.319235i	−0.197372	−	0.980329i	$-0.563241\pi$
$157$	6.92820	−	4.00000i	0.552931	−	0.319235i	0.750303	+	0.661094i	$0.229907\pi$
$158$	−12.1244	+	7.00000i	−0.964562	+	0.556890i
$159$		0			0
$160$		0			0
$161$	24.0000			1.89146
$162$		0			0
$163$			16.0000i			1.25322i	0.779334	+	0.626608i	$0.215557\pi$
$163$			16.0000i			1.25322i	−0.779334	+	0.626608i	$0.784443\pi$
$164$	1.50000	−	2.59808i	0.117130	−	0.202876i
$165$		0			0
$166$	6.00000	+	10.3923i	0.465690	+	0.806599i
$167$	15.5885	−	9.00000i	1.20627	−	0.696441i	0.244328	−	0.969693i	$-0.421432\pi$
$167$	15.5885	−	9.00000i	1.20627	−	0.696441i	0.961943	+	0.273252i	$0.0880992\pi$
$168$		0			0
$169$	1.50000	−	2.59808i	0.115385	−	0.199852i
$170$		0			0
$171$		0			0
$172$			11.0000i			0.838742i
$173$	15.5885	+	9.00000i	1.18517	+	0.684257i	0.957205	−	0.289412i	$-0.0934598\pi$
$173$	15.5885	+	9.00000i	1.18517	+	0.684257i	0.227964	+	0.973670i	$0.426793\pi$
$174$		0			0
$175$		0			0
$176$	1.50000	+	2.59808i	0.113067	+	0.195837i
$177$		0			0
$178$	−5.19615	−	3.00000i	−0.389468	−	0.224860i
$179$		0			0			−	1.00000i	$-0.5\pi$
$179$		0			0				1.00000i	$0.5\pi$
$180$		0			0
$181$	−16.0000			−1.18927			−0.594635	−	0.803996i	$-0.702704\pi$
$181$	−16.0000			−1.18927			−0.594635	+	0.803996i	$0.702704\pi$
$182$	−13.8564	−	8.00000i	−1.02711	−	0.592999i
$183$		0			0
$184$	−3.00000	−	5.19615i	−0.221163	−	0.383065i
$185$		0			0
$186$		0			0
$187$	−7.79423	−	4.50000i	−0.569970	−	0.329073i
$188$		0			0
$189$		0			0
$190$		0			0
$191$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$191$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$192$		0			0
$193$	11.2583	−	6.50000i	0.810392	−	0.467880i	−0.0366998	−	0.999326i	$-0.511685\pi$
$193$	11.2583	−	6.50000i	0.810392	−	0.467880i	0.847092	+	0.531446i	$0.178351\pi$
$194$	5.50000	+	9.52628i	0.394877	+	0.683947i
$195$		0			0
$196$	−4.50000	+	7.79423i	−0.321429	+	0.556731i
$197$		0			0		1.00000			$0$
$197$		0			0		−1.00000			$\pi$
$198$		0			0
$199$	−20.0000			−1.41776			−0.708881	−	0.705328i	$-0.750800\pi$
$199$	−20.0000			−1.41776			−0.708881	+	0.705328i	$0.750800\pi$
$200$		0			0
$201$		0			0
$202$	10.3923	−	6.00000i	0.731200	−	0.422159i
$203$	−20.7846	+	12.0000i	−1.45879	+	0.842235i
$204$		0			0
$205$		0			0
$206$	−4.00000			−0.278693
$207$		0			0
$208$			4.00000i			0.277350i
$209$	−7.50000	+	12.9904i	−0.518786	+	0.898563i
$210$		0			0
$211$	2.00000	+	3.46410i	0.137686	+	0.238479i	0.926620	−	0.375999i	$-0.122700\pi$
$211$	2.00000	+	3.46410i	0.137686	+	0.238479i	−0.788935	+	0.614477i	$0.789367\pi$
$212$	−5.19615	+	3.00000i	−0.356873	+	0.206041i
$213$		0			0
$214$	4.50000	−	7.79423i	0.307614	−	0.532803i
$215$		0			0
$216$		0			0
$217$		−	8.00000i		−	0.543075i
$218$	−3.46410	−	2.00000i	−0.234619	−	0.135457i
$219$		0			0
$220$		0			0
$221$	−6.00000	−	10.3923i	−0.403604	−	0.699062i
$222$		0			0
$223$	−19.0526	−	11.0000i	−1.27585	−	0.736614i	−0.299770	−	0.954011i	$-0.596910\pi$
$223$	−19.0526	−	11.0000i	−1.27585	−	0.736614i	−0.976083	+	0.217397i	$0.930243\pi$
$224$	4.00000			0.267261
$225$		0			0
$226$	−18.0000			−1.19734
$227$	−2.59808	−	1.50000i	−0.172440	−	0.0995585i	0.411296	−	0.911502i	$-0.365076\pi$
$227$	−2.59808	−	1.50000i	−0.172440	−	0.0995585i	−0.583736	+	0.811943i	$0.698410\pi$
$228$		0			0
$229$	10.0000	+	17.3205i	0.660819	+	1.14457i	0.980401	+	0.197013i	$0.0631241\pi$
$229$	10.0000	+	17.3205i	0.660819	+	1.14457i	−0.319582	+	0.947559i	$0.603543\pi$
$230$		0			0
$231$		0			0
$232$	5.19615	+	3.00000i	0.341144	+	0.196960i
$233$			21.0000i			1.37576i	0.725826	+	0.687878i	$0.241458\pi$
$233$			21.0000i			1.37576i	−0.725826	+	0.687878i	$0.758542\pi$
$234$		0			0
$235$		0			0
$236$	−1.50000	+	2.59808i	−0.0976417	+	0.169120i
$237$		0			0
$238$	−10.3923	+	6.00000i	−0.673633	+	0.388922i
$239$	−3.00000	−	5.19615i	−0.194054	−	0.336111i	0.752536	−	0.658551i	$-0.228830\pi$
$239$	−3.00000	−	5.19615i	−0.194054	−	0.336111i	−0.946590	+	0.322440i	$0.895497\pi$
$240$		0			0
$241$	−8.50000	+	14.7224i	−0.547533	+	0.948355i	0.450910	+	0.892570i	$0.351100\pi$
$241$	−8.50000	+	14.7224i	−0.547533	+	0.948355i	−0.998443	+	0.0557856i	$0.982234\pi$
$242$		−	2.00000i		−	0.128565i
$243$		0			0
$244$	10.0000			0.640184
$245$		0			0
$246$		0			0
$247$	−17.3205	+	10.0000i	−1.10208	+	0.636285i
$248$	−1.73205	+	1.00000i	−0.109985	+	0.0635001i
$249$		0			0
$250$		0			0
$251$	21.0000			1.32551			0.662754	−	0.748837i	$-0.269387\pi$
$251$	21.0000			1.32551			0.662754	+	0.748837i	$0.269387\pi$
$252$		0			0
$253$		−	18.0000i		−	1.13165i
$254$	1.00000	−	1.73205i	0.0627456	−	0.108679i
$255$		0			0
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	−7.79423	+	4.50000i	−0.486191	+	0.280702i	−0.722993	−	0.690856i	$-0.757234\pi$
$257$	−7.79423	+	4.50000i	−0.486191	+	0.280702i	0.236802	+	0.971558i	$0.423901\pi$
$258$		0			0
$259$	8.00000	−	13.8564i	0.497096	−	0.860995i
$260$		0			0
$261$		0			0
$262$		−	12.0000i		−	0.741362i
$263$	−20.7846	−	12.0000i	−1.28163	−	0.739952i	−0.304487	−	0.952517i	$-0.598485\pi$
$263$	−20.7846	−	12.0000i	−1.28163	−	0.739952i	−0.977147	+	0.212565i	$0.931818\pi$
$264$		0			0
$265$		0			0
$266$	10.0000	+	17.3205i	0.613139	+	1.06199i
$267$		0			0
$268$	4.33013	+	2.50000i	0.264505	+	0.152712i
$269$	6.00000			0.365826			0.182913	−	0.983129i	$-0.441447\pi$
$269$	6.00000			0.365826			0.182913	+	0.983129i	$0.441447\pi$
$270$		0			0
$271$	−16.0000			−0.971931			−0.485965	−	0.873978i	$-0.661532\pi$
$271$	−16.0000			−0.971931			−0.485965	+	0.873978i	$0.661532\pi$
$272$	2.59808	+	1.50000i	0.157532	+	0.0909509i
$273$		0			0
$274$	4.50000	+	7.79423i	0.271855	+	0.470867i
$275$		0			0
$276$		0			0
$277$	19.0526	+	11.0000i	1.14476	+	0.660926i	0.947604	−	0.319447i	$-0.103497\pi$
$277$	19.0526	+	11.0000i	1.14476	+	0.660926i	0.197153	+	0.980373i	$0.436830\pi$
$278$			1.00000i			0.0599760i
$279$		0			0
$280$		0			0
$281$	−3.00000	+	5.19615i	−0.178965	+	0.309976i	−0.941526	−	0.336939i	$-0.890608\pi$
$281$	−3.00000	+	5.19615i	−0.178965	+	0.309976i	0.762561	+	0.646916i	$0.223942\pi$
$282$		0			0
$283$	−17.3205	+	10.0000i	−1.02960	+	0.594438i	−0.916869	−	0.399188i	$-0.869292\pi$
$283$	−17.3205	+	10.0000i	−1.02960	+	0.594438i	−0.112728	+	0.993626i	$0.535959\pi$
$284$	−3.00000	−	5.19615i	−0.178017	−	0.308335i
$285$		0			0
$286$	−6.00000	+	10.3923i	−0.354787	+	0.614510i
$287$		−	12.0000i		−	0.708338i
$288$		0			0
$289$	8.00000			0.470588
$290$		0			0
$291$		0			0
$292$	−6.06218	+	3.50000i	−0.354762	+	0.204822i
$293$	−15.5885	+	9.00000i	−0.910687	+	0.525786i	−0.880652	−	0.473763i	$-0.842895\pi$
$293$	−15.5885	+	9.00000i	−0.910687	+	0.525786i	−0.0300351	+	0.999549i	$0.509562\pi$
$294$		0			0
$295$		0			0
$296$	−4.00000			−0.232495
$297$		0			0
$298$		0			0
$299$	12.0000	−	20.7846i	0.693978	−	1.20201i
$300$		0			0
$301$	22.0000	+	38.1051i	1.26806	+	2.19634i
$302$	−8.66025	+	5.00000i	−0.498342	+	0.287718i
$303$		0			0
$304$	2.50000	−	4.33013i	0.143385	−	0.248350i
$305$		0			0
$306$		0			0
$307$		−	7.00000i		−	0.399511i	−0.979846	−	0.199756i	$-0.935985\pi$
$307$		−	7.00000i		−	0.399511i	0.979846	−	0.199756i	$-0.0640148\pi$
$308$	10.3923	+	6.00000i	0.592157	+	0.341882i
$309$		0			0
$310$		0			0
$311$	−3.00000	−	5.19615i	−0.170114	−	0.294647i	0.768345	−	0.640036i	$-0.221080\pi$
$311$	−3.00000	−	5.19615i	−0.170114	−	0.294647i	−0.938460	+	0.345389i	$0.887747\pi$
$312$		0			0
$313$	−0.866025	−	0.500000i	−0.0489506	−	0.0282617i	0.475325	−	0.879810i	$-0.342331\pi$
$313$	−0.866025	−	0.500000i	−0.0489506	−	0.0282617i	−0.524276	+	0.851549i	$0.675664\pi$
$314$	−8.00000			−0.451466
$315$		0			0
$316$	14.0000			0.787562
$317$	20.7846	+	12.0000i	1.16738	+	0.673987i	0.953062	−	0.302777i	$-0.0979136\pi$
$317$	20.7846	+	12.0000i	1.16738	+	0.673987i	0.214318	+	0.976764i	$0.431247\pi$
$318$		0			0
$319$	9.00000	+	15.5885i	0.503903	+	0.872786i
$320$		0			0
$321$		0			0
$322$	−20.7846	−	12.0000i	−1.15828	−	0.668734i
$323$			15.0000i			0.834622i
$324$		0			0
$325$		0			0
$326$	8.00000	−	13.8564i	0.443079	−	0.767435i
$327$		0			0
$328$	−2.59808	+	1.50000i	−0.143455	+	0.0828236i
$329$		0			0
$330$		0			0
$331$	2.00000	−	3.46410i	0.109930	−	0.190404i	−0.805812	−	0.592172i	$-0.798271\pi$
$331$	2.00000	−	3.46410i	0.109930	−	0.190404i	0.915742	+	0.401768i	$0.131604\pi$
$332$		−	12.0000i		−	0.658586i
$333$		0			0
$334$	−18.0000			−0.984916
$335$		0			0
$336$		0			0
$337$	−26.8468	+	15.5000i	−1.46244	+	0.844339i	−0.999124	−	0.0418554i	$-0.986673\pi$
$337$	−26.8468	+	15.5000i	−1.46244	+	0.844339i	−0.463314	+	0.886194i	$0.653340\pi$
$338$	−2.59808	+	1.50000i	−0.141317	+	0.0815892i
$339$		0			0
$340$		0			0
$341$	−6.00000			−0.324918
$342$		0			0
$343$			8.00000i			0.431959i
$344$	5.50000	−	9.52628i	0.296540	−	0.513623i
$345$		0			0
$346$	−9.00000	−	15.5885i	−0.483843	−	0.838041i
$347$	−18.1865	+	10.5000i	−0.976304	+	0.563670i	−0.901152	−	0.433503i	$-0.857278\pi$
$347$	−18.1865	+	10.5000i	−0.976304	+	0.563670i	−0.0751519	+	0.997172i	$0.523944\pi$
$348$		0			0
$349$	−8.00000	+	13.8564i	−0.428230	+	0.741716i	−0.996716	−	0.0809766i	$-0.974196\pi$
$349$	−8.00000	+	13.8564i	−0.428230	+	0.741716i	0.568486	+	0.822693i	$0.307529\pi$
$350$		0			0
$351$		0			0
$352$		−	3.00000i		−	0.159901i
$353$	−7.79423	−	4.50000i	−0.414845	−	0.239511i	0.278024	−	0.960574i	$-0.410320\pi$
$353$	−7.79423	−	4.50000i	−0.414845	−	0.239511i	−0.692869	+	0.721063i	$0.743654\pi$
$354$		0			0
$355$		0			0
$356$	3.00000	+	5.19615i	0.159000	+	0.275396i
$357$		0			0
$358$		0			0
$359$	−24.0000			−1.26667			−0.633336	−	0.773877i	$-0.718315\pi$
$359$	−24.0000			−1.26667			−0.633336	+	0.773877i	$0.718315\pi$
$360$		0			0
$361$	6.00000			0.315789
$362$	13.8564	+	8.00000i	0.728277	+	0.420471i
$363$		0			0
$364$	8.00000	+	13.8564i	0.419314	+	0.726273i
$365$		0			0
$366$		0			0
$367$	−6.92820	−	4.00000i	−0.361649	−	0.208798i	0.308155	−	0.951336i	$-0.400289\pi$
$367$	−6.92820	−	4.00000i	−0.361649	−	0.208798i	−0.669804	+	0.742538i	$0.733622\pi$
$368$			6.00000i			0.312772i
$369$		0			0
$370$		0			0
$371$	−12.0000	+	20.7846i	−0.623009	+	1.07908i
$372$		0			0
$373$	8.66025	−	5.00000i	0.448411	−	0.258890i	−0.258748	−	0.965945i	$-0.583310\pi$
$373$	8.66025	−	5.00000i	0.448411	−	0.258890i	0.707159	+	0.707055i	$0.249977\pi$
$374$	4.50000	+	7.79423i	0.232689	+	0.403030i
$375$		0			0
$376$		0			0
$377$			24.0000i			1.23606i
$378$		0			0
$379$	−29.0000			−1.48963			−0.744815	−	0.667271i	$-0.767462\pi$
$379$	−29.0000			−1.48963			−0.744815	+	0.667271i	$0.767462\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$	10.3923	−	6.00000i	0.531022	−	0.306586i	−0.210411	−	0.977613i	$-0.567480\pi$
$383$	10.3923	−	6.00000i	0.531022	−	0.306586i	0.741433	+	0.671027i	$0.234147\pi$
$384$		0			0
$385$		0			0
$386$	−13.0000			−0.661683
$387$		0			0
$388$		−	11.0000i		−	0.558440i
$389$	−18.0000	+	31.1769i	−0.912636	+	1.58073i	−0.102311	+	0.994753i	$0.532624\pi$
$389$	−18.0000	+	31.1769i	−0.912636	+	1.58073i	−0.810326	+	0.585980i	$0.800710\pi$
$390$		0			0
$391$	−9.00000	−	15.5885i	−0.455150	−	0.788342i
$392$	7.79423	−	4.50000i	0.393668	−	0.227284i
$393$		0			0
$394$		0			0
$395$		0			0
$396$		0			0
$397$			8.00000i			0.401508i	0.979642	+	0.200754i	$0.0643393\pi$
$397$			8.00000i			0.401508i	−0.979642	+	0.200754i	$0.935661\pi$
$398$	17.3205	+	10.0000i	0.868199	+	0.501255i
$399$		0			0
$400$		0			0
$401$	16.5000	+	28.5788i	0.823971	+	1.42716i	0.902703	+	0.430263i	$0.141579\pi$
$401$	16.5000	+	28.5788i	0.823971	+	1.42716i	−0.0787327	+	0.996896i	$0.525087\pi$
$402$		0			0
$403$	−6.92820	−	4.00000i	−0.345118	−	0.199254i
$404$	−12.0000			−0.597022
$405$		0			0
$406$	24.0000			1.19110
$407$	−10.3923	−	6.00000i	−0.515127	−	0.297409i
$408$		0			0
$409$	−15.5000	−	26.8468i	−0.766426	−	1.32749i	−0.939490	−	0.342578i	$-0.888700\pi$
$409$	−15.5000	−	26.8468i	−0.766426	−	1.32749i	0.173064	−	0.984911i	$-0.444633\pi$
$410$		0			0
$411$		0			0
$412$	3.46410	+	2.00000i	0.170664	+	0.0985329i
$413$			12.0000i			0.590481i
$414$		0			0
$415$		0			0
$416$	2.00000	−	3.46410i	0.0980581	−	0.169842i
$417$		0			0
$418$	12.9904	−	7.50000i	0.635380	−	0.366837i
$419$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$419$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$420$		0			0
$421$	−1.00000	+	1.73205i	−0.0487370	+	0.0844150i	−0.889365	−	0.457198i	$-0.848853\pi$
$421$	−1.00000	+	1.73205i	−0.0487370	+	0.0844150i	0.840628	+	0.541613i	$0.182186\pi$
$422$		−	4.00000i		−	0.194717i
$423$		0			0
$424$	6.00000			0.291386
$425$		0			0
$426$		0			0
$427$	34.6410	−	20.0000i	1.67640	−	0.967868i
$428$	−7.79423	+	4.50000i	−0.376748	+	0.217516i
$429$		0			0
$430$		0			0
$431$	−24.0000			−1.15604			−0.578020	−	0.816023i	$-0.696174\pi$
$431$	−24.0000			−1.15604			−0.578020	+	0.816023i	$0.696174\pi$
$432$		0			0
$433$			13.0000i			0.624740i	0.949960	+	0.312370i	$0.101123\pi$
$433$			13.0000i			0.624740i	−0.949960	+	0.312370i	$0.898877\pi$
$434$	−4.00000	+	6.92820i	−0.192006	+	0.332564i
$435$		0			0
$436$	2.00000	+	3.46410i	0.0957826	+	0.165900i
$437$	−25.9808	+	15.0000i	−1.24283	+	0.717547i
$438$		0			0
$439$	−5.00000	+	8.66025i	−0.238637	+	0.413331i	−0.960323	−	0.278889i	$-0.910034\pi$
$439$	−5.00000	+	8.66025i	−0.238637	+	0.413331i	0.721686	+	0.692220i	$0.243367\pi$
$440$		0			0
$441$		0			0
$442$			12.0000i			0.570782i
$443$	−2.59808	−	1.50000i	−0.123438	−	0.0712672i	0.437009	−	0.899457i	$-0.356038\pi$
$443$	−2.59808	−	1.50000i	−0.123438	−	0.0712672i	−0.560448	+	0.828190i	$0.689371\pi$
$444$		0			0
$445$		0			0
$446$	11.0000	+	19.0526i	0.520865	+	0.902165i
$447$		0			0
$448$	−3.46410	−	2.00000i	−0.163663	−	0.0944911i
$449$	−15.0000			−0.707894			−0.353947	−	0.935266i	$-0.615161\pi$
$449$	−15.0000			−0.707894			−0.353947	+	0.935266i	$0.615161\pi$
$450$		0			0
$451$	−9.00000			−0.423793
$452$	15.5885	+	9.00000i	0.733219	+	0.423324i
$453$		0			0
$454$	1.50000	+	2.59808i	0.0703985	+	0.121934i
$455$		0			0
$456$		0			0
$457$	0.866025	+	0.500000i	0.0405110	+	0.0233890i	0.520119	−	0.854094i	$-0.325888\pi$
$457$	0.866025	+	0.500000i	0.0405110	+	0.0233890i	−0.479608	+	0.877483i	$0.659221\pi$
$458$		−	20.0000i		−	0.934539i
$459$		0			0
$460$		0			0
$461$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$461$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$462$		0			0
$463$	−17.3205	+	10.0000i	−0.804952	+	0.464739i	−0.845200	−	0.534450i	$-0.820519\pi$
$463$	−17.3205	+	10.0000i	−0.804952	+	0.464739i	0.0402476	+	0.999190i	$0.487185\pi$
$464$	−3.00000	−	5.19615i	−0.139272	−	0.241225i
$465$		0			0
$466$	10.5000	−	18.1865i	0.486403	−	0.842475i
$467$		−	21.0000i		−	0.971764i	−0.874024	−	0.485882i	$-0.838498\pi$
$467$		−	21.0000i		−	0.971764i	0.874024	−	0.485882i	$-0.161502\pi$
$468$		0			0
$469$	20.0000			0.923514
$470$		0			0
$471$		0			0
$472$	2.59808	−	1.50000i	0.119586	−	0.0690431i
$473$	28.5788	−	16.5000i	1.31406	−	0.758671i
$474$		0			0
$475$		0			0
$476$	12.0000			0.550019
$477$		0			0
$478$			6.00000i			0.274434i
$479$	3.00000	−	5.19615i	0.137073	−	0.237418i	−0.789314	−	0.613990i	$-0.789564\pi$
$479$	3.00000	−	5.19615i	0.137073	−	0.237418i	0.926388	+	0.376571i	$0.122897\pi$
$480$		0			0
$481$	−8.00000	−	13.8564i	−0.364769	−	0.631798i
$482$	14.7224	−	8.50000i	0.670588	−	0.387164i
$483$		0			0
$484$	−1.00000	+	1.73205i	−0.0454545	+	0.0787296i
$485$		0			0
$486$		0			0
$487$			2.00000i			0.0906287i	0.998973	+	0.0453143i	$0.0144289\pi$
$487$			2.00000i			0.0906287i	−0.998973	+	0.0453143i	$0.985571\pi$
$488$	−8.66025	−	5.00000i	−0.392031	−	0.226339i
$489$		0			0
$490$		0			0
$491$	−16.5000	−	28.5788i	−0.744635	−	1.28974i	−0.950365	−	0.311136i	$-0.899290\pi$
$491$	−16.5000	−	28.5788i	−0.744635	−	1.28974i	0.205731	−	0.978609i	$-0.434043\pi$
$492$		0			0
$493$	15.5885	+	9.00000i	0.702069	+	0.405340i
$494$	20.0000			0.899843
$495$		0			0
$496$	2.00000			0.0898027
$497$	−20.7846	−	12.0000i	−0.932317	−	0.538274i
$498$		0			0
$499$	−15.5000	−	26.8468i	−0.693875	−	1.20183i	−0.970558	−	0.240866i	$-0.922569\pi$
$499$	−15.5000	−	26.8468i	−0.693875	−	1.20183i	0.276683	−	0.960961i	$-0.410765\pi$
$500$		0			0
$501$		0			0
$502$	−18.1865	−	10.5000i	−0.811705	−	0.468638i
$503$			6.00000i			0.267527i	0.991013	+	0.133763i	$0.0427062\pi$
$503$			6.00000i			0.267527i	−0.991013	+	0.133763i	$0.957294\pi$
$504$		0			0
$505$		0			0
$506$	−9.00000	+	15.5885i	−0.400099	+	0.692991i
$507$		0			0
$508$	−1.73205	+	1.00000i	−0.0768473	+	0.0443678i
$509$	6.00000	+	10.3923i	0.265945	+	0.460631i	0.967811	−	0.251679i	$-0.0809826\pi$
$509$	6.00000	+	10.3923i	0.265945	+	0.460631i	−0.701866	+	0.712309i	$0.747649\pi$
$510$		0			0
$511$	−14.0000	+	24.2487i	−0.619324	+	1.07270i
$512$			1.00000i			0.0441942i
$513$		0			0
$514$	9.00000			0.396973
$515$		0			0
$516$		0			0
$517$		0			0
$518$	−13.8564	+	8.00000i	−0.608816	+	0.351500i
$519$		0			0
$520$		0			0
$521$	3.00000			0.131432			0.0657162	−	0.997838i	$-0.479067\pi$
$521$	3.00000			0.131432			0.0657162	+	0.997838i	$0.479067\pi$
$522$		0			0
$523$		−	20.0000i		−	0.874539i	−0.899331	−	0.437269i	$-0.855946\pi$
$523$		−	20.0000i		−	0.874539i	0.899331	−	0.437269i	$-0.144054\pi$
$524$	−6.00000	+	10.3923i	−0.262111	+	0.453990i
$525$		0			0
$526$	12.0000	+	20.7846i	0.523225	+	0.906252i
$527$	−5.19615	+	3.00000i	−0.226348	+	0.130682i
$528$		0			0
$529$	6.50000	−	11.2583i	0.282609	−	0.489493i
$530$		0			0
$531$		0			0
$532$		−	20.0000i		−	0.867110i
$533$	−10.3923	−	6.00000i	−0.450141	−	0.259889i
$534$		0			0
$535$		0			0
$536$	−2.50000	−	4.33013i	−0.107984	−	0.187033i
$537$		0			0
$538$	−5.19615	−	3.00000i	−0.224022	−	0.129339i
$539$	27.0000			1.16297
$540$		0			0
$541$	8.00000			0.343947			0.171973	−	0.985102i	$-0.444986\pi$
$541$	8.00000			0.343947			0.171973	+	0.985102i	$0.444986\pi$
$542$	13.8564	+	8.00000i	0.595184	+	0.343629i
$543$		0			0
$544$	−1.50000	−	2.59808i	−0.0643120	−	0.111392i
$545$		0			0
$546$		0			0
$547$	0.866025	+	0.500000i	0.0370286	+	0.0213785i	0.518400	−	0.855138i	$-0.326528\pi$
$547$	0.866025	+	0.500000i	0.0370286	+	0.0213785i	−0.481371	+	0.876517i	$0.659861\pi$
$548$		−	9.00000i		−	0.384461i
$549$		0			0
$550$		0			0
$551$	15.0000	−	25.9808i	0.639021	−	1.10682i
$552$		0			0
$553$	48.4974	−	28.0000i	2.06232	−	1.19068i
$554$	−11.0000	−	19.0526i	−0.467345	−	0.809466i
$555$		0			0
$556$	0.500000	−	0.866025i	0.0212047	−	0.0367277i
$557$			12.0000i			0.508456i	0.967144	+	0.254228i	$0.0818214\pi$
$557$			12.0000i			0.508456i	−0.967144	+	0.254228i	$0.918179\pi$
$558$		0			0
$559$	44.0000			1.86100
$560$		0			0
$561$		0			0
$562$	5.19615	−	3.00000i	0.219186	−	0.126547i
$563$	−2.59808	+	1.50000i	−0.109496	+	0.0632175i	−0.553748	−	0.832684i	$-0.686803\pi$
$563$	−2.59808	+	1.50000i	−0.109496	+	0.0632175i	0.444252	+	0.895902i	$0.353470\pi$
$564$		0			0
$565$		0			0
$566$	20.0000			0.840663
$567$		0			0
$568$			6.00000i			0.251754i
$569$	19.5000	−	33.7750i	0.817483	−	1.41592i	−0.0900490	−	0.995937i	$-0.528702\pi$
$569$	19.5000	−	33.7750i	0.817483	−	1.41592i	0.907532	−	0.419984i	$-0.137964\pi$
$570$		0			0
$571$	−14.5000	−	25.1147i	−0.606806	−	1.05102i	−0.991763	−	0.128085i	$-0.959117\pi$
$571$	−14.5000	−	25.1147i	−0.606806	−	1.05102i	0.384957	−	0.922934i	$-0.374216\pi$
$572$	10.3923	−	6.00000i	0.434524	−	0.250873i
$573$		0			0
$574$	−6.00000	+	10.3923i	−0.250435	+	0.433766i
$575$		0			0
$576$		0			0
$577$		−	7.00000i		−	0.291414i	−0.989328	−	0.145707i	$-0.953454\pi$
$577$		−	7.00000i		−	0.291414i	0.989328	−	0.145707i	$-0.0465456\pi$
$578$	−6.92820	−	4.00000i	−0.288175	−	0.166378i
$579$		0			0
$580$		0			0
$581$	−24.0000	−	41.5692i	−0.995688	−	1.72458i
$582$		0			0
$583$	15.5885	+	9.00000i	0.645608	+	0.372742i
$584$	7.00000			0.289662
$585$		0			0
$586$	18.0000			0.743573
$587$	33.7750	+	19.5000i	1.39404	+	0.804851i	0.993760	−	0.111540i	$-0.0355784\pi$
$587$	33.7750	+	19.5000i	1.39404	+	0.804851i	0.400283	+	0.916392i	$0.368912\pi$
$588$		0			0
$589$	5.00000	+	8.66025i	0.206021	+	0.356840i
$590$		0			0
$591$		0			0
$592$	3.46410	+	2.00000i	0.142374	+	0.0821995i
$593$		−	18.0000i		−	0.739171i	−0.929197	−	0.369586i	$-0.879500\pi$
$593$		−	18.0000i		−	0.739171i	0.929197	−	0.369586i	$-0.120500\pi$
$594$		0			0
$595$		0			0
$596$		0			0
$597$		0			0
$598$	−20.7846	+	12.0000i	−0.849946	+	0.490716i
$599$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$599$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$600$		0			0
$601$	12.5000	−	21.6506i	0.509886	−	0.883148i	−0.490049	−	0.871695i	$-0.663021\pi$
$601$	12.5000	−	21.6506i	0.509886	−	0.883148i	0.999934	−	0.0114528i	$-0.00364562\pi$
$602$		−	44.0000i		−	1.79331i
$603$		0			0
$604$	10.0000			0.406894
$605$		0			0
$606$		0			0
$607$	6.92820	−	4.00000i	0.281207	−	0.162355i	−0.352763	−	0.935713i	$-0.614758\pi$
$607$	6.92820	−	4.00000i	0.281207	−	0.162355i	0.633970	+	0.773358i	$0.281424\pi$
$608$	−4.33013	+	2.50000i	−0.175610	+	0.101388i
$609$		0			0
$610$		0			0
$611$		0			0
$612$		0			0
$613$		−	2.00000i		−	0.0807792i	−0.999184	−	0.0403896i	$-0.987140\pi$
$613$		−	2.00000i		−	0.0807792i	0.999184	−	0.0403896i	$-0.0128599\pi$
$614$	−3.50000	+	6.06218i	−0.141249	+	0.244650i
$615$		0			0
$616$	−6.00000	−	10.3923i	−0.241747	−	0.418718i
$617$	33.7750	−	19.5000i	1.35973	−	0.785040i	0.370143	−	0.928975i	$-0.379309\pi$
$617$	33.7750	−	19.5000i	1.35973	−	0.785040i	0.989587	+	0.143934i	$0.0459755\pi$
$618$		0			0
$619$	−9.50000	+	16.4545i	−0.381837	+	0.661361i	−0.991325	−	0.131434i	$-0.958042\pi$
$619$	−9.50000	+	16.4545i	−0.381837	+	0.661361i	0.609488	+	0.792796i	$0.291375\pi$
$620$		0			0
$621$		0			0
$622$			6.00000i			0.240578i
$623$	20.7846	+	12.0000i	0.832718	+	0.480770i
$624$		0			0
$625$		0			0
$626$	0.500000	+	0.866025i	0.0199840	+	0.0346133i
$627$		0			0
$628$	6.92820	+	4.00000i	0.276465	+	0.159617i
$629$	−12.0000			−0.478471
$630$		0			0
$631$	−34.0000			−1.35352			−0.676759	−	0.736204i	$-0.736616\pi$
$631$	−34.0000			−1.35352			−0.676759	+	0.736204i	$0.736616\pi$
$632$	−12.1244	−	7.00000i	−0.482281	−	0.278445i
$633$		0			0
$634$	−12.0000	−	20.7846i	−0.476581	−	0.825462i
$635$		0			0
$636$		0			0
$637$	31.1769	+	18.0000i	1.23527	+	0.713186i
$638$		−	18.0000i		−	0.712627i
$639$		0			0
$640$		0			0
$641$	4.50000	−	7.79423i	0.177739	−	0.307854i	−0.763367	−	0.645966i	$-0.776455\pi$
$641$	4.50000	−	7.79423i	0.177739	−	0.307854i	0.941106	+	0.338112i	$0.109788\pi$
$642$		0			0
$643$	−19.9186	+	11.5000i	−0.785512	+	0.453516i	−0.838380	−	0.545086i	$-0.816497\pi$
$643$	−19.9186	+	11.5000i	−0.785512	+	0.453516i	0.0528680	+	0.998602i	$0.483164\pi$
$644$	12.0000	+	20.7846i	0.472866	+	0.819028i
$645$		0			0
$646$	7.50000	−	12.9904i	0.295084	−	0.511100i
$647$		−	6.00000i		−	0.235884i	−0.993020	−	0.117942i	$-0.962370\pi$
$647$		−	6.00000i		−	0.235884i	0.993020	−	0.117942i	$-0.0376297\pi$
$648$		0			0
$649$	9.00000			0.353281
$650$		0			0
$651$		0			0
$652$	−13.8564	+	8.00000i	−0.542659	+	0.313304i
$653$	36.3731	−	21.0000i	1.42339	−	0.821794i	0.426801	−	0.904345i	$-0.359640\pi$
$653$	36.3731	−	21.0000i	1.42339	−	0.821794i	0.996587	+	0.0825519i	$0.0263070\pi$
$654$		0			0
$655$		0			0
$656$	3.00000			0.117130
$657$		0			0
$658$		0			0
$659$	18.0000	−	31.1769i	0.701180	−	1.21448i	−0.266872	−	0.963732i	$-0.585990\pi$
$659$	18.0000	−	31.1769i	0.701180	−	1.21448i	0.968052	−	0.250748i	$-0.0806766\pi$
$660$		0			0
$661$	−16.0000	−	27.7128i	−0.622328	−	1.07790i	−0.989051	−	0.147573i	$-0.952854\pi$
$661$	−16.0000	−	27.7128i	−0.622328	−	1.07790i	0.366723	−	0.930330i	$-0.380480\pi$
$662$	−3.46410	+	2.00000i	−0.134636	+	0.0777322i
$663$		0			0
$664$	−6.00000	+	10.3923i	−0.232845	+	0.403300i
$665$		0			0
$666$		0			0
$667$			36.0000i			1.39393i
$668$	15.5885	+	9.00000i	0.603136	+	0.348220i
$669$		0			0
$670$		0			0
$671$	−15.0000	−	25.9808i	−0.579069	−	1.00298i
$672$		0			0
$673$	12.1244	+	7.00000i	0.467360	+	0.269830i	0.715134	−	0.698988i	$-0.246366\pi$
$673$	12.1244	+	7.00000i	0.467360	+	0.269830i	−0.247774	+	0.968818i	$0.579699\pi$
$674$	31.0000			1.19408
$675$		0			0
$676$	3.00000			0.115385
$677$	−31.1769	−	18.0000i	−1.19823	−	0.691796i	−0.238067	−	0.971249i	$-0.576514\pi$
$677$	−31.1769	−	18.0000i	−1.19823	−	0.691796i	−0.960159	+	0.279453i	$0.909847\pi$
$678$		0			0
$679$	−22.0000	−	38.1051i	−0.844283	−	1.46234i
$680$		0			0
$681$		0			0
$682$	5.19615	+	3.00000i	0.198971	+	0.114876i
$683$		−	21.0000i		−	0.803543i	−0.915740	−	0.401771i	$-0.868395\pi$
$683$		−	21.0000i		−	0.803543i	0.915740	−	0.401771i	$-0.131605\pi$
$684$		0			0
$685$		0			0
$686$	4.00000	−	6.92820i	0.152721	−	0.264520i
$687$		0			0
$688$	−9.52628	+	5.50000i	−0.363186	+	0.209686i
$689$	12.0000	+	20.7846i	0.457164	+	0.791831i
$690$		0			0
$691$	−4.00000	+	6.92820i	−0.152167	+	0.263561i	−0.932024	−	0.362397i	$-0.881959\pi$
$691$	−4.00000	+	6.92820i	−0.152167	+	0.263561i	0.779857	+	0.625958i	$0.215292\pi$
$692$			18.0000i			0.684257i
$693$		0			0
$694$	21.0000			0.797149
$695$		0			0
$696$		0			0
$697$	−7.79423	+	4.50000i	−0.295227	+	0.170450i
$698$	13.8564	−	8.00000i	0.524473	−	0.302804i
$699$		0			0
$700$		0			0
$701$	−42.0000			−1.58632			−0.793159	−	0.609015i	$-0.791565\pi$
$701$	−42.0000			−1.58632			−0.793159	+	0.609015i	$0.791565\pi$
$702$		0			0
$703$			20.0000i			0.754314i
$704$	−1.50000	+	2.59808i	−0.0565334	+	0.0979187i
$705$		0			0
$706$	4.50000	+	7.79423i	0.169360	+	0.293340i
$707$	−41.5692	+	24.0000i	−1.56337	+	0.902613i
$708$		0			0
$709$	−17.0000	+	29.4449i	−0.638448	+	1.10583i	0.347325	+	0.937745i	$0.387090\pi$
$709$	−17.0000	+	29.4449i	−0.638448	+	1.10583i	−0.985773	+	0.168080i	$0.946243\pi$
$710$		0			0
$711$		0			0
$712$		−	6.00000i		−	0.224860i
$713$	−10.3923	−	6.00000i	−0.389195	−	0.224702i
$714$		0			0
$715$		0			0
$716$		0			0
$717$		0			0
$718$	20.7846	+	12.0000i	0.775675	+	0.447836i
$719$		0			0			−	1.00000i	$-0.5\pi$
$719$		0			0				1.00000i	$0.5\pi$
$720$		0			0
$721$	16.0000			0.595871
$722$	−5.19615	−	3.00000i	−0.193381	−	0.111648i
$723$		0			0
$724$	−8.00000	−	13.8564i	−0.297318	−	0.514969i
$725$		0			0
$726$		0			0
$727$	24.2487	+	14.0000i	0.899335	+	0.519231i	0.876984	−	0.480519i	$-0.159552\pi$
$727$	24.2487	+	14.0000i	0.899335	+	0.519231i	0.0223506	+	0.999750i	$0.492885\pi$
$728$		−	16.0000i		−	0.592999i
$729$		0			0
$730$		0			0
$731$	16.5000	−	28.5788i	0.610275	−	1.05703i
$732$		0			0
$733$	−27.7128	+	16.0000i	−1.02360	+	0.590973i	−0.915144	−	0.403128i	$-0.867923\pi$
$733$	−27.7128	+	16.0000i	−1.02360	+	0.590973i	−0.108453	+	0.994102i	$0.534590\pi$
$734$	4.00000	+	6.92820i	0.147643	+	0.255725i
$735$		0			0
$736$	3.00000	−	5.19615i	0.110581	−	0.191533i
$737$		−	15.0000i		−	0.552532i
$738$		0			0
$739$	−29.0000			−1.06678			−0.533391	−	0.845869i	$-0.679083\pi$
$739$	−29.0000			−1.06678			−0.533391	+	0.845869i	$0.679083\pi$
$740$		0			0
$741$		0			0
$742$	20.7846	−	12.0000i	0.763027	−	0.440534i
$743$	−5.19615	+	3.00000i	−0.190628	+	0.110059i	−0.592277	−	0.805735i	$-0.701771\pi$
$743$	−5.19615	+	3.00000i	−0.190628	+	0.110059i	0.401648	+	0.915794i	$0.368437\pi$
$744$		0			0
$745$		0			0
$746$	−10.0000			−0.366126
$747$		0			0
$748$		−	9.00000i		−	0.329073i
$749$	−18.0000	+	31.1769i	−0.657706	+	1.13918i
$750$		0			0
$751$	14.0000	+	24.2487i	0.510867	+	0.884848i	0.999921	+	0.0125942i	$0.00400897\pi$
$751$	14.0000	+	24.2487i	0.510867	+	0.884848i	−0.489053	+	0.872254i	$0.662658\pi$
$752$		0			0
$753$		0			0
$754$	12.0000	−	20.7846i	0.437014	−	0.756931i
$755$		0			0
$756$		0			0
$757$			38.0000i			1.38113i	0.723269	+	0.690567i	$0.242639\pi$
$757$			38.0000i			1.38113i	−0.723269	+	0.690567i	$0.757361\pi$
$758$	25.1147	+	14.5000i	0.912208	+	0.526664i
$759$		0			0
$760$		0			0
$761$	9.00000	+	15.5885i	0.326250	+	0.565081i	0.981764	−	0.190101i	$-0.0608816\pi$
$761$	9.00000	+	15.5885i	0.326250	+	0.565081i	−0.655515	+	0.755182i	$0.727548\pi$
$762$		0			0
$763$	13.8564	+	8.00000i	0.501636	+	0.289619i
$764$		0			0
$765$		0			0
$766$	−12.0000			−0.433578
$767$	10.3923	+	6.00000i	0.375244	+	0.216647i
$768$		0			0
$769$	25.0000	+	43.3013i	0.901523	+	1.56148i	0.825518	+	0.564376i	$0.190883\pi$
$769$	25.0000	+	43.3013i	0.901523	+	1.56148i	0.0760054	+	0.997107i	$0.475783\pi$
$770$		0			0
$771$		0			0
$772$	11.2583	+	6.50000i	0.405196	+	0.233940i
$773$		−	30.0000i		−	1.07903i	−0.841978	−	0.539513i	$-0.818609\pi$
$773$		−	30.0000i		−	1.07903i	0.841978	−	0.539513i	$-0.181391\pi$
$774$		0			0
$775$		0			0
$776$	−5.50000	+	9.52628i	−0.197438	+	0.341974i
$777$		0			0
$778$	31.1769	−	18.0000i	1.11775	−	0.645331i
$779$	7.50000	+	12.9904i	0.268715	+	0.465429i
$780$		0			0
$781$	−9.00000	+	15.5885i	−0.322045	+	0.557799i
$782$			18.0000i			0.643679i
$783$		0			0
$784$	−9.00000			−0.321429
$785$		0			0
$786$		0			0
$787$	−3.46410	+	2.00000i	−0.123482	+	0.0712923i	−0.560469	−	0.828176i	$-0.689379\pi$
$787$	−3.46410	+	2.00000i	−0.123482	+	0.0712923i	0.436987	+	0.899468i	$0.356046\pi$
$788$		0			0
$789$		0			0
$790$		0			0
$791$	72.0000			2.56003
$792$		0			0
$793$		−	40.0000i		−	1.42044i
$794$	4.00000	−	6.92820i	0.141955	−	0.245873i
$795$		0			0
$796$	−10.0000	−	17.3205i	−0.354441	−	0.613909i
$797$	41.5692	−	24.0000i	1.47246	−	0.850124i	0.472937	−	0.881096i	$-0.343194\pi$
$797$	41.5692	−	24.0000i	1.47246	−	0.850124i	0.999520	+	0.0309726i	$0.00986046\pi$
$798$		0			0
$799$		0			0
$800$		0			0
$801$		0			0
$802$		−	33.0000i		−	1.16527i
$803$	18.1865	+	10.5000i	0.641789	+	0.370537i
$804$		0			0
$805$		0			0
$806$	4.00000	+	6.92820i	0.140894	+	0.244036i
$807$		0			0
$808$	10.3923	+	6.00000i	0.365600	+	0.211079i
$809$	−39.0000			−1.37117			−0.685583	−	0.727994i	$-0.740453\pi$
$809$	−39.0000			−1.37117			−0.685583	+	0.727994i	$0.740453\pi$
$810$		0			0
$811$	35.0000			1.22902			0.614508	−	0.788911i	$-0.289355\pi$
$811$	35.0000			1.22902			0.614508	+	0.788911i	$0.289355\pi$
$812$	−20.7846	−	12.0000i	−0.729397	−	0.421117i
$813$		0			0
$814$	6.00000	+	10.3923i	0.210300	+	0.364250i
$815$		0			0
$816$		0			0
$817$	−47.6314	−	27.5000i	−1.66641	−	0.962103i
$818$			31.0000i			1.08389i
$819$		0			0
$820$		0			0
$821$	−24.0000	+	41.5692i	−0.837606	+	1.45078i	0.0542853	+	0.998525i	$0.482712\pi$
$821$	−24.0000	+	41.5692i	−0.837606	+	1.45078i	−0.891891	+	0.452250i	$0.850621\pi$
$822$		0			0
$823$	3.46410	−	2.00000i	0.120751	−	0.0697156i	−0.438408	−	0.898776i	$-0.644457\pi$
$823$	3.46410	−	2.00000i	0.120751	−	0.0697156i	0.559159	+	0.829060i	$0.311124\pi$
$824$	−2.00000	−	3.46410i	−0.0696733	−	0.120678i
$825$		0			0
$826$	6.00000	−	10.3923i	0.208767	−	0.361595i
$827$			36.0000i			1.25184i	0.779886	+	0.625921i	$0.215277\pi$
$827$			36.0000i			1.25184i	−0.779886	+	0.625921i	$0.784723\pi$
$828$		0			0
$829$	−44.0000			−1.52818			−0.764092	−	0.645108i	$-0.776812\pi$
$829$	−44.0000			−1.52818			−0.764092	+	0.645108i	$0.776812\pi$
$830$		0			0
$831$		0			0
$832$	−3.46410	+	2.00000i	−0.120096	+	0.0693375i
$833$	23.3827	−	13.5000i	0.810162	−	0.467747i
$834$		0			0
$835$		0			0
$836$	−15.0000			−0.518786
$837$		0			0
$838$		0			0
$839$	15.0000	−	25.9808i	0.517858	−	0.896956i	−0.481927	−	0.876211i	$-0.660063\pi$
$839$	15.0000	−	25.9808i	0.517858	−	0.896956i	0.999785	−	0.0207443i	$-0.00660359\pi$
$840$		0			0
$841$	−3.50000	−	6.06218i	−0.120690	−	0.209041i
$842$	1.73205	−	1.00000i	0.0596904	−	0.0344623i
$843$		0			0
$844$	−2.00000	+	3.46410i	−0.0688428	+	0.119239i
$845$		0			0
$846$		0			0
$847$			8.00000i			0.274883i
$848$	−5.19615	−	3.00000i	−0.178437	−	0.103020i
$849$		0			0
$850$		0			0
$851$	−12.0000	−	20.7846i	−0.411355	−	0.712487i
$852$		0			0
$853$	38.1051	+	22.0000i	1.30469	+	0.753266i	0.981205	−	0.192966i	$-0.0618108\pi$
$853$	38.1051	+	22.0000i	1.30469	+	0.753266i	0.323489	+	0.946232i	$0.395144\pi$
$854$	−40.0000			−1.36877
$855$		0			0
$856$	9.00000			0.307614
$857$	−15.5885	−	9.00000i	−0.532492	−	0.307434i	0.209539	−	0.977800i	$-0.432804\pi$
$857$	−15.5885	−	9.00000i	−0.532492	−	0.307434i	−0.742030	+	0.670366i	$0.766137\pi$
$858$		0			0
$859$	−9.50000	−	16.4545i	−0.324136	−	0.561420i	0.657201	−	0.753715i	$-0.271740\pi$
$859$	−9.50000	−	16.4545i	−0.324136	−	0.561420i	−0.981337	+	0.192295i	$0.938407\pi$
$860$		0			0
$861$		0			0
$862$	20.7846	+	12.0000i	0.707927	+	0.408722i
$863$		−	6.00000i		−	0.204242i	−0.994772	−	0.102121i	$-0.967437\pi$
$863$		−	6.00000i		−	0.204242i	0.994772	−	0.102121i	$-0.0325630\pi$
$864$		0			0
$865$		0			0
$866$	6.50000	−	11.2583i	0.220879	−	0.382574i
$867$		0			0
$868$	6.92820	−	4.00000i	0.235159	−	0.135769i
$869$	−21.0000	−	36.3731i	−0.712376	−	1.23387i
$870$		0			0
$871$	10.0000	−	17.3205i	0.338837	−	0.586883i
$872$		−	4.00000i		−	0.135457i
$873$		0			0
$874$	30.0000			1.01477
$875$		0			0
$876$		0			0
$877$	1.73205	−	1.00000i	0.0584872	−	0.0337676i	−0.470471	−	0.882415i	$-0.655916\pi$
$877$	1.73205	−	1.00000i	0.0584872	−	0.0337676i	0.528958	+	0.848648i	$0.322583\pi$
$878$	8.66025	−	5.00000i	0.292269	−	0.168742i
$879$		0			0
$880$		0			0
$881$	−30.0000			−1.01073			−0.505363	−	0.862907i	$-0.668641\pi$
$881$	−30.0000			−1.01073			−0.505363	+	0.862907i	$0.668641\pi$
$882$		0			0
$883$		−	41.0000i		−	1.37976i	−0.723924	−	0.689880i	$-0.757663\pi$
$883$		−	41.0000i		−	1.37976i	0.723924	−	0.689880i	$-0.242337\pi$
$884$	6.00000	−	10.3923i	0.201802	−	0.349531i
$885$		0			0
$886$	1.50000	+	2.59808i	0.0503935	+	0.0872841i
$887$	36.3731	−	21.0000i	1.22129	−	0.705111i	0.256096	−	0.966651i	$-0.417564\pi$
$887$	36.3731	−	21.0000i	1.22129	−	0.705111i	0.965193	+	0.261540i	$0.0842305\pi$
$888$		0			0
$889$	−4.00000	+	6.92820i	−0.134156	+	0.232364i
$890$		0			0
$891$		0			0
$892$		−	22.0000i		−	0.736614i
$893$		0			0
$894$		0			0
$895$		0			0
$896$	2.00000	+	3.46410i	0.0668153	+	0.115728i
$897$		0			0
$898$	12.9904	+	7.50000i	0.433495	+	0.250278i
$899$	12.0000			0.400222
$900$		0			0
$901$	18.0000			0.599667
$902$	7.79423	+	4.50000i	0.259519	+	0.149834i
$903$		0			0
$904$	−9.00000	−	15.5885i	−0.299336	−	0.518464i
$905$		0			0
$906$		0			0
$907$	−4.33013	−	2.50000i	−0.143780	−	0.0830111i	0.426385	−	0.904542i	$-0.359787\pi$
$907$	−4.33013	−	2.50000i	−0.143780	−	0.0830111i	−0.570164	+	0.821531i	$0.693120\pi$
$908$		−	3.00000i		−	0.0995585i
$909$		0			0
$910$		0			0
$911$	−15.0000	+	25.9808i	−0.496972	+	0.860781i	−0.999994	−	0.00349271i	$-0.998888\pi$
$911$	−15.0000	+	25.9808i	−0.496972	+	0.860781i	0.503022	+	0.864274i	$0.332222\pi$
$912$		0			0
$913$	−31.1769	+	18.0000i	−1.03181	+	0.595713i
$914$	−0.500000	−	0.866025i	−0.0165385	−	0.0286456i
$915$		0			0
$916$	−10.0000	+	17.3205i	−0.330409	+	0.572286i
$917$			48.0000i			1.58510i
$918$		0			0
$919$	34.0000			1.12156			0.560778	−	0.827966i	$-0.310502\pi$
$919$	34.0000			1.12156			0.560778	+	0.827966i	$0.310502\pi$
$920$		0			0
$921$		0			0
$922$		0			0
$923$	−20.7846	+	12.0000i	−0.684134	+	0.394985i
$924$		0			0
$925$		0			0
$926$	20.0000			0.657241
$927$		0			0
$928$			6.00000i			0.196960i
$929$	−15.0000	+	25.9808i	−0.492134	+	0.852401i	−0.999959	−	0.00905914i	$-0.997116\pi$
$929$	−15.0000	+	25.9808i	−0.492134	+	0.852401i	0.507825	+	0.861460i	$0.330450\pi$
$930$		0			0
$931$	−22.5000	−	38.9711i	−0.737408	−	1.27723i
$932$	−18.1865	+	10.5000i	−0.595720	+	0.343939i
$933$		0			0
$934$	−10.5000	+	18.1865i	−0.343570	+	0.595082i
$935$		0			0
$936$		0			0
$937$		−	10.0000i		−	0.326686i	−0.986569	−	0.163343i	$-0.947772\pi$
$937$		−	10.0000i		−	0.326686i	0.986569	−	0.163343i	$-0.0522277\pi$
$938$	−17.3205	−	10.0000i	−0.565535	−	0.326512i
$939$		0			0
$940$		0			0
$941$	12.0000	+	20.7846i	0.391189	+	0.677559i	0.992607	−	0.121376i	$-0.0387306\pi$
$941$	12.0000	+	20.7846i	0.391189	+	0.677559i	−0.601418	+	0.798935i	$0.705397\pi$
$942$		0			0
$943$	−15.5885	−	9.00000i	−0.507630	−	0.293080i
$944$	−3.00000			−0.0976417
$945$		0			0
$946$	−33.0000			−1.07292
$947$	23.3827	+	13.5000i	0.759835	+	0.438691i	0.829237	−	0.558898i	$-0.188776\pi$
$947$	23.3827	+	13.5000i	0.759835	+	0.438691i	−0.0694014	+	0.997589i	$0.522109\pi$
$948$		0			0
$949$	14.0000	+	24.2487i	0.454459	+	0.787146i
$950$		0			0
$951$		0			0
$952$	−10.3923	−	6.00000i	−0.336817	−	0.194461i
$953$			51.0000i			1.65205i	0.563632	+	0.826026i	$0.309404\pi$
$953$			51.0000i			1.65205i	−0.563632	+	0.826026i	$0.690596\pi$
$954$		0			0
$955$		0			0
$956$	3.00000	−	5.19615i	0.0970269	−	0.168056i
$957$		0			0
$958$	−5.19615	+	3.00000i	−0.167880	+	0.0969256i
$959$	−18.0000	−	31.1769i	−0.581250	−	1.00676i
$960$		0			0
$961$	13.5000	−	23.3827i	0.435484	−	0.754280i
$962$			16.0000i			0.515861i
$963$		0			0
$964$	−17.0000			−0.547533
$965$		0			0
$966$		0			0
$967$	−19.0526	+	11.0000i	−0.612689	+	0.353736i	−0.774017	−	0.633165i	$-0.781756\pi$
$967$	−19.0526	+	11.0000i	−0.612689	+	0.353736i	0.161328	+	0.986901i	$0.448422\pi$
$968$	1.73205	−	1.00000i	0.0556702	−	0.0321412i
$969$		0			0
$970$		0			0
$971$	−60.0000			−1.92549			−0.962746	−	0.270408i	$-0.912841\pi$
$971$	−60.0000			−1.92549			−0.962746	+	0.270408i	$0.912841\pi$
$972$		0			0
$973$		−	4.00000i		−	0.128234i
$974$	1.00000	−	1.73205i	0.0320421	−	0.0554985i
$975$		0			0
$976$	5.00000	+	8.66025i	0.160046	+	0.277208i
$977$	7.79423	−	4.50000i	0.249359	−	0.143968i	−0.370111	−	0.928987i	$-0.620681\pi$
$977$	7.79423	−	4.50000i	0.249359	−	0.143968i	0.619471	+	0.785020i	$0.287347\pi$
$978$		0			0
$979$	9.00000	−	15.5885i	0.287641	−	0.498209i
$980$		0			0
$981$		0			0
$982$			33.0000i			1.05307i
$983$	−31.1769	−	18.0000i	−0.994389	−	0.574111i	−0.0878058	−	0.996138i	$-0.527985\pi$
$983$	−31.1769	−	18.0000i	−0.994389	−	0.574111i	−0.906583	+	0.422027i	$0.861319\pi$
$984$		0			0
$985$		0			0
$986$	−9.00000	−	15.5885i	−0.286618	−	0.496438i
$987$		0			0
$988$	−17.3205	−	10.0000i	−0.551039	−	0.318142i
$989$	66.0000			2.09868
$990$		0			0
$991$	20.0000			0.635321			0.317660	−	0.948205i	$-0.397103\pi$
$991$	20.0000			0.635321			0.317660	+	0.948205i	$0.397103\pi$
$992$	−1.73205	−	1.00000i	−0.0549927	−	0.0317500i
$993$		0			0
$994$	12.0000	+	20.7846i	0.380617	+	0.659248i
$995$		0			0
$996$		0			0
$997$	−22.5167	−	13.0000i	−0.713110	−	0.411714i	0.0991016	−	0.995077i	$-0.468403\pi$
$997$	−22.5167	−	13.0000i	−0.713110	−	0.411714i	−0.812211	+	0.583363i	$0.801736\pi$
$998$			31.0000i			0.981288i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1350.2.j.c.1099.1		4
3.2	odd	2		450.2.j.a.349.2		4
5.2	odd	4		1350.2.e.g.451.1		2
5.3	odd	4		270.2.e.a.181.1		2
5.4	even	2	inner	1350.2.j.c.1099.2		4
9.2	odd	6		4050.2.c.p.649.1		2
9.4	even	3	inner	1350.2.j.c.199.2		4
9.5	odd	6		450.2.j.a.49.1		4
9.7	even	3		4050.2.c.d.649.2		2
15.2	even	4		450.2.e.d.151.1		2
15.8	even	4		90.2.e.b.61.1	yes	2
15.14	odd	2		450.2.j.a.349.1		4
20.3	even	4		2160.2.q.d.721.1		2
45.2	even	12		4050.2.a.bi.1.1		1
45.4	even	6	inner	1350.2.j.c.199.1		4
45.7	odd	12		4050.2.a.q.1.1		1
45.13	odd	12		270.2.e.a.91.1		2
45.14	odd	6		450.2.j.a.49.2		4
45.22	odd	12		1350.2.e.g.901.1		2
45.23	even	12		90.2.e.b.31.1	✓	2
45.29	odd	6		4050.2.c.p.649.2		2
45.32	even	12		450.2.e.d.301.1		2
45.34	even	6		4050.2.c.d.649.1		2
45.38	even	12		810.2.a.a.1.1		1
45.43	odd	12		810.2.a.e.1.1		1
60.23	odd	4		720.2.q.c.241.1		2
180.23	odd	12		720.2.q.c.481.1		2
180.43	even	12		6480.2.a.l.1.1		1
180.83	odd	12		6480.2.a.z.1.1		1
180.103	even	12		2160.2.q.d.1441.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
90.2.e.b.31.1	✓	2	45.23	even	12
90.2.e.b.61.1	yes	2	15.8	even	4
270.2.e.a.91.1		2	45.13	odd	12
270.2.e.a.181.1		2	5.3	odd	4
450.2.e.d.151.1		2	15.2	even	4
450.2.e.d.301.1		2	45.32	even	12
450.2.j.a.49.1		4	9.5	odd	6
450.2.j.a.49.2		4	45.14	odd	6
450.2.j.a.349.1		4	15.14	odd	2
450.2.j.a.349.2		4	3.2	odd	2
720.2.q.c.241.1		2	60.23	odd	4
720.2.q.c.481.1		2	180.23	odd	12
810.2.a.a.1.1		1	45.38	even	12
810.2.a.e.1.1		1	45.43	odd	12
1350.2.e.g.451.1		2	5.2	odd	4
1350.2.e.g.901.1		2	45.22	odd	12
1350.2.j.c.199.1		4	45.4	even	6	inner
1350.2.j.c.199.2		4	9.4	even	3	inner
1350.2.j.c.1099.1		4	1.1	even	1	trivial
1350.2.j.c.1099.2		4	5.4	even	2	inner
2160.2.q.d.721.1		2	20.3	even	4
2160.2.q.d.1441.1		2	180.103	even	12
4050.2.a.q.1.1		1	45.7	odd	12
4050.2.a.bi.1.1		1	45.2	even	12
4050.2.c.d.649.1		2	45.34	even	6
4050.2.c.d.649.2		2	9.7	even	3
4050.2.c.p.649.1		2	9.2	odd	6
4050.2.c.p.649.2		2	45.29	odd	6
6480.2.a.l.1.1		1	180.43	even	12
6480.2.a.z.1.1		1	180.83	odd	12

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 1350 = 2 \cdot 3^{3} \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1350.j (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.866025 - 0.500000i) q^{2} +(0.500000 + 0.866025i) q^{4} +(3.46410 + 2.00000i) q^{7} -1.00000i q^{8} +(1.50000 - 2.59808i) q^{11} +(3.46410 - 2.00000i) q^{13} +(-2.00000 - 3.46410i) q^{14} +(-0.500000 + 0.866025i) q^{16} -3.00000i q^{17} -5.00000 q^{19} +(-2.59808 + 1.50000i) q^{22} +(5.19615 - 3.00000i) q^{23} -4.00000 q^{26} +4.00000i q^{28} +(-3.00000 + 5.19615i) q^{29} +(-1.00000 - 1.73205i) q^{31} +(0.866025 - 0.500000i) q^{32} +(-1.50000 + 2.59808i) q^{34} -4.00000i q^{37} +(4.33013 + 2.50000i) q^{38} +(-1.50000 - 2.59808i) q^{41} +(9.52628 + 5.50000i) q^{43} +3.00000 q^{44} -6.00000 q^{46} +(4.50000 + 7.79423i) q^{49} +(3.46410 + 2.00000i) q^{52} +6.00000i q^{53} +(2.00000 - 3.46410i) q^{56} +(5.19615 - 3.00000i) q^{58} +(1.50000 + 2.59808i) q^{59} +(5.00000 - 8.66025i) q^{61} +2.00000i q^{62} -1.00000 q^{64} +(4.33013 - 2.50000i) q^{67} +(2.59808 - 1.50000i) q^{68} -6.00000 q^{71} +7.00000i q^{73} +(-2.00000 + 3.46410i) q^{74} +(-2.50000 - 4.33013i) q^{76} +(10.3923 - 6.00000i) q^{77} +(7.00000 - 12.1244i) q^{79} +3.00000i q^{82} +(-10.3923 - 6.00000i) q^{83} +(-5.50000 - 9.52628i) q^{86} +(-2.59808 - 1.50000i) q^{88} +6.00000 q^{89} +16.0000 q^{91} +(5.19615 + 3.00000i) q^{92} +(-9.52628 - 5.50000i) q^{97} -9.00000i q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 2 q^{4} + 6 q^{11} - 8 q^{14} - 2 q^{16} - 20 q^{19} - 16 q^{26} - 12 q^{29} - 4 q^{31} - 6 q^{34} - 6 q^{41} + 12 q^{44} - 24 q^{46} + 18 q^{49} + 8 q^{56} + 6 q^{59} + 20 q^{61} - 4 q^{64} - 24 q^{71}+ \cdots + 64 q^{91}+O(q^{100}) \) 4 * q + 2 * q^4 + 6 * q^11 - 8 * q^14 - 2 * q^16 - 20 * q^19 - 16 * q^26 - 12 * q^29 - 4 * q^31 - 6 * q^34 - 6 * q^41 + 12 * q^44 - 24 * q^46 + 18 * q^49 + 8 * q^56 + 6 * q^59 + 20 * q^61 - 4 * q^64 - 24 * q^71 - 8 * q^74 - 10 * q^76 + 28 * q^79 - 22 * q^86 + 24 * q^89 + 64 * q^91

Introduction

L-functions

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