LMFDB - Embedded newform 1232.2.q.e.177.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1232,2,Mod(177,1232)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1232, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 0, 2, 0]))

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

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

chi := DirichletCharacter("1232.177");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1232 = 2^{4} \cdot 7 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1232.q (of order $3$, degree $2$, not minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$9.83756952902$
Analytic rank:	$0$
Dimension:	$2$
Coefficient field:	$\Q(\zeta_{6})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - x + 1 $ x^2 - x + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 154)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			177.1
Root			$0.500000 - 0.866025i$ of defining polynomial
Character	$\chi$	$=$	1232.177
Dual form			1232.2.q.e.529.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.50000 + 2.59808i) q^{3} +(-1.00000 + 1.73205i) q^{5} +(2.50000 - 0.866025i) q^{7} +(-3.00000 + 5.19615i) q^{9} +O(q^{10})$	\(q+(1.50000 + 2.59808i) q^{3} +(-1.00000 + 1.73205i) q^{5} +(2.50000 - 0.866025i) q^{7} +(-3.00000 + 5.19615i) q^{9} +(-0.500000 - 0.866025i) q^{11} -7.00000 q^{13} -6.00000 q^{15} +(-1.00000 - 1.73205i) q^{17} +(6.00000 + 5.19615i) q^{21} +(-4.00000 + 6.92820i) q^{23} +(0.500000 + 0.866025i) q^{25} -9.00000 q^{27} -5.00000 q^{29} +(2.00000 + 3.46410i) q^{31} +(1.50000 - 2.59808i) q^{33} +(-1.00000 + 5.19615i) q^{35} +(-2.00000 + 3.46410i) q^{37} +(-10.5000 - 18.1865i) q^{39} +4.00000 q^{41} +8.00000 q^{43} +(-6.00000 - 10.3923i) q^{45} +(1.00000 - 1.73205i) q^{47} +(5.50000 - 4.33013i) q^{49} +(3.00000 - 5.19615i) q^{51} +(3.00000 + 5.19615i) q^{53} +2.00000 q^{55} +(1.50000 + 2.59808i) q^{59} +(-0.500000 + 0.866025i) q^{61} +(-3.00000 + 15.5885i) q^{63} +(7.00000 - 12.1244i) q^{65} +(4.50000 + 7.79423i) q^{67} -24.0000 q^{69} +2.00000 q^{71} +(-2.00000 - 3.46410i) q^{73} +(-1.50000 + 2.59808i) q^{75} +(-2.00000 - 1.73205i) q^{77} +(4.50000 - 7.79423i) q^{79} +(-4.50000 - 7.79423i) q^{81} -6.00000 q^{83} +4.00000 q^{85} +(-7.50000 - 12.9904i) q^{87} +(-3.00000 + 5.19615i) q^{89} +(-17.5000 + 6.06218i) q^{91} +(-6.00000 + 10.3923i) q^{93} +7.00000 q^{97} +6.00000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q + 3 q^{3} - 2 q^{5} + 5 q^{7} - 6 q^{9}+O(q^{10}) $ 2 * q + 3 * q^3 - 2 * q^5 + 5 * q^7 - 6 * q^9	$ 2 q + 3 q^{3} - 2 q^{5} + 5 q^{7} - 6 q^{9} - q^{11} - 14 q^{13} - 12 q^{15} - 2 q^{17} + 12 q^{21} - 8 q^{23} + q^{25} - 18 q^{27} - 10 q^{29} + 4 q^{31} + 3 q^{33} - 2 q^{35} - 4 q^{37} - 21 q^{39} + 8 q^{41} + 16 q^{43} - 12 q^{45} + 2 q^{47} + 11 q^{49} + 6 q^{51} + 6 q^{53} + 4 q^{55} + 3 q^{59} - q^{61} - 6 q^{63} + 14 q^{65} + 9 q^{67} - 48 q^{69} + 4 q^{71} - 4 q^{73} - 3 q^{75} - 4 q^{77} + 9 q^{79} - 9 q^{81} - 12 q^{83} + 8 q^{85} - 15 q^{87} - 6 q^{89} - 35 q^{91} - 12 q^{93} + 14 q^{97} + 12 q^{99}+O(q^{100}) $ 2 * q + 3 * q^3 - 2 * q^5 + 5 * q^7 - 6 * q^9 - q^11 - 14 * q^13 - 12 * q^15 - 2 * q^17 + 12 * q^21 - 8 * q^23 + q^25 - 18 * q^27 - 10 * q^29 + 4 * q^31 + 3 * q^33 - 2 * q^35 - 4 * q^37 - 21 * q^39 + 8 * q^41 + 16 * q^43 - 12 * q^45 + 2 * q^47 + 11 * q^49 + 6 * q^51 + 6 * q^53 + 4 * q^55 + 3 * q^59 - q^61 - 6 * q^63 + 14 * q^65 + 9 * q^67 - 48 * q^69 + 4 * q^71 - 4 * q^73 - 3 * q^75 - 4 * q^77 + 9 * q^79 - 9 * q^81 - 12 * q^83 + 8 * q^85 - 15 * q^87 - 6 * q^89 - 35 * q^91 - 12 * q^93 + 14 * q^97 + 12 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1232\mathbb{Z}\right)^\times$.

$n$	$309$	$353$	$463$	$673$
$\chi(n)$	$1$	$e\left(\frac{1}{3}\right)$	$1$	$1$

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			0
$2$		0			0
$3$	1.50000	+	2.59808i	0.866025	+	1.50000i	0.866025	+	0.500000i	$0.166667\pi$
$3$	1.50000	+	2.59808i	0.866025	+	1.50000i			1.00000i	$0.5\pi$
$4$		0			0
$5$	−1.00000	+	1.73205i	−0.447214	+	0.774597i	−0.998203	−	0.0599153i	$-0.980917\pi$
$5$	−1.00000	+	1.73205i	−0.447214	+	0.774597i	0.550990	+	0.834512i	$0.314250\pi$
$6$		0			0
$7$	2.50000	−	0.866025i	0.944911	−	0.327327i
$7$	2.50000	−	0.866025i	0.944911	−	0.327327i
$8$		0			0
$9$	−3.00000	+	5.19615i	−1.00000	+	1.73205i
$10$		0			0
$11$	−0.500000	−	0.866025i	−0.150756	−	0.261116i
$11$	−0.500000	−	0.866025i	−0.150756	−	0.261116i
$12$		0			0
$13$	−7.00000			−1.94145			−0.970725	−	0.240192i	$-0.922790\pi$
$13$	−7.00000			−1.94145			−0.970725	+	0.240192i	$0.922790\pi$
$14$		0			0
$15$	−6.00000			−1.54919
$16$		0			0
$17$	−1.00000	−	1.73205i	−0.242536	−	0.420084i	0.718900	−	0.695113i	$-0.244646\pi$
$17$	−1.00000	−	1.73205i	−0.242536	−	0.420084i	−0.961436	+	0.275029i	$0.911312\pi$
$18$		0			0
$19$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$19$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$20$		0			0
$21$	6.00000	+	5.19615i	1.30931	+	1.13389i
$22$		0			0
$23$	−4.00000	+	6.92820i	−0.834058	+	1.44463i	0.0607377	+	0.998154i	$0.480655\pi$
$23$	−4.00000	+	6.92820i	−0.834058	+	1.44463i	−0.894795	+	0.446476i	$0.852679\pi$
$24$		0			0
$25$	0.500000	+	0.866025i	0.100000	+	0.173205i
$26$		0			0
$27$	−9.00000			−1.73205
$28$		0			0
$29$	−5.00000			−0.928477			−0.464238	−	0.885710i	$-0.653672\pi$
$29$	−5.00000			−0.928477			−0.464238	+	0.885710i	$0.653672\pi$
$30$		0			0
$31$	2.00000	+	3.46410i	0.359211	+	0.622171i	0.987829	−	0.155543i	$-0.0497126\pi$
$31$	2.00000	+	3.46410i	0.359211	+	0.622171i	−0.628619	+	0.777714i	$0.716379\pi$
$32$		0			0
$33$	1.50000	−	2.59808i	0.261116	−	0.452267i
$34$		0			0
$35$	−1.00000	+	5.19615i	−0.169031	+	0.878310i
$36$		0			0
$37$	−2.00000	+	3.46410i	−0.328798	+	0.569495i	−0.982274	−	0.187453i	$-0.939977\pi$
$37$	−2.00000	+	3.46410i	−0.328798	+	0.569495i	0.653476	+	0.756948i	$0.273310\pi$
$38$		0			0
$39$	−10.5000	−	18.1865i	−1.68135	−	2.91218i
$40$		0			0
$41$	4.00000			0.624695			0.312348	−	0.949968i	$-0.398885\pi$
$41$	4.00000			0.624695			0.312348	+	0.949968i	$0.398885\pi$
$42$		0			0
$43$	8.00000			1.21999			0.609994	−	0.792406i	$-0.291172\pi$
$43$	8.00000			1.21999			0.609994	+	0.792406i	$0.291172\pi$
$44$		0			0
$45$	−6.00000	−	10.3923i	−0.894427	−	1.54919i
$46$		0			0
$47$	1.00000	−	1.73205i	0.145865	−	0.252646i	−0.783830	−	0.620975i	$-0.786737\pi$
$47$	1.00000	−	1.73205i	0.145865	−	0.252646i	0.929695	+	0.368329i	$0.120070\pi$
$48$		0			0
$49$	5.50000	−	4.33013i	0.785714	−	0.618590i
$50$		0			0
$51$	3.00000	−	5.19615i	0.420084	−	0.727607i
$52$		0			0
$53$	3.00000	+	5.19615i	0.412082	+	0.713746i	0.995117	−	0.0987002i	$-0.0314685\pi$
$53$	3.00000	+	5.19615i	0.412082	+	0.713746i	−0.583036	+	0.812447i	$0.698135\pi$
$54$		0			0
$55$	2.00000			0.269680
$56$		0			0
$57$		0			0
$58$		0			0
$59$	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
$61$	−0.500000	+	0.866025i	−0.0640184	+	0.110883i	−0.896258	−	0.443533i	$-0.853725\pi$
$61$	−0.500000	+	0.866025i	−0.0640184	+	0.110883i	0.832240	+	0.554416i	$0.187058\pi$
$62$		0			0
$63$	−3.00000	+	15.5885i	−0.377964	+	1.96396i
$64$		0			0
$65$	7.00000	−	12.1244i	0.868243	−	1.50384i
$66$		0			0
$67$	4.50000	+	7.79423i	0.549762	+	0.952217i	0.998290	+	0.0584478i	$0.0186151\pi$
$67$	4.50000	+	7.79423i	0.549762	+	0.952217i	−0.448528	+	0.893769i	$0.648052\pi$
$68$		0			0
$69$	−24.0000			−2.88926
$70$		0			0
$71$	2.00000			0.237356			0.118678	−	0.992933i	$-0.462134\pi$
$71$	2.00000			0.237356			0.118678	+	0.992933i	$0.462134\pi$
$72$		0			0
$73$	−2.00000	−	3.46410i	−0.234082	−	0.405442i	0.724923	−	0.688830i	$-0.241875\pi$
$73$	−2.00000	−	3.46410i	−0.234082	−	0.405442i	−0.959006	+	0.283387i	$0.908542\pi$
$74$		0			0
$75$	−1.50000	+	2.59808i	−0.173205	+	0.300000i
$76$		0			0
$77$	−2.00000	−	1.73205i	−0.227921	−	0.197386i
$78$		0			0
$79$	4.50000	−	7.79423i	0.506290	−	0.876919i	−0.493684	−	0.869641i	$-0.664350\pi$
$79$	4.50000	−	7.79423i	0.506290	−	0.876919i	0.999974	−	0.00727784i	$-0.00231663\pi$
$80$		0			0
$81$	−4.50000	−	7.79423i	−0.500000	−	0.866025i
$82$		0			0
$83$	−6.00000			−0.658586			−0.329293	−	0.944228i	$-0.606810\pi$
$83$	−6.00000			−0.658586			−0.329293	+	0.944228i	$0.606810\pi$
$84$		0			0
$85$	4.00000			0.433861
$86$		0			0
$87$	−7.50000	−	12.9904i	−0.804084	−	1.39272i
$88$		0			0
$89$	−3.00000	+	5.19615i	−0.317999	+	0.550791i	−0.980071	−	0.198650i	$-0.936344\pi$
$89$	−3.00000	+	5.19615i	−0.317999	+	0.550791i	0.662071	+	0.749441i	$0.269678\pi$
$90$		0			0
$91$	−17.5000	+	6.06218i	−1.83450	+	0.635489i
$92$		0			0
$93$	−6.00000	+	10.3923i	−0.622171	+	1.07763i
$94$		0			0
$95$		0			0
$96$		0			0
$97$	7.00000			0.710742			0.355371	−	0.934725i	$-0.384354\pi$
$97$	7.00000			0.710742			0.355371	+	0.934725i	$0.384354\pi$
$98$		0			0
$99$	6.00000			0.603023
$100$		0			0
$101$	4.50000	+	7.79423i	0.447767	+	0.775555i	0.998240	−	0.0592978i	$-0.0188862\pi$
$101$	4.50000	+	7.79423i	0.447767	+	0.775555i	−0.550474	+	0.834853i	$0.685553\pi$
$102$		0			0
$103$	9.00000	−	15.5885i	0.886796	−	1.53598i	0.0431555	−	0.999068i	$-0.486259\pi$
$103$	9.00000	−	15.5885i	0.886796	−	1.53598i	0.843641	−	0.536908i	$-0.180408\pi$
$104$		0			0
$105$	−15.0000	+	5.19615i	−1.46385	+	0.507093i
$106$		0			0
$107$	1.00000	−	1.73205i	0.0966736	−	0.167444i	−0.813632	−	0.581380i	$-0.802513\pi$
$107$	1.00000	−	1.73205i	0.0966736	−	0.167444i	0.910306	+	0.413936i	$0.135846\pi$
$108$		0			0
$109$	1.00000	+	1.73205i	0.0957826	+	0.165900i	0.909935	−	0.414751i	$-0.136131\pi$
$109$	1.00000	+	1.73205i	0.0957826	+	0.165900i	−0.814152	+	0.580651i	$0.802798\pi$
$110$		0			0
$111$	−12.0000			−1.13899
$112$		0			0
$113$	5.00000			0.470360			0.235180	−	0.971952i	$-0.424432\pi$
$113$	5.00000			0.470360			0.235180	+	0.971952i	$0.424432\pi$
$114$		0			0
$115$	−8.00000	−	13.8564i	−0.746004	−	1.29212i
$116$		0			0
$117$	21.0000	−	36.3731i	1.94145	−	3.36269i
$118$		0			0
$119$	−4.00000	−	3.46410i	−0.366679	−	0.317554i
$120$		0			0
$121$	−0.500000	+	0.866025i	−0.0454545	+	0.0787296i
$122$		0			0
$123$	6.00000	+	10.3923i	0.541002	+	0.937043i
$124$		0			0
$125$	−12.0000			−1.07331
$126$		0			0
$127$	19.0000			1.68598			0.842989	−	0.537931i	$-0.180794\pi$
$127$	19.0000			1.68598			0.842989	+	0.537931i	$0.180794\pi$
$128$		0			0
$129$	12.0000	+	20.7846i	1.05654	+	1.82998i
$130$		0			0
$131$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$131$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$132$		0			0
$133$		0			0
$134$		0			0
$135$	9.00000	−	15.5885i	0.774597	−	1.34164i
$136$		0			0
$137$	−1.50000	−	2.59808i	−0.128154	−	0.221969i	0.794808	−	0.606861i	$-0.207572\pi$
$137$	−1.50000	−	2.59808i	−0.128154	−	0.221969i	−0.922961	+	0.384893i	$0.874238\pi$
$138$		0			0
$139$	4.00000			0.339276			0.169638	−	0.985506i	$-0.445740\pi$
$139$	4.00000			0.339276			0.169638	+	0.985506i	$0.445740\pi$
$140$		0			0
$141$	6.00000			0.505291
$142$		0			0
$143$	3.50000	+	6.06218i	0.292685	+	0.506945i
$144$		0			0
$145$	5.00000	−	8.66025i	0.415227	−	0.719195i
$146$		0			0
$147$	19.5000	+	7.79423i	1.60833	+	0.642857i
$148$		0			0
$149$	5.00000	−	8.66025i	0.409616	−	0.709476i	−0.585231	−	0.810867i	$-0.698996\pi$
$149$	5.00000	−	8.66025i	0.409616	−	0.709476i	0.994847	+	0.101391i	$0.0323294\pi$
$150$		0			0
$151$	−1.50000	−	2.59808i	−0.122068	−	0.211428i	0.798515	−	0.601975i	$-0.205619\pi$
$151$	−1.50000	−	2.59808i	−0.122068	−	0.211428i	−0.920583	+	0.390547i	$0.872286\pi$
$152$		0			0
$153$	12.0000			0.970143
$154$		0			0
$155$	−8.00000			−0.642575
$156$		0			0
$157$	−8.00000	−	13.8564i	−0.638470	−	1.10586i	−0.985769	−	0.168107i	$-0.946235\pi$
$157$	−8.00000	−	13.8564i	−0.638470	−	1.10586i	0.347299	−	0.937754i	$-0.387099\pi$
$158$		0			0
$159$	−9.00000	+	15.5885i	−0.713746	+	1.23625i
$160$		0			0
$161$	−4.00000	+	20.7846i	−0.315244	+	1.63806i
$162$		0			0
$163$	−8.50000	+	14.7224i	−0.665771	+	1.15315i	0.313304	+	0.949653i	$0.398564\pi$
$163$	−8.50000	+	14.7224i	−0.665771	+	1.15315i	−0.979076	+	0.203497i	$0.934769\pi$
$164$		0			0
$165$	3.00000	+	5.19615i	0.233550	+	0.404520i
$166$		0			0
$167$	−19.0000			−1.47026			−0.735132	−	0.677924i	$-0.762880\pi$
$167$	−19.0000			−1.47026			−0.735132	+	0.677924i	$0.762880\pi$
$168$		0			0
$169$	36.0000			2.76923
$170$		0			0
$171$		0			0
$172$		0			0
$173$	−12.5000	+	21.6506i	−0.950357	+	1.64607i	−0.205706	+	0.978614i	$0.565949\pi$
$173$	−12.5000	+	21.6506i	−0.950357	+	1.64607i	−0.744652	+	0.667453i	$0.767384\pi$
$174$		0			0
$175$	2.00000	+	1.73205i	0.151186	+	0.130931i
$176$		0			0
$177$	−4.50000	+	7.79423i	−0.338241	+	0.585850i
$178$		0			0
$179$	9.50000	+	16.4545i	0.710063	+	1.22987i	0.964833	+	0.262864i	$0.0846670\pi$
$179$	9.50000	+	16.4545i	0.710063	+	1.22987i	−0.254770	+	0.967002i	$0.582000\pi$
$180$		0			0
$181$	−22.0000			−1.63525			−0.817624	−	0.575753i	$-0.804709\pi$
$181$	−22.0000			−1.63525			−0.817624	+	0.575753i	$0.804709\pi$
$182$		0			0
$183$	−3.00000			−0.221766
$184$		0			0
$185$	−4.00000	−	6.92820i	−0.294086	−	0.509372i
$186$		0			0
$187$	−1.00000	+	1.73205i	−0.0731272	+	0.126660i
$188$		0			0
$189$	−22.5000	+	7.79423i	−1.63663	+	0.566947i
$190$		0			0
$191$	1.00000	−	1.73205i	0.0723575	−	0.125327i	−0.827577	−	0.561353i	$-0.810281\pi$
$191$	1.00000	−	1.73205i	0.0723575	−	0.125327i	0.899934	+	0.436026i	$0.143614\pi$
$192$		0			0
$193$	−4.00000	−	6.92820i	−0.287926	−	0.498703i	0.685388	−	0.728178i	$-0.259632\pi$
$193$	−4.00000	−	6.92820i	−0.287926	−	0.498703i	−0.973315	+	0.229475i	$0.926299\pi$
$194$		0			0
$195$	42.0000			3.00768
$196$		0			0
$197$	15.0000			1.06871			0.534353	−	0.845262i	$-0.320555\pi$
$197$	15.0000			1.06871			0.534353	+	0.845262i	$0.320555\pi$
$198$		0			0
$199$	2.00000	+	3.46410i	0.141776	+	0.245564i	0.928166	−	0.372168i	$-0.121385\pi$
$199$	2.00000	+	3.46410i	0.141776	+	0.245564i	−0.786389	+	0.617731i	$0.788052\pi$
$200$		0			0
$201$	−13.5000	+	23.3827i	−0.952217	+	1.64929i
$202$		0			0
$203$	−12.5000	+	4.33013i	−0.877328	+	0.303915i
$204$		0			0
$205$	−4.00000	+	6.92820i	−0.279372	+	0.483887i
$206$		0			0
$207$	−24.0000	−	41.5692i	−1.66812	−	2.88926i
$208$		0			0
$209$		0			0
$210$		0			0
$211$	20.0000			1.37686			0.688428	−	0.725304i	$-0.258301\pi$
$211$	20.0000			1.37686			0.688428	+	0.725304i	$0.258301\pi$
$212$		0			0
$213$	3.00000	+	5.19615i	0.205557	+	0.356034i
$214$		0			0
$215$	−8.00000	+	13.8564i	−0.545595	+	0.944999i
$216$		0			0
$217$	8.00000	+	6.92820i	0.543075	+	0.470317i
$218$		0			0
$219$	6.00000	−	10.3923i	0.405442	−	0.702247i
$220$		0			0
$221$	7.00000	+	12.1244i	0.470871	+	0.815572i
$222$		0			0
$223$	−4.00000			−0.267860			−0.133930	−	0.990991i	$-0.542760\pi$
$223$	−4.00000			−0.267860			−0.133930	+	0.990991i	$0.542760\pi$
$224$		0			0
$225$	−6.00000			−0.400000
$226$		0			0
$227$	−1.00000	−	1.73205i	−0.0663723	−	0.114960i	0.830930	−	0.556378i	$-0.187809\pi$
$227$	−1.00000	−	1.73205i	−0.0663723	−	0.114960i	−0.897302	+	0.441417i	$0.854476\pi$
$228$		0			0
$229$	14.0000	−	24.2487i	0.925146	−	1.60240i	0.133820	−	0.991006i	$-0.457276\pi$
$229$	14.0000	−	24.2487i	0.925146	−	1.60240i	0.791326	−	0.611394i	$-0.209391\pi$
$230$		0			0
$231$	1.50000	−	7.79423i	0.0986928	−	0.512823i
$232$		0			0
$233$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$233$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$234$		0			0
$235$	2.00000	+	3.46410i	0.130466	+	0.225973i
$236$		0			0
$237$	27.0000			1.75384
$238$		0			0
$239$	5.00000			0.323423			0.161712	−	0.986838i	$-0.448299\pi$
$239$	5.00000			0.323423			0.161712	+	0.986838i	$0.448299\pi$
$240$		0			0
$241$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$241$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$242$		0			0
$243$		0			0
$244$		0			0
$245$	2.00000	+	13.8564i	0.127775	+	0.885253i
$246$		0			0
$247$		0			0
$248$		0			0
$249$	−9.00000	−	15.5885i	−0.570352	−	0.987878i
$250$		0			0
$251$	24.0000			1.51487			0.757433	−	0.652913i	$-0.226453\pi$
$251$	24.0000			1.51487			0.757433	+	0.652913i	$0.226453\pi$
$252$		0			0
$253$	8.00000			0.502956
$254$		0			0
$255$	6.00000	+	10.3923i	0.375735	+	0.650791i
$256$		0			0
$257$	−1.50000	+	2.59808i	−0.0935674	+	0.162064i	−0.909010	−	0.416775i	$-0.863160\pi$
$257$	−1.50000	+	2.59808i	−0.0935674	+	0.162064i	0.815442	+	0.578838i	$0.196494\pi$
$258$		0			0
$259$	−2.00000	+	10.3923i	−0.124274	+	0.645746i
$260$		0			0
$261$	15.0000	−	25.9808i	0.928477	−	1.60817i
$262$		0			0
$263$	13.5000	+	23.3827i	0.832446	+	1.44184i	0.896093	+	0.443866i	$0.146393\pi$
$263$	13.5000	+	23.3827i	0.832446	+	1.44184i	−0.0636476	+	0.997972i	$0.520273\pi$
$264$		0			0
$265$	−12.0000			−0.737154
$266$		0			0
$267$	−18.0000			−1.10158
$268$		0			0
$269$	12.0000	+	20.7846i	0.731653	+	1.26726i	0.956176	+	0.292791i	$0.0945841\pi$
$269$	12.0000	+	20.7846i	0.731653	+	1.26726i	−0.224523	+	0.974469i	$0.572083\pi$
$270$		0			0
$271$	−5.50000	+	9.52628i	−0.334101	+	0.578680i	−0.983312	−	0.181928i	$-0.941766\pi$
$271$	−5.50000	+	9.52628i	−0.334101	+	0.578680i	0.649211	+	0.760609i	$0.275099\pi$
$272$		0			0
$273$	−42.0000	−	36.3731i	−2.54196	−	2.20140i
$274$		0			0
$275$	0.500000	−	0.866025i	0.0301511	−	0.0522233i
$276$		0			0
$277$	4.50000	+	7.79423i	0.270379	+	0.468310i	0.968959	−	0.247222i	$-0.0795177\pi$
$277$	4.50000	+	7.79423i	0.270379	+	0.468310i	−0.698580	+	0.715532i	$0.746184\pi$
$278$		0			0
$279$	−24.0000			−1.43684
$280$		0			0
$281$	−28.0000			−1.67034			−0.835170	−	0.549992i	$-0.814631\pi$
$281$	−28.0000			−1.67034			−0.835170	+	0.549992i	$0.814631\pi$
$282$		0			0
$283$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$283$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	10.0000	−	3.46410i	0.590281	−	0.204479i
$288$		0			0
$289$	6.50000	−	11.2583i	0.382353	−	0.662255i
$290$		0			0
$291$	10.5000	+	18.1865i	0.615521	+	1.06611i
$292$		0			0
$293$	−18.0000			−1.05157			−0.525786	−	0.850617i	$-0.676229\pi$
$293$	−18.0000			−1.05157			−0.525786	+	0.850617i	$0.676229\pi$
$294$		0			0
$295$	−6.00000			−0.349334
$296$		0			0
$297$	4.50000	+	7.79423i	0.261116	+	0.452267i
$298$		0			0
$299$	28.0000	−	48.4974i	1.61928	−	2.80468i
$300$		0			0
$301$	20.0000	−	6.92820i	1.15278	−	0.399335i
$302$		0			0
$303$	−13.5000	+	23.3827i	−0.775555	+	1.34330i
$304$		0			0
$305$	−1.00000	−	1.73205i	−0.0572598	−	0.0991769i
$306$		0			0
$307$	−2.00000			−0.114146			−0.0570730	−	0.998370i	$-0.518177\pi$
$307$	−2.00000			−0.114146			−0.0570730	+	0.998370i	$0.518177\pi$
$308$		0			0
$309$	54.0000			3.07195
$310$		0			0
$311$	−5.00000	−	8.66025i	−0.283524	−	0.491078i	0.688726	−	0.725022i	$-0.258170\pi$
$311$	−5.00000	−	8.66025i	−0.283524	−	0.491078i	−0.972250	+	0.233944i	$0.924837\pi$
$312$		0			0
$313$	−0.500000	+	0.866025i	−0.0282617	+	0.0489506i	−0.879810	−	0.475325i	$-0.842331\pi$
$313$	−0.500000	+	0.866025i	−0.0282617	+	0.0489506i	0.851549	+	0.524276i	$0.175664\pi$
$314$		0			0
$315$	−24.0000	−	20.7846i	−1.35225	−	1.17108i
$316$		0			0
$317$	6.00000	−	10.3923i	0.336994	−	0.583690i	−0.646872	−	0.762598i	$-0.723923\pi$
$317$	6.00000	−	10.3923i	0.336994	−	0.583690i	0.983866	+	0.178908i	$0.0572566\pi$
$318$		0			0
$319$	2.50000	+	4.33013i	0.139973	+	0.242441i
$320$		0			0
$321$	6.00000			0.334887
$322$		0			0
$323$		0			0
$324$		0			0
$325$	−3.50000	−	6.06218i	−0.194145	−	0.336269i
$326$		0			0
$327$	−3.00000	+	5.19615i	−0.165900	+	0.287348i
$328$		0			0
$329$	1.00000	−	5.19615i	0.0551318	−	0.286473i
$330$		0			0
$331$	6.50000	−	11.2583i	0.357272	−	0.618814i	−0.630232	−	0.776407i	$-0.717040\pi$
$331$	6.50000	−	11.2583i	0.357272	−	0.618814i	0.987504	+	0.157593i	$0.0503735\pi$
$332$		0			0
$333$	−12.0000	−	20.7846i	−0.657596	−	1.13899i
$334$		0			0
$335$	−18.0000			−0.983445
$336$		0			0
$337$	−12.0000			−0.653682			−0.326841	−	0.945079i	$-0.605984\pi$
$337$	−12.0000			−0.653682			−0.326841	+	0.945079i	$0.605984\pi$
$338$		0			0
$339$	7.50000	+	12.9904i	0.407344	+	0.705541i
$340$		0			0
$341$	2.00000	−	3.46410i	0.108306	−	0.187592i
$342$		0			0
$343$	10.0000	−	15.5885i	0.539949	−	0.841698i
$344$		0			0
$345$	24.0000	−	41.5692i	1.29212	−	2.23801i
$346$		0			0
$347$	−11.0000	−	19.0526i	−0.590511	−	1.02279i	−0.994164	−	0.107883i	$-0.965593\pi$
$347$	−11.0000	−	19.0526i	−0.590511	−	1.02279i	0.403653	−	0.914912i	$-0.367740\pi$
$348$		0			0
$349$	2.00000			0.107058			0.0535288	−	0.998566i	$-0.482953\pi$
$349$	2.00000			0.107058			0.0535288	+	0.998566i	$0.482953\pi$
$350$		0			0
$351$	63.0000			3.36269
$352$		0			0
$353$	9.00000	+	15.5885i	0.479022	+	0.829690i	0.999711	−	0.0240566i	$-0.00765819\pi$
$353$	9.00000	+	15.5885i	0.479022	+	0.829690i	−0.520689	+	0.853746i	$0.674325\pi$
$354$		0			0
$355$	−2.00000	+	3.46410i	−0.106149	+	0.183855i
$356$		0			0
$357$	3.00000	−	15.5885i	0.158777	−	0.825029i
$358$		0			0
$359$	−9.50000	+	16.4545i	−0.501391	+	0.868434i	0.498608	+	0.866828i	$0.333845\pi$
$359$	−9.50000	+	16.4545i	−0.501391	+	0.868434i	−0.999999	+	0.00160673i	$0.999489\pi$
$360$		0			0
$361$	9.50000	+	16.4545i	0.500000	+	0.866025i
$362$		0			0
$363$	−3.00000			−0.157459
$364$		0			0
$365$	8.00000			0.418739
$366$		0			0
$367$	2.00000	+	3.46410i	0.104399	+	0.180825i	0.913493	−	0.406855i	$-0.133375\pi$
$367$	2.00000	+	3.46410i	0.104399	+	0.180825i	−0.809093	+	0.587680i	$0.800041\pi$
$368$		0			0
$369$	−12.0000	+	20.7846i	−0.624695	+	1.08200i
$370$		0			0
$371$	12.0000	+	10.3923i	0.623009	+	0.539542i
$372$		0			0
$373$	−5.50000	+	9.52628i	−0.284779	+	0.493252i	−0.972556	−	0.232671i	$-0.925254\pi$
$373$	−5.50000	+	9.52628i	−0.284779	+	0.493252i	0.687776	+	0.725923i	$0.258587\pi$
$374$		0			0
$375$	−18.0000	−	31.1769i	−0.929516	−	1.60997i
$376$		0			0
$377$	35.0000			1.80259
$378$		0			0
$379$	−1.00000			−0.0513665			−0.0256833	−	0.999670i	$-0.508176\pi$
$379$	−1.00000			−0.0513665			−0.0256833	+	0.999670i	$0.508176\pi$
$380$		0			0
$381$	28.5000	+	49.3634i	1.46010	+	2.52897i
$382$		0			0
$383$	13.0000	−	22.5167i	0.664269	−	1.15055i	−0.315214	−	0.949021i	$-0.602076\pi$
$383$	13.0000	−	22.5167i	0.664269	−	1.15055i	0.979483	−	0.201527i	$-0.0645904\pi$
$384$		0			0
$385$	5.00000	−	1.73205i	0.254824	−	0.0882735i
$386$		0			0
$387$	−24.0000	+	41.5692i	−1.21999	+	2.11308i
$388$		0			0
$389$	−9.00000	−	15.5885i	−0.456318	−	0.790366i	0.542445	−	0.840091i	$-0.317499\pi$
$389$	−9.00000	−	15.5885i	−0.456318	−	0.790366i	−0.998763	+	0.0497253i	$0.984165\pi$
$390$		0			0
$391$	16.0000			0.809155
$392$		0			0
$393$		0			0
$394$		0			0
$395$	9.00000	+	15.5885i	0.452839	+	0.784340i
$396$		0			0
$397$	−3.00000	+	5.19615i	−0.150566	+	0.260787i	−0.931436	−	0.363906i	$-0.881443\pi$
$397$	−3.00000	+	5.19615i	−0.150566	+	0.260787i	0.780870	+	0.624694i	$0.214776\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$	4.50000	−	7.79423i	0.224719	−	0.389225i	−0.731516	−	0.681824i	$-0.761187\pi$
$401$	4.50000	−	7.79423i	0.224719	−	0.389225i	0.956235	+	0.292599i	$0.0945202\pi$
$402$		0			0
$403$	−14.0000	−	24.2487i	−0.697390	−	1.20791i
$404$		0			0
$405$	18.0000			0.894427
$406$		0			0
$407$	4.00000			0.198273
$408$		0			0
$409$	−11.0000	−	19.0526i	−0.543915	−	0.942088i	−0.998674	−	0.0514740i	$-0.983608\pi$
$409$	−11.0000	−	19.0526i	−0.543915	−	0.942088i	0.454759	−	0.890614i	$-0.349725\pi$
$410$		0			0
$411$	4.50000	−	7.79423i	0.221969	−	0.384461i
$412$		0			0
$413$	6.00000	+	5.19615i	0.295241	+	0.255686i
$414$		0			0
$415$	6.00000	−	10.3923i	0.294528	−	0.510138i
$416$		0			0
$417$	6.00000	+	10.3923i	0.293821	+	0.508913i
$418$		0			0
$419$	−16.0000			−0.781651			−0.390826	−	0.920465i	$-0.627810\pi$
$419$	−16.0000			−0.781651			−0.390826	+	0.920465i	$0.627810\pi$
$420$		0			0
$421$	−20.0000			−0.974740			−0.487370	−	0.873195i	$-0.662044\pi$
$421$	−20.0000			−0.974740			−0.487370	+	0.873195i	$0.662044\pi$
$422$		0			0
$423$	6.00000	+	10.3923i	0.291730	+	0.505291i
$424$		0			0
$425$	1.00000	−	1.73205i	0.0485071	−	0.0840168i
$426$		0			0
$427$	−0.500000	+	2.59808i	−0.0241967	+	0.125730i
$428$		0			0
$429$	−10.5000	+	18.1865i	−0.506945	+	0.878054i
$430$		0			0
$431$	12.5000	+	21.6506i	0.602104	+	1.04287i	0.992502	+	0.122228i	$0.0390040\pi$
$431$	12.5000	+	21.6506i	0.602104	+	1.04287i	−0.390398	+	0.920646i	$0.627663\pi$
$432$		0			0
$433$	−34.0000			−1.63394			−0.816968	−	0.576683i	$-0.804347\pi$
$433$	−34.0000			−1.63394			−0.816968	+	0.576683i	$0.804347\pi$
$434$		0			0
$435$	30.0000			1.43839
$436$		0			0
$437$		0			0
$438$		0			0
$439$	−2.50000	+	4.33013i	−0.119318	+	0.206666i	−0.919498	−	0.393095i	$-0.871404\pi$
$439$	−2.50000	+	4.33013i	−0.119318	+	0.206666i	0.800179	+	0.599761i	$0.204738\pi$
$440$		0			0
$441$	6.00000	+	41.5692i	0.285714	+	1.97949i
$442$		0			0
$443$	18.0000	−	31.1769i	0.855206	−	1.48126i	−0.0212481	−	0.999774i	$-0.506764\pi$
$443$	18.0000	−	31.1769i	0.855206	−	1.48126i	0.876454	−	0.481486i	$-0.159903\pi$
$444$		0			0
$445$	−6.00000	−	10.3923i	−0.284427	−	0.492642i
$446$		0			0
$447$	30.0000			1.41895
$448$		0			0
$449$	−6.00000			−0.283158			−0.141579	−	0.989927i	$-0.545218\pi$
$449$	−6.00000			−0.283158			−0.141579	+	0.989927i	$0.545218\pi$
$450$		0			0
$451$	−2.00000	−	3.46410i	−0.0941763	−	0.163118i
$452$		0			0
$453$	4.50000	−	7.79423i	0.211428	−	0.366205i
$454$		0			0
$455$	7.00000	−	36.3731i	0.328165	−	1.70520i
$456$		0			0
$457$	−7.00000	+	12.1244i	−0.327446	+	0.567153i	−0.982004	−	0.188858i	$-0.939521\pi$
$457$	−7.00000	+	12.1244i	−0.327446	+	0.567153i	0.654558	+	0.756012i	$0.272855\pi$
$458$		0			0
$459$	9.00000	+	15.5885i	0.420084	+	0.727607i
$460$		0			0
$461$	27.0000			1.25752			0.628758	−	0.777601i	$-0.283564\pi$
$461$	27.0000			1.25752			0.628758	+	0.777601i	$0.283564\pi$
$462$		0			0
$463$	2.00000			0.0929479			0.0464739	−	0.998920i	$-0.485202\pi$
$463$	2.00000			0.0929479			0.0464739	+	0.998920i	$0.485202\pi$
$464$		0			0
$465$	−12.0000	−	20.7846i	−0.556487	−	0.963863i
$466$		0			0
$467$	6.00000	−	10.3923i	0.277647	−	0.480899i	−0.693153	−	0.720791i	$-0.743779\pi$
$467$	6.00000	−	10.3923i	0.277647	−	0.480899i	0.970799	+	0.239892i	$0.0771121\pi$
$468$		0			0
$469$	18.0000	+	15.5885i	0.831163	+	0.719808i
$470$		0			0
$471$	24.0000	−	41.5692i	1.10586	−	1.91541i
$472$		0			0
$473$	−4.00000	−	6.92820i	−0.183920	−	0.318559i
$474$		0			0
$475$		0			0
$476$		0			0
$477$	−36.0000			−1.64833
$478$		0			0
$479$	−0.500000	−	0.866025i	−0.0228456	−	0.0395697i	0.854377	−	0.519654i	$-0.173939\pi$
$479$	−0.500000	−	0.866025i	−0.0228456	−	0.0395697i	−0.877222	+	0.480085i	$0.840606\pi$
$480$		0			0
$481$	14.0000	−	24.2487i	0.638345	−	1.10565i
$482$		0			0
$483$	−60.0000	+	20.7846i	−2.73009	+	0.945732i
$484$		0			0
$485$	−7.00000	+	12.1244i	−0.317854	+	0.550539i
$486$		0			0
$487$	−20.0000	−	34.6410i	−0.906287	−	1.56973i	−0.819181	−	0.573535i	$-0.805572\pi$
$487$	−20.0000	−	34.6410i	−0.906287	−	1.56973i	−0.0871056	−	0.996199i	$-0.527762\pi$
$488$		0			0
$489$	−51.0000			−2.30630
$490$		0			0
$491$	−30.0000			−1.35388			−0.676941	−	0.736038i	$-0.736695\pi$
$491$	−30.0000			−1.35388			−0.676941	+	0.736038i	$0.736695\pi$
$492$		0			0
$493$	5.00000	+	8.66025i	0.225189	+	0.390038i
$494$		0			0
$495$	−6.00000	+	10.3923i	−0.269680	+	0.467099i
$496$		0			0
$497$	5.00000	−	1.73205i	0.224281	−	0.0776931i
$498$		0			0
$499$	10.0000	−	17.3205i	0.447661	−	0.775372i	−0.550572	−	0.834788i	$-0.685590\pi$
$499$	10.0000	−	17.3205i	0.447661	−	0.775372i	0.998233	+	0.0594153i	$0.0189236\pi$
$500$		0			0
$501$	−28.5000	−	49.3634i	−1.27329	−	2.20540i
$502$		0			0
$503$	−3.00000			−0.133763			−0.0668817	−	0.997761i	$-0.521305\pi$
$503$	−3.00000			−0.133763			−0.0668817	+	0.997761i	$0.521305\pi$
$504$		0			0
$505$	−18.0000			−0.800989
$506$		0			0
$507$	54.0000	+	93.5307i	2.39822	+	4.15385i
$508$		0			0
$509$	11.0000	−	19.0526i	0.487566	−	0.844490i	−0.512331	−	0.858788i	$-0.671218\pi$
$509$	11.0000	−	19.0526i	0.487566	−	0.844490i	0.999898	+	0.0142980i	$0.00455136\pi$
$510$		0			0
$511$	−8.00000	−	6.92820i	−0.353899	−	0.306486i
$512$		0			0
$513$		0			0
$514$		0			0
$515$	18.0000	+	31.1769i	0.793175	+	1.37382i
$516$		0			0
$517$	−2.00000			−0.0879599
$518$		0			0
$519$	−75.0000			−3.29213
$520$		0			0
$521$	−5.00000	−	8.66025i	−0.219054	−	0.379413i	0.735465	−	0.677563i	$-0.236964\pi$
$521$	−5.00000	−	8.66025i	−0.219054	−	0.379413i	−0.954519	+	0.298150i	$0.903630\pi$
$522$		0			0
$523$	−5.00000	+	8.66025i	−0.218635	+	0.378686i	−0.954391	−	0.298560i	$-0.903494\pi$
$523$	−5.00000	+	8.66025i	−0.218635	+	0.378686i	0.735756	+	0.677247i	$0.236827\pi$
$524$		0			0
$525$	−1.50000	+	7.79423i	−0.0654654	+	0.340168i
$526$		0			0
$527$	4.00000	−	6.92820i	0.174243	−	0.301797i
$528$		0			0
$529$	−20.5000	−	35.5070i	−0.891304	−	1.54378i
$530$		0			0
$531$	−18.0000			−0.781133
$532$		0			0
$533$	−28.0000			−1.21281
$534$		0			0
$535$	2.00000	+	3.46410i	0.0864675	+	0.149766i
$536$		0			0
$537$	−28.5000	+	49.3634i	−1.22987	+	2.13019i
$538$		0			0
$539$	−6.50000	−	2.59808i	−0.279975	−	0.111907i
$540$		0			0
$541$	−2.50000	+	4.33013i	−0.107483	+	0.186167i	−0.914750	−	0.404020i	$-0.867613\pi$
$541$	−2.50000	+	4.33013i	−0.107483	+	0.186167i	0.807267	+	0.590187i	$0.200946\pi$
$542$		0			0
$543$	−33.0000	−	57.1577i	−1.41617	−	2.45287i
$544$		0			0
$545$	−4.00000			−0.171341
$546$		0			0
$547$	−30.0000			−1.28271			−0.641354	−	0.767245i	$-0.721627\pi$
$547$	−30.0000			−1.28271			−0.641354	+	0.767245i	$0.721627\pi$
$548$		0			0
$549$	−3.00000	−	5.19615i	−0.128037	−	0.221766i
$550$		0			0
$551$		0			0
$552$		0			0
$553$	4.50000	−	23.3827i	0.191359	−	0.994333i
$554$		0			0
$555$	12.0000	−	20.7846i	0.509372	−	0.882258i
$556$		0			0
$557$	−13.0000	−	22.5167i	−0.550828	−	0.954062i	−0.998215	−	0.0597213i	$-0.980979\pi$
$557$	−13.0000	−	22.5167i	−0.550828	−	0.954062i	0.447387	−	0.894340i	$-0.352355\pi$
$558$		0			0
$559$	−56.0000			−2.36855
$560$		0			0
$561$	−6.00000			−0.253320
$562$		0			0
$563$	10.0000	+	17.3205i	0.421450	+	0.729972i	0.996082	−	0.0884397i	$-0.0281881\pi$
$563$	10.0000	+	17.3205i	0.421450	+	0.729972i	−0.574632	+	0.818412i	$0.694855\pi$
$564$		0			0
$565$	−5.00000	+	8.66025i	−0.210352	+	0.364340i
$566$		0			0
$567$	−18.0000	−	15.5885i	−0.755929	−	0.654654i
$568$		0			0
$569$	6.00000	−	10.3923i	0.251533	−	0.435668i	−0.712415	−	0.701758i	$-0.752399\pi$
$569$	6.00000	−	10.3923i	0.251533	−	0.435668i	0.963948	+	0.266090i	$0.0857319\pi$
$570$		0			0
$571$	11.0000	+	19.0526i	0.460336	+	0.797325i	0.998978	−	0.0452101i	$-0.0143957\pi$
$571$	11.0000	+	19.0526i	0.460336	+	0.797325i	−0.538642	+	0.842535i	$0.681062\pi$
$572$		0			0
$573$	6.00000			0.250654
$574$		0			0
$575$	−8.00000			−0.333623
$576$		0			0
$577$	21.5000	+	37.2391i	0.895057	+	1.55028i	0.833734	+	0.552166i	$0.186198\pi$
$577$	21.5000	+	37.2391i	0.895057	+	1.55028i	0.0613223	+	0.998118i	$0.480468\pi$
$578$		0			0
$579$	12.0000	−	20.7846i	0.498703	−	0.863779i
$580$		0			0
$581$	−15.0000	+	5.19615i	−0.622305	+	0.215573i
$582$		0			0
$583$	3.00000	−	5.19615i	0.124247	−	0.215203i
$584$		0			0
$585$	42.0000	+	72.7461i	1.73649	+	3.00768i
$586$		0			0
$587$	−27.0000			−1.11441			−0.557205	−	0.830375i	$-0.688126\pi$
$587$	−27.0000			−1.11441			−0.557205	+	0.830375i	$0.688126\pi$
$588$		0			0
$589$		0			0
$590$		0			0
$591$	22.5000	+	38.9711i	0.925526	+	1.60306i
$592$		0			0
$593$	−3.00000	+	5.19615i	−0.123195	+	0.213380i	−0.921026	−	0.389501i	$-0.872647\pi$
$593$	−3.00000	+	5.19615i	−0.123195	+	0.213380i	0.797831	+	0.602881i	$0.205981\pi$
$594$		0			0
$595$	10.0000	−	3.46410i	0.409960	−	0.142014i
$596$		0			0
$597$	−6.00000	+	10.3923i	−0.245564	+	0.425329i
$598$		0			0
$599$	18.0000	+	31.1769i	0.735460	+	1.27385i	0.954521	+	0.298143i	$0.0963673\pi$
$599$	18.0000	+	31.1769i	0.735460	+	1.27385i	−0.219061	+	0.975711i	$0.570299\pi$
$600$		0			0
$601$	26.0000			1.06056			0.530281	−	0.847822i	$-0.322086\pi$
$601$	26.0000			1.06056			0.530281	+	0.847822i	$0.322086\pi$
$602$		0			0
$603$	−54.0000			−2.19905
$604$		0			0
$605$	−1.00000	−	1.73205i	−0.0406558	−	0.0704179i
$606$		0			0
$607$	4.00000	−	6.92820i	0.162355	−	0.281207i	−0.773358	−	0.633970i	$-0.781424\pi$
$607$	4.00000	−	6.92820i	0.162355	−	0.281207i	0.935713	+	0.352763i	$0.114758\pi$
$608$		0			0
$609$	−30.0000	−	25.9808i	−1.21566	−	1.05279i
$610$		0			0
$611$	−7.00000	+	12.1244i	−0.283190	+	0.490499i
$612$		0			0
$613$	19.0000	+	32.9090i	0.767403	+	1.32918i	0.938967	+	0.344008i	$0.111785\pi$
$613$	19.0000	+	32.9090i	0.767403	+	1.32918i	−0.171564	+	0.985173i	$0.554882\pi$
$614$		0			0
$615$	−24.0000			−0.967773
$616$		0			0
$617$	−15.0000			−0.603877			−0.301939	−	0.953327i	$-0.597634\pi$
$617$	−15.0000			−0.603877			−0.301939	+	0.953327i	$0.597634\pi$
$618$		0			0
$619$	−14.0000	−	24.2487i	−0.562708	−	0.974638i	−0.997259	−	0.0739910i	$-0.976426\pi$
$619$	−14.0000	−	24.2487i	−0.562708	−	0.974638i	0.434551	−	0.900647i	$-0.356907\pi$
$620$		0			0
$621$	36.0000	−	62.3538i	1.44463	−	2.50217i
$622$		0			0
$623$	−3.00000	+	15.5885i	−0.120192	+	0.624538i
$624$		0			0
$625$	9.50000	−	16.4545i	0.380000	−	0.658179i
$626$		0			0
$627$		0			0
$628$		0			0
$629$	8.00000			0.318981
$630$		0			0
$631$	18.0000			0.716569			0.358284	−	0.933613i	$-0.383362\pi$
$631$	18.0000			0.716569			0.358284	+	0.933613i	$0.383362\pi$
$632$		0			0
$633$	30.0000	+	51.9615i	1.19239	+	2.06529i
$634$		0			0
$635$	−19.0000	+	32.9090i	−0.753992	+	1.30595i
$636$		0			0
$637$	−38.5000	+	30.3109i	−1.52543	+	1.20096i
$638$		0			0
$639$	−6.00000	+	10.3923i	−0.237356	+	0.411113i
$640$		0			0
$641$	13.5000	+	23.3827i	0.533218	+	0.923561i	0.999247	+	0.0387913i	$0.0123508\pi$
$641$	13.5000	+	23.3827i	0.533218	+	0.923561i	−0.466029	+	0.884769i	$0.654316\pi$
$642$		0			0
$643$	−31.0000			−1.22252			−0.611260	−	0.791430i	$-0.709337\pi$
$643$	−31.0000			−1.22252			−0.611260	+	0.791430i	$0.709337\pi$
$644$		0			0
$645$	−48.0000			−1.89000
$646$		0			0
$647$	15.0000	+	25.9808i	0.589711	+	1.02141i	0.994270	+	0.106897i	$0.0340916\pi$
$647$	15.0000	+	25.9808i	0.589711	+	1.02141i	−0.404559	+	0.914512i	$0.632575\pi$
$648$		0			0
$649$	1.50000	−	2.59808i	0.0588802	−	0.101983i
$650$		0			0
$651$	−6.00000	+	31.1769i	−0.235159	+	1.22192i
$652$		0			0
$653$	−20.0000	+	34.6410i	−0.782660	+	1.35561i	0.147726	+	0.989028i	$0.452805\pi$
$653$	−20.0000	+	34.6410i	−0.782660	+	1.35561i	−0.930387	+	0.366579i	$0.880529\pi$
$654$		0			0
$655$		0			0
$656$		0			0
$657$	24.0000			0.936329
$658$		0			0
$659$	−28.0000			−1.09073			−0.545363	−	0.838200i	$-0.683608\pi$
$659$	−28.0000			−1.09073			−0.545363	+	0.838200i	$0.683608\pi$
$660$		0			0
$661$	11.0000	+	19.0526i	0.427850	+	0.741059i	0.996682	−	0.0813955i	$-0.0259377\pi$
$661$	11.0000	+	19.0526i	0.427850	+	0.741059i	−0.568831	+	0.822454i	$0.692604\pi$
$662$		0			0
$663$	−21.0000	+	36.3731i	−0.815572	+	1.41261i
$664$		0			0
$665$		0			0
$666$		0			0
$667$	20.0000	−	34.6410i	0.774403	−	1.34131i
$668$		0			0
$669$	−6.00000	−	10.3923i	−0.231973	−	0.401790i
$670$		0			0
$671$	1.00000			0.0386046
$672$		0			0
$673$	34.0000			1.31060			0.655302	−	0.755367i	$-0.272541\pi$
$673$	34.0000			1.31060			0.655302	+	0.755367i	$0.272541\pi$
$674$		0			0
$675$	−4.50000	−	7.79423i	−0.173205	−	0.300000i
$676$		0			0
$677$	−7.00000	+	12.1244i	−0.269032	+	0.465977i	−0.968612	−	0.248577i	$-0.920037\pi$
$677$	−7.00000	+	12.1244i	−0.269032	+	0.465977i	0.699580	+	0.714554i	$0.253370\pi$
$678$		0			0
$679$	17.5000	−	6.06218i	0.671588	−	0.232645i
$680$		0			0
$681$	3.00000	−	5.19615i	0.114960	−	0.199117i
$682$		0			0
$683$	10.5000	+	18.1865i	0.401771	+	0.695888i	0.993940	−	0.109926i	$-0.0350613\pi$
$683$	10.5000	+	18.1865i	0.401771	+	0.695888i	−0.592168	+	0.805814i	$0.701728\pi$
$684$		0			0
$685$	6.00000			0.229248
$686$		0			0
$687$	84.0000			3.20480
$688$		0			0
$689$	−21.0000	−	36.3731i	−0.800036	−	1.38570i
$690$		0			0
$691$	16.5000	−	28.5788i	0.627690	−	1.08719i	−0.360325	−	0.932827i	$-0.617334\pi$
$691$	16.5000	−	28.5788i	0.627690	−	1.08719i	0.988014	−	0.154363i	$-0.0493326\pi$
$692$		0			0
$693$	15.0000	−	5.19615i	0.569803	−	0.197386i
$694$		0			0
$695$	−4.00000	+	6.92820i	−0.151729	+	0.262802i
$696$		0			0
$697$	−4.00000	−	6.92820i	−0.151511	−	0.262424i
$698$		0			0
$699$		0			0
$700$		0			0
$701$	−27.0000			−1.01978			−0.509888	−	0.860241i	$-0.670313\pi$
$701$	−27.0000			−1.01978			−0.509888	+	0.860241i	$0.670313\pi$
$702$		0			0
$703$		0			0
$704$		0			0
$705$	−6.00000	+	10.3923i	−0.225973	+	0.391397i
$706$		0			0
$707$	18.0000	+	15.5885i	0.676960	+	0.586264i
$708$		0			0
$709$	24.0000	−	41.5692i	0.901339	−	1.56116i	0.0755813	−	0.997140i	$-0.475919\pi$
$709$	24.0000	−	41.5692i	0.901339	−	1.56116i	0.825758	−	0.564025i	$-0.190748\pi$
$710$		0			0
$711$	27.0000	+	46.7654i	1.01258	+	1.75384i
$712$		0			0
$713$	−32.0000			−1.19841
$714$		0			0
$715$	−14.0000			−0.523570
$716$		0			0
$717$	7.50000	+	12.9904i	0.280093	+	0.485135i
$718$		0			0
$719$	−19.0000	+	32.9090i	−0.708580	+	1.22730i	0.256803	+	0.966464i	$0.417331\pi$
$719$	−19.0000	+	32.9090i	−0.708580	+	1.22730i	−0.965384	+	0.260834i	$0.916003\pi$
$720$		0			0
$721$	9.00000	−	46.7654i	0.335178	−	1.74163i
$722$		0			0
$723$		0			0
$724$		0			0
$725$	−2.50000	−	4.33013i	−0.0928477	−	0.160817i
$726$		0			0
$727$	22.0000			0.815935			0.407967	−	0.912996i	$-0.366238\pi$
$727$	22.0000			0.815935			0.407967	+	0.912996i	$0.366238\pi$
$728$		0			0
$729$	−27.0000			−1.00000
$730$		0			0
$731$	−8.00000	−	13.8564i	−0.295891	−	0.512498i
$732$		0			0
$733$	9.50000	−	16.4545i	0.350891	−	0.607760i	−0.635515	−	0.772088i	$-0.719212\pi$
$733$	9.50000	−	16.4545i	0.350891	−	0.607760i	0.986406	+	0.164328i	$0.0525456\pi$
$734$		0			0
$735$	−33.0000	+	25.9808i	−1.21722	+	0.958315i
$736$		0			0
$737$	4.50000	−	7.79423i	0.165760	−	0.287104i
$738$		0			0
$739$	21.0000	+	36.3731i	0.772497	+	1.33800i	0.936190	+	0.351494i	$0.114326\pi$
$739$	21.0000	+	36.3731i	0.772497	+	1.33800i	−0.163693	+	0.986511i	$0.552341\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$	−12.0000			−0.440237			−0.220119	−	0.975473i	$-0.570644\pi$
$743$	−12.0000			−0.440237			−0.220119	+	0.975473i	$0.570644\pi$
$744$		0			0
$745$	10.0000	+	17.3205i	0.366372	+	0.634574i
$746$		0			0
$747$	18.0000	−	31.1769i	0.658586	−	1.14070i
$748$		0			0
$749$	1.00000	−	5.19615i	0.0365392	−	0.189863i
$750$		0			0
$751$	14.0000	−	24.2487i	0.510867	−	0.884848i	−0.489053	−	0.872254i	$-0.662658\pi$
$751$	14.0000	−	24.2487i	0.510867	−	0.884848i	0.999921	−	0.0125942i	$-0.00400897\pi$
$752$		0			0
$753$	36.0000	+	62.3538i	1.31191	+	2.27230i
$754$		0			0
$755$	6.00000			0.218362
$756$		0			0
$757$	−22.0000			−0.799604			−0.399802	−	0.916602i	$-0.630921\pi$
$757$	−22.0000			−0.799604			−0.399802	+	0.916602i	$0.630921\pi$
$758$		0			0
$759$	12.0000	+	20.7846i	0.435572	+	0.754434i
$760$		0			0
$761$	3.00000	−	5.19615i	0.108750	−	0.188360i	−0.806514	−	0.591215i	$-0.798649\pi$
$761$	3.00000	−	5.19615i	0.108750	−	0.188360i	0.915264	+	0.402854i	$0.131982\pi$
$762$		0			0
$763$	4.00000	+	3.46410i	0.144810	+	0.125409i
$764$		0			0
$765$	−12.0000	+	20.7846i	−0.433861	+	0.751469i
$766$		0			0
$767$	−10.5000	−	18.1865i	−0.379133	−	0.656678i
$768$		0			0
$769$	−14.0000			−0.504853			−0.252426	−	0.967616i	$-0.581229\pi$
$769$	−14.0000			−0.504853			−0.252426	+	0.967616i	$0.581229\pi$
$770$		0			0
$771$	−9.00000			−0.324127
$772$		0			0
$773$	−12.0000	−	20.7846i	−0.431610	−	0.747570i	0.565402	−	0.824815i	$-0.308721\pi$
$773$	−12.0000	−	20.7846i	−0.431610	−	0.747570i	−0.997012	+	0.0772449i	$0.975388\pi$
$774$		0			0
$775$	−2.00000	+	3.46410i	−0.0718421	+	0.124434i
$776$		0			0
$777$	−30.0000	+	10.3923i	−1.07624	+	0.372822i
$778$		0			0
$779$		0			0
$780$		0			0
$781$	−1.00000	−	1.73205i	−0.0357828	−	0.0619777i
$782$		0			0
$783$	45.0000			1.60817
$784$		0			0
$785$	32.0000			1.14213
$786$		0			0
$787$	−20.0000	−	34.6410i	−0.712923	−	1.23482i	−0.963755	−	0.266788i	$-0.914038\pi$
$787$	−20.0000	−	34.6410i	−0.712923	−	1.23482i	0.250832	−	0.968031i	$-0.419296\pi$
$788$		0			0
$789$	−40.5000	+	70.1481i	−1.44184	+	2.49734i
$790$		0			0
$791$	12.5000	−	4.33013i	0.444449	−	0.153962i
$792$		0			0
$793$	3.50000	−	6.06218i	0.124289	−	0.215274i
$794$		0			0
$795$	−18.0000	−	31.1769i	−0.638394	−	1.10573i
$796$		0			0
$797$	50.0000			1.77109			0.885545	−	0.464553i	$-0.153785\pi$
$797$	50.0000			1.77109			0.885545	+	0.464553i	$0.153785\pi$
$798$		0			0
$799$	−4.00000			−0.141510
$800$		0			0
$801$	−18.0000	−	31.1769i	−0.635999	−	1.10158i
$802$		0			0
$803$	−2.00000	+	3.46410i	−0.0705785	+	0.122245i
$804$		0			0
$805$	−32.0000	−	27.7128i	−1.12785	−	0.976748i
$806$		0			0
$807$	−36.0000	+	62.3538i	−1.26726	+	2.19496i
$808$		0			0
$809$	−6.00000	−	10.3923i	−0.210949	−	0.365374i	0.741063	−	0.671436i	$-0.234322\pi$
$809$	−6.00000	−	10.3923i	−0.210949	−	0.365374i	−0.952012	+	0.306062i	$0.900989\pi$
$810$		0			0
$811$	−8.00000			−0.280918			−0.140459	−	0.990086i	$-0.544858\pi$
$811$	−8.00000			−0.280918			−0.140459	+	0.990086i	$0.544858\pi$
$812$		0			0
$813$	−33.0000			−1.15736
$814$		0			0
$815$	−17.0000	−	29.4449i	−0.595484	−	1.03141i
$816$		0			0
$817$		0			0
$818$		0			0
$819$	21.0000	−	109.119i	0.733799	−	3.81293i
$820$		0			0
$821$	22.5000	−	38.9711i	0.785255	−	1.36010i	−0.143591	−	0.989637i	$-0.545865\pi$
$821$	22.5000	−	38.9711i	0.785255	−	1.36010i	0.928846	−	0.370465i	$-0.120802\pi$
$822$		0			0
$823$	13.0000	+	22.5167i	0.453152	+	0.784881i	0.998580	−	0.0532760i	$-0.0169663\pi$
$823$	13.0000	+	22.5167i	0.453152	+	0.784881i	−0.545428	+	0.838157i	$0.683633\pi$
$824$		0			0
$825$	3.00000			0.104447
$826$		0			0
$827$	4.00000			0.139094			0.0695468	−	0.997579i	$-0.477845\pi$
$827$	4.00000			0.139094			0.0695468	+	0.997579i	$0.477845\pi$
$828$		0			0
$829$	1.00000	+	1.73205i	0.0347314	+	0.0601566i	0.882869	−	0.469620i	$-0.155609\pi$
$829$	1.00000	+	1.73205i	0.0347314	+	0.0601566i	−0.848137	+	0.529777i	$0.822276\pi$
$830$		0			0
$831$	−13.5000	+	23.3827i	−0.468310	+	0.811136i
$832$		0			0
$833$	−13.0000	−	5.19615i	−0.450423	−	0.180036i
$834$		0			0
$835$	19.0000	−	32.9090i	0.657522	−	1.13886i
$836$		0			0
$837$	−18.0000	−	31.1769i	−0.622171	−	1.07763i
$838$		0			0
$839$	18.0000			0.621429			0.310715	−	0.950503i	$-0.399432\pi$
$839$	18.0000			0.621429			0.310715	+	0.950503i	$0.399432\pi$
$840$		0			0
$841$	−4.00000			−0.137931
$842$		0			0
$843$	−42.0000	−	72.7461i	−1.44656	−	2.50551i
$844$		0			0
$845$	−36.0000	+	62.3538i	−1.23844	+	2.14504i
$846$		0			0
$847$	−0.500000	+	2.59808i	−0.0171802	+	0.0892710i
$848$		0			0
$849$		0			0
$850$		0			0
$851$	−16.0000	−	27.7128i	−0.548473	−	0.949983i
$852$		0			0
$853$	−10.0000			−0.342393			−0.171197	−	0.985237i	$-0.554763\pi$
$853$	−10.0000			−0.342393			−0.171197	+	0.985237i	$0.554763\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	−22.0000	−	38.1051i	−0.751506	−	1.30165i	−0.947093	−	0.320960i	$-0.895995\pi$
$857$	−22.0000	−	38.1051i	−0.751506	−	1.30165i	0.195587	−	0.980686i	$-0.437339\pi$
$858$		0			0
$859$	6.50000	−	11.2583i	0.221777	−	0.384129i	−0.733571	−	0.679613i	$-0.762148\pi$
$859$	6.50000	−	11.2583i	0.221777	−	0.384129i	0.955348	+	0.295484i	$0.0954809\pi$
$860$		0			0
$861$	24.0000	+	20.7846i	0.817918	+	0.708338i
$862$		0			0
$863$	2.00000	−	3.46410i	0.0680808	−	0.117919i	−0.829976	−	0.557800i	$-0.811646\pi$
$863$	2.00000	−	3.46410i	0.0680808	−	0.117919i	0.898056	+	0.439880i	$0.144979\pi$
$864$		0			0
$865$	−25.0000	−	43.3013i	−0.850026	−	1.47229i
$866$		0			0
$867$	39.0000			1.32451
$868$		0			0
$869$	−9.00000			−0.305304
$870$		0			0
$871$	−31.5000	−	54.5596i	−1.06734	−	1.84868i
$872$		0			0
$873$	−21.0000	+	36.3731i	−0.710742	+	1.23104i
$874$		0			0
$875$	−30.0000	+	10.3923i	−1.01419	+	0.351324i
$876$		0			0
$877$	14.5000	−	25.1147i	0.489630	−	0.848064i	−0.510299	−	0.859997i	$-0.670465\pi$
$877$	14.5000	−	25.1147i	0.489630	−	0.848064i	0.999929	+	0.0119329i	$0.00379845\pi$
$878$		0			0
$879$	−27.0000	−	46.7654i	−0.910687	−	1.57736i
$880$		0			0
$881$	21.0000			0.707508			0.353754	−	0.935339i	$-0.384905\pi$
$881$	21.0000			0.707508			0.353754	+	0.935339i	$0.384905\pi$
$882$		0			0
$883$	29.0000			0.975928			0.487964	−	0.872864i	$-0.337740\pi$
$883$	29.0000			0.975928			0.487964	+	0.872864i	$0.337740\pi$
$884$		0			0
$885$	−9.00000	−	15.5885i	−0.302532	−	0.524000i
$886$		0			0
$887$	−20.5000	+	35.5070i	−0.688323	+	1.19221i	0.284058	+	0.958807i	$0.408319\pi$
$887$	−20.5000	+	35.5070i	−0.688323	+	1.19221i	−0.972380	+	0.233403i	$0.925014\pi$
$888$		0			0
$889$	47.5000	−	16.4545i	1.59310	−	0.551866i
$890$		0			0
$891$	−4.50000	+	7.79423i	−0.150756	+	0.261116i
$892$		0			0
$893$		0			0
$894$		0			0
$895$	−38.0000			−1.27020
$896$		0			0
$897$	168.000			5.60936
$898$		0			0
$899$	−10.0000	−	17.3205i	−0.333519	−	0.577671i
$900$		0			0
$901$	6.00000	−	10.3923i	0.199889	−	0.346218i
$902$		0			0
$903$	48.0000	+	41.5692i	1.59734	+	1.38334i
$904$		0			0
$905$	22.0000	−	38.1051i	0.731305	−	1.26666i
$906$		0			0
$907$	−14.0000	−	24.2487i	−0.464862	−	0.805165i	0.534333	−	0.845274i	$-0.320563\pi$
$907$	−14.0000	−	24.2487i	−0.464862	−	0.805165i	−0.999195	+	0.0401089i	$0.987230\pi$
$908$		0			0
$909$	−54.0000			−1.79107
$910$		0			0
$911$	−30.0000			−0.993944			−0.496972	−	0.867766i	$-0.665555\pi$
$911$	−30.0000			−0.993944			−0.496972	+	0.867766i	$0.665555\pi$
$912$		0			0
$913$	3.00000	+	5.19615i	0.0992855	+	0.171968i
$914$		0			0
$915$	3.00000	−	5.19615i	0.0991769	−	0.171780i
$916$		0			0
$917$		0			0
$918$		0			0
$919$	18.0000	−	31.1769i	0.593765	−	1.02843i	−0.399955	−	0.916535i	$-0.630974\pi$
$919$	18.0000	−	31.1769i	0.593765	−	1.02843i	0.993720	−	0.111897i	$-0.0356925\pi$
$920$		0			0
$921$	−3.00000	−	5.19615i	−0.0988534	−	0.171219i
$922$		0			0
$923$	−14.0000			−0.460816
$924$		0			0
$925$	−4.00000			−0.131519
$926$		0			0
$927$	54.0000	+	93.5307i	1.77359	+	3.07195i
$928$		0			0
$929$	−7.50000	+	12.9904i	−0.246067	+	0.426201i	−0.962431	−	0.271526i	$-0.912472\pi$
$929$	−7.50000	+	12.9904i	−0.246067	+	0.426201i	0.716364	+	0.697727i	$0.245805\pi$
$930$		0			0
$931$		0			0
$932$		0			0
$933$	15.0000	−	25.9808i	0.491078	−	0.850572i
$934$		0			0
$935$	−2.00000	−	3.46410i	−0.0654070	−	0.113288i
$936$		0			0
$937$	−30.0000			−0.980057			−0.490029	−	0.871706i	$-0.663014\pi$
$937$	−30.0000			−0.980057			−0.490029	+	0.871706i	$0.663014\pi$
$938$		0			0
$939$	−3.00000			−0.0979013
$940$		0			0
$941$	5.50000	+	9.52628i	0.179295	+	0.310548i	0.941639	−	0.336624i	$-0.109285\pi$
$941$	5.50000	+	9.52628i	0.179295	+	0.310548i	−0.762344	+	0.647172i	$0.775952\pi$
$942$		0			0
$943$	−16.0000	+	27.7128i	−0.521032	+	0.902453i
$944$		0			0
$945$	9.00000	−	46.7654i	0.292770	−	1.52128i
$946$		0			0
$947$	−2.00000	+	3.46410i	−0.0649913	+	0.112568i	−0.896690	−	0.442659i	$-0.854035\pi$
$947$	−2.00000	+	3.46410i	−0.0649913	+	0.112568i	0.831699	+	0.555227i	$0.187369\pi$
$948$		0			0
$949$	14.0000	+	24.2487i	0.454459	+	0.787146i
$950$		0			0
$951$	36.0000			1.16738
$952$		0			0
$953$	14.0000			0.453504			0.226752	−	0.973952i	$-0.427189\pi$
$953$	14.0000			0.453504			0.226752	+	0.973952i	$0.427189\pi$
$954$		0			0
$955$	2.00000	+	3.46410i	0.0647185	+	0.112096i
$956$		0			0
$957$	−7.50000	+	12.9904i	−0.242441	+	0.419919i
$958$		0			0
$959$	−6.00000	−	5.19615i	−0.193750	−	0.167793i
$960$		0			0
$961$	7.50000	−	12.9904i	0.241935	−	0.419045i
$962$		0			0
$963$	6.00000	+	10.3923i	0.193347	+	0.334887i
$964$		0			0
$965$	16.0000			0.515058
$966$		0			0
$967$	−8.00000			−0.257263			−0.128631	−	0.991692i	$-0.541058\pi$
$967$	−8.00000			−0.257263			−0.128631	+	0.991692i	$0.541058\pi$
$968$		0			0
$969$		0			0
$970$		0			0
$971$	20.5000	−	35.5070i	0.657876	−	1.13948i	−0.323288	−	0.946301i	$-0.604788\pi$
$971$	20.5000	−	35.5070i	0.657876	−	1.13948i	0.981164	−	0.193175i	$-0.0618784\pi$
$972$		0			0
$973$	10.0000	−	3.46410i	0.320585	−	0.111054i
$974$		0			0
$975$	10.5000	−	18.1865i	0.336269	−	0.582435i
$976$		0			0
$977$	23.0000	+	39.8372i	0.735835	+	1.27450i	0.954356	+	0.298672i	$0.0965435\pi$
$977$	23.0000	+	39.8372i	0.735835	+	1.27450i	−0.218521	+	0.975832i	$0.570123\pi$
$978$		0			0
$979$	6.00000			0.191761
$980$		0			0
$981$	−12.0000			−0.383131
$982$		0			0
$983$	−9.00000	−	15.5885i	−0.287055	−	0.497195i	0.686050	−	0.727554i	$-0.259343\pi$
$983$	−9.00000	−	15.5885i	−0.287055	−	0.497195i	−0.973106	+	0.230360i	$0.926010\pi$
$984$		0			0
$985$	−15.0000	+	25.9808i	−0.477940	+	0.827816i
$986$		0			0
$987$	15.0000	−	5.19615i	0.477455	−	0.165395i
$988$		0			0
$989$	−32.0000	+	55.4256i	−1.01754	+	1.76243i
$990$		0			0
$991$	5.00000	+	8.66025i	0.158830	+	0.275102i	0.934447	−	0.356102i	$-0.115894\pi$
$991$	5.00000	+	8.66025i	0.158830	+	0.275102i	−0.775617	+	0.631204i	$0.782561\pi$
$992$		0			0
$993$	39.0000			1.23763
$994$		0			0
$995$	−8.00000			−0.253617
$996$		0			0
$997$	3.00000	+	5.19615i	0.0950110	+	0.164564i	0.909613	−	0.415456i	$-0.136378\pi$
$997$	3.00000	+	5.19615i	0.0950110	+	0.164564i	−0.814602	+	0.580020i	$0.803045\pi$
$998$		0			0
$999$	18.0000	−	31.1769i	0.569495	−	0.986394i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1232.2.q.e.177.1		2
4.3	odd	2		154.2.e.a.23.1	✓	2
7.2	even	3		8624.2.a.b.1.1		1
7.4	even	3	inner	1232.2.q.e.529.1		2
7.5	odd	6		8624.2.a.be.1.1		1
12.11	even	2		1386.2.k.o.793.1		2
28.3	even	6		1078.2.e.f.67.1		2
28.11	odd	6		154.2.e.a.67.1	yes	2
28.19	even	6		1078.2.a.g.1.1		1
28.23	odd	6		1078.2.a.m.1.1		1
28.27	even	2		1078.2.e.f.177.1		2
84.11	even	6		1386.2.k.o.991.1		2
84.23	even	6		9702.2.a.i.1.1		1
84.47	odd	6		9702.2.a.y.1.1		1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
154.2.e.a.23.1	✓	2	4.3	odd	2
154.2.e.a.67.1	yes	2	28.11	odd	6
1078.2.a.g.1.1		1	28.19	even	6
1078.2.a.m.1.1		1	28.23	odd	6
1078.2.e.f.67.1		2	28.3	even	6
1078.2.e.f.177.1		2	28.27	even	2
1232.2.q.e.177.1		2	1.1	even	1	trivial
1232.2.q.e.529.1		2	7.4	even	3	inner
1386.2.k.o.793.1		2	12.11	even	2
1386.2.k.o.991.1		2	84.11	even	6
8624.2.a.b.1.1		1	7.2	even	3
8624.2.a.be.1.1		1	7.5	odd	6
9702.2.a.i.1.1		1	84.23	even	6
9702.2.a.y.1.1		1	84.47	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 1232 = 2^{4} \cdot 7 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1232.q (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(1.50000 + 2.59808i) q^{3} +(-1.00000 + 1.73205i) q^{5} +(2.50000 - 0.866025i) q^{7} +(-3.00000 + 5.19615i) q^{9} +O(q^{10})\)	\(q+(1.50000 + 2.59808i) q^{3} +(-1.00000 + 1.73205i) q^{5} +(2.50000 - 0.866025i) q^{7} +(-3.00000 + 5.19615i) q^{9} +(-0.500000 - 0.866025i) q^{11} -7.00000 q^{13} -6.00000 q^{15} +(-1.00000 - 1.73205i) q^{17} +(6.00000 + 5.19615i) q^{21} +(-4.00000 + 6.92820i) q^{23} +(0.500000 + 0.866025i) q^{25} -9.00000 q^{27} -5.00000 q^{29} +(2.00000 + 3.46410i) q^{31} +(1.50000 - 2.59808i) q^{33} +(-1.00000 + 5.19615i) q^{35} +(-2.00000 + 3.46410i) q^{37} +(-10.5000 - 18.1865i) q^{39} +4.00000 q^{41} +8.00000 q^{43} +(-6.00000 - 10.3923i) q^{45} +(1.00000 - 1.73205i) q^{47} +(5.50000 - 4.33013i) q^{49} +(3.00000 - 5.19615i) q^{51} +(3.00000 + 5.19615i) q^{53} +2.00000 q^{55} +(1.50000 + 2.59808i) q^{59} +(-0.500000 + 0.866025i) q^{61} +(-3.00000 + 15.5885i) q^{63} +(7.00000 - 12.1244i) q^{65} +(4.50000 + 7.79423i) q^{67} -24.0000 q^{69} +2.00000 q^{71} +(-2.00000 - 3.46410i) q^{73} +(-1.50000 + 2.59808i) q^{75} +(-2.00000 - 1.73205i) q^{77} +(4.50000 - 7.79423i) q^{79} +(-4.50000 - 7.79423i) q^{81} -6.00000 q^{83} +4.00000 q^{85} +(-7.50000 - 12.9904i) q^{87} +(-3.00000 + 5.19615i) q^{89} +(-17.5000 + 6.06218i) q^{91} +(-6.00000 + 10.3923i) q^{93} +7.00000 q^{97} +6.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q + 3 q^{3} - 2 q^{5} + 5 q^{7} - 6 q^{9}+O(q^{10}) \) 2 * q + 3 * q^3 - 2 * q^5 + 5 * q^7 - 6 * q^9	\( 2 q + 3 q^{3} - 2 q^{5} + 5 q^{7} - 6 q^{9} - q^{11} - 14 q^{13} - 12 q^{15} - 2 q^{17} + 12 q^{21} - 8 q^{23} + q^{25} - 18 q^{27} - 10 q^{29} + 4 q^{31} + 3 q^{33} - 2 q^{35} - 4 q^{37} - 21 q^{39} + 8 q^{41} + 16 q^{43} - 12 q^{45} + 2 q^{47} + 11 q^{49} + 6 q^{51} + 6 q^{53} + 4 q^{55} + 3 q^{59} - q^{61} - 6 q^{63} + 14 q^{65} + 9 q^{67} - 48 q^{69} + 4 q^{71} - 4 q^{73} - 3 q^{75} - 4 q^{77} + 9 q^{79} - 9 q^{81} - 12 q^{83} + 8 q^{85} - 15 q^{87} - 6 q^{89} - 35 q^{91} - 12 q^{93} + 14 q^{97} + 12 q^{99}+O(q^{100}) \) 2 * q + 3 * q^3 - 2 * q^5 + 5 * q^7 - 6 * q^9 - q^11 - 14 * q^13 - 12 * q^15 - 2 * q^17 + 12 * q^21 - 8 * q^23 + q^25 - 18 * q^27 - 10 * q^29 + 4 * q^31 + 3 * q^33 - 2 * q^35 - 4 * q^37 - 21 * q^39 + 8 * q^41 + 16 * q^43 - 12 * q^45 + 2 * q^47 + 11 * q^49 + 6 * q^51 + 6 * q^53 + 4 * q^55 + 3 * q^59 - q^61 - 6 * q^63 + 14 * q^65 + 9 * q^67 - 48 * q^69 + 4 * q^71 - 4 * q^73 - 3 * q^75 - 4 * q^77 + 9 * q^79 - 9 * q^81 - 12 * q^83 + 8 * q^85 - 15 * q^87 - 6 * q^89 - 35 * q^91 - 12 * q^93 + 14 * q^97 + 12 * q^99

Introduction

L-functions

Modular forms

Varieties

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Representations

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Database

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