LMFDB - Embedded newform 1344.2.bb.d.31.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1344,2,Mod(31,1344)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1344, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 3, 0, 1]))

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

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

chi := DirichletCharacter("1344.31");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1344 = 2^{6} \cdot 3 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1344.bb (of order $6$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$10.7318940317$
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:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			31.1
Root			$-0.866025 + 0.500000i$ of defining polynomial
Character	$\chi$	$=$	1344.31
Dual form			1344.2.bb.d.607.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.866025 - 0.500000i) q^{3} +(1.50000 + 2.59808i) q^{5} +(0.866025 + 2.50000i) q^{7} +(0.500000 + 0.866025i) q^{9} +O(q^{10})$	\(q+(-0.866025 - 0.500000i) q^{3} +(1.50000 + 2.59808i) q^{5} +(0.866025 + 2.50000i) q^{7} +(0.500000 + 0.866025i) q^{9} +(2.59808 - 4.50000i) q^{11} -2.00000 q^{13} -3.00000i q^{15} +(6.92820 - 4.00000i) q^{19} +(0.500000 - 2.59808i) q^{21} +(5.19615 - 3.00000i) q^{23} +(-2.00000 + 3.46410i) q^{25} -1.00000i q^{27} +5.19615i q^{29} +(-4.33013 + 7.50000i) q^{31} +(-4.50000 + 2.59808i) q^{33} +(-5.19615 + 6.00000i) q^{35} +(6.00000 - 3.46410i) q^{37} +(1.73205 + 1.00000i) q^{39} +10.3923i q^{41} -3.46410 q^{43} +(-1.50000 + 2.59808i) q^{45} +(-5.50000 + 4.33013i) q^{49} +(4.50000 + 2.59808i) q^{53} +15.5885 q^{55} -8.00000 q^{57} +(-7.79423 - 4.50000i) q^{59} +(-4.00000 - 6.92820i) q^{61} +(-1.73205 + 2.00000i) q^{63} +(-3.00000 - 5.19615i) q^{65} +(1.73205 - 3.00000i) q^{67} -6.00000 q^{69} +12.0000i q^{71} +(12.0000 + 6.92820i) q^{73} +(3.46410 - 2.00000i) q^{75} +(13.5000 + 2.59808i) q^{77} +(4.33013 - 2.50000i) q^{79} +(-0.500000 + 0.866025i) q^{81} +9.00000i q^{83} +(2.59808 - 4.50000i) q^{87} +(-1.73205 - 5.00000i) q^{91} +(7.50000 - 4.33013i) q^{93} +(20.7846 + 12.0000i) q^{95} +5.19615i q^{97} +5.19615 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 6 q^{5} + 2 q^{9}+O(q^{10}) $ 4 * q + 6 * q^5 + 2 * q^9	$ 4 q + 6 q^{5} + 2 q^{9} - 8 q^{13} + 2 q^{21} - 8 q^{25} - 18 q^{33} + 24 q^{37} - 6 q^{45} - 22 q^{49} + 18 q^{53} - 32 q^{57} - 16 q^{61} - 12 q^{65} - 24 q^{69} + 48 q^{73} + 54 q^{77} - 2 q^{81} + 30 q^{93}+O(q^{100}) $ 4 * q + 6 * q^5 + 2 * q^9 - 8 * q^13 + 2 * q^21 - 8 * q^25 - 18 * q^33 + 24 * q^37 - 6 * q^45 - 22 * q^49 + 18 * q^53 - 32 * q^57 - 16 * q^61 - 12 * q^65 - 24 * q^69 + 48 * q^73 + 54 * q^77 - 2 * q^81 + 30 * q^93

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1344\mathbb{Z}\right)^\times$.

$n$	$127$	$449$	$577$	$1093$
$\chi(n)$	$-1$	$1$	$e\left(\frac{1}{6}\right)$	$-1$

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			0
$2$		0			0
$3$	−0.866025	−	0.500000i	−0.500000	−	0.288675i
$3$	−0.866025	−	0.500000i	−0.500000	−	0.288675i
$4$		0			0
$5$	1.50000	+	2.59808i	0.670820	+	1.16190i	0.977672	+	0.210138i	$0.0673912\pi$
$5$	1.50000	+	2.59808i	0.670820	+	1.16190i	−0.306851	+	0.951757i	$0.599275\pi$
$6$		0			0
$7$	0.866025	+	2.50000i	0.327327	+	0.944911i
$7$	0.866025	+	2.50000i	0.327327	+	0.944911i
$8$		0			0
$9$	0.500000	+	0.866025i	0.166667	+	0.288675i
$10$		0			0
$11$	2.59808	−	4.50000i	0.783349	−	1.35680i	−0.146631	−	0.989191i	$-0.546843\pi$
$11$	2.59808	−	4.50000i	0.783349	−	1.35680i	0.929980	−	0.367610i	$-0.119824\pi$
$12$		0			0
$13$	−2.00000			−0.554700			−0.277350	−	0.960769i	$-0.589456\pi$
$13$	−2.00000			−0.554700			−0.277350	+	0.960769i	$0.589456\pi$
$14$		0			0
$15$		−	3.00000i		−	0.774597i
$16$		0			0
$17$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$17$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$18$		0			0
$19$	6.92820	−	4.00000i	1.58944	−	0.917663i	0.596040	−	0.802955i	$-0.296740\pi$
$19$	6.92820	−	4.00000i	1.58944	−	0.917663i	0.993399	−	0.114708i	$-0.0365932\pi$
$20$		0			0
$21$	0.500000	−	2.59808i	0.109109	−	0.566947i
$22$		0			0
$23$	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
$25$	−2.00000	+	3.46410i	−0.400000	+	0.692820i
$26$		0			0
$27$		−	1.00000i		−	0.192450i
$28$		0			0
$29$			5.19615i			0.964901i	0.875923	+	0.482451i	$0.160253\pi$
$29$			5.19615i			0.964901i	−0.875923	+	0.482451i	$0.839747\pi$
$30$		0			0
$31$	−4.33013	+	7.50000i	−0.777714	+	1.34704i	0.155543	+	0.987829i	$0.450287\pi$
$31$	−4.33013	+	7.50000i	−0.777714	+	1.34704i	−0.933257	+	0.359211i	$0.883046\pi$
$32$		0			0
$33$	−4.50000	+	2.59808i	−0.783349	+	0.452267i
$34$		0			0
$35$	−5.19615	+	6.00000i	−0.878310	+	1.01419i
$36$		0			0
$37$	6.00000	−	3.46410i	0.986394	−	0.569495i	0.0821995	−	0.996616i	$-0.473806\pi$
$37$	6.00000	−	3.46410i	0.986394	−	0.569495i	0.904194	+	0.427121i	$0.140472\pi$
$38$		0			0
$39$	1.73205	+	1.00000i	0.277350	+	0.160128i
$40$		0			0
$41$			10.3923i			1.62301i	0.584349	+	0.811503i	$0.301350\pi$
$41$			10.3923i			1.62301i	−0.584349	+	0.811503i	$0.698650\pi$
$42$		0			0
$43$	−3.46410			−0.528271			−0.264135	−	0.964486i	$-0.585087\pi$
$43$	−3.46410			−0.528271			−0.264135	+	0.964486i	$0.585087\pi$
$44$		0			0
$45$	−1.50000	+	2.59808i	−0.223607	+	0.387298i
$46$		0			0
$47$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$47$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$48$		0			0
$49$	−5.50000	+	4.33013i	−0.785714	+	0.618590i
$50$		0			0
$51$		0			0
$52$		0			0
$53$	4.50000	+	2.59808i	0.618123	+	0.356873i	0.776138	−	0.630563i	$-0.217176\pi$
$53$	4.50000	+	2.59808i	0.618123	+	0.356873i	−0.158015	+	0.987437i	$0.550509\pi$
$54$		0			0
$55$	15.5885			2.10195
$56$		0			0
$57$	−8.00000			−1.05963
$58$		0			0
$59$	−7.79423	−	4.50000i	−1.01472	−	0.585850i	−0.102151	−	0.994769i	$-0.532573\pi$
$59$	−7.79423	−	4.50000i	−1.01472	−	0.585850i	−0.912571	+	0.408919i	$0.865906\pi$
$60$		0			0
$61$	−4.00000	−	6.92820i	−0.512148	−	0.887066i	−0.999901	−	0.0140840i	$-0.995517\pi$
$61$	−4.00000	−	6.92820i	−0.512148	−	0.887066i	0.487753	−	0.872982i	$-0.337817\pi$
$62$		0			0
$63$	−1.73205	+	2.00000i	−0.218218	+	0.251976i
$64$		0			0
$65$	−3.00000	−	5.19615i	−0.372104	−	0.644503i
$66$		0			0
$67$	1.73205	−	3.00000i	0.211604	−	0.366508i	−0.740613	−	0.671932i	$-0.765465\pi$
$67$	1.73205	−	3.00000i	0.211604	−	0.366508i	0.952217	+	0.305424i	$0.0987981\pi$
$68$		0			0
$69$	−6.00000			−0.722315
$70$		0			0
$71$			12.0000i			1.42414i	0.702109	+	0.712069i	$0.252242\pi$
$71$			12.0000i			1.42414i	−0.702109	+	0.712069i	$0.747758\pi$
$72$		0			0
$73$	12.0000	+	6.92820i	1.40449	+	0.810885i	0.994850	−	0.101361i	$-0.0323196\pi$
$73$	12.0000	+	6.92820i	1.40449	+	0.810885i	0.409644	+	0.912245i	$0.365653\pi$
$74$		0			0
$75$	3.46410	−	2.00000i	0.400000	−	0.230940i
$76$		0			0
$77$	13.5000	+	2.59808i	1.53847	+	0.296078i
$78$		0			0
$79$	4.33013	−	2.50000i	0.487177	−	0.281272i	−0.236225	−	0.971698i	$-0.575910\pi$
$79$	4.33013	−	2.50000i	0.487177	−	0.281272i	0.723403	+	0.690426i	$0.242577\pi$
$80$		0			0
$81$	−0.500000	+	0.866025i	−0.0555556	+	0.0962250i
$82$		0			0
$83$			9.00000i			0.987878i	0.869496	+	0.493939i	$0.164443\pi$
$83$			9.00000i			0.987878i	−0.869496	+	0.493939i	$0.835557\pi$
$84$		0			0
$85$		0			0
$86$		0			0
$87$	2.59808	−	4.50000i	0.278543	−	0.482451i
$88$		0			0
$89$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$89$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$90$		0			0
$91$	−1.73205	−	5.00000i	−0.181568	−	0.524142i
$92$		0			0
$93$	7.50000	−	4.33013i	0.777714	−	0.449013i
$94$		0			0
$95$	20.7846	+	12.0000i	2.13246	+	1.23117i
$96$		0			0
$97$			5.19615i			0.527589i	0.964579	+	0.263795i	$0.0849741\pi$
$97$			5.19615i			0.527589i	−0.964579	+	0.263795i	$0.915026\pi$
$98$		0			0
$99$	5.19615			0.522233
$100$		0			0
$101$	−3.00000	+	5.19615i	−0.298511	+	0.517036i	−0.975796	−	0.218685i	$-0.929823\pi$
$101$	−3.00000	+	5.19615i	−0.298511	+	0.517036i	0.677284	+	0.735721i	$0.263157\pi$
$102$		0			0
$103$	−1.73205	−	3.00000i	−0.170664	−	0.295599i	0.767988	−	0.640464i	$-0.221258\pi$
$103$	−1.73205	−	3.00000i	−0.170664	−	0.295599i	−0.938652	+	0.344865i	$0.887925\pi$
$104$		0			0
$105$	7.50000	−	2.59808i	0.731925	−	0.253546i
$106$		0			0
$107$	2.59808	+	4.50000i	0.251166	+	0.435031i	0.963847	−	0.266456i	$-0.0858528\pi$
$107$	2.59808	+	4.50000i	0.251166	+	0.435031i	−0.712681	+	0.701488i	$0.752519\pi$
$108$		0			0
$109$	−3.00000	−	1.73205i	−0.287348	−	0.165900i	0.349397	−	0.936975i	$-0.386386\pi$
$109$	−3.00000	−	1.73205i	−0.287348	−	0.165900i	−0.636745	+	0.771074i	$0.719720\pi$
$110$		0			0
$111$	−6.92820			−0.657596
$112$		0			0
$113$	−6.00000			−0.564433			−0.282216	−	0.959351i	$-0.591070\pi$
$113$	−6.00000			−0.564433			−0.282216	+	0.959351i	$0.591070\pi$
$114$		0			0
$115$	15.5885	+	9.00000i	1.45363	+	0.839254i
$116$		0			0
$117$	−1.00000	−	1.73205i	−0.0924500	−	0.160128i
$118$		0			0
$119$		0			0
$120$		0			0
$121$	−8.00000	−	13.8564i	−0.727273	−	1.25967i
$122$		0			0
$123$	5.19615	−	9.00000i	0.468521	−	0.811503i
$124$		0			0
$125$	3.00000			0.268328
$126$		0			0
$127$		−	17.0000i		−	1.50851i	−0.656584	−	0.754253i	$-0.727999\pi$
$127$		−	17.0000i		−	1.50851i	0.656584	−	0.754253i	$-0.272001\pi$
$128$		0			0
$129$	3.00000	+	1.73205i	0.264135	+	0.152499i
$130$		0			0
$131$	2.59808	−	1.50000i	0.226995	−	0.131056i	−0.382190	−	0.924084i	$-0.624830\pi$
$131$	2.59808	−	1.50000i	0.226995	−	0.131056i	0.609185	+	0.793028i	$0.291497\pi$
$132$		0			0
$133$	16.0000	+	13.8564i	1.38738	+	1.20150i
$134$		0			0
$135$	2.59808	−	1.50000i	0.223607	−	0.129099i
$136$		0			0
$137$	9.00000	−	15.5885i	0.768922	−	1.33181i	−0.169226	−	0.985577i	$-0.554127\pi$
$137$	9.00000	−	15.5885i	0.768922	−	1.33181i	0.938148	−	0.346235i	$-0.112540\pi$
$138$		0			0
$139$		−	20.0000i		−	1.69638i	−0.529694	−	0.848189i	$-0.677693\pi$
$139$		−	20.0000i		−	1.69638i	0.529694	−	0.848189i	$-0.322307\pi$
$140$		0			0
$141$		0			0
$142$		0			0
$143$	−5.19615	+	9.00000i	−0.434524	+	0.752618i
$144$		0			0
$145$	−13.5000	+	7.79423i	−1.12111	+	0.647275i
$146$		0			0
$147$	6.92820	−	1.00000i	0.571429	−	0.0824786i
$148$		0			0
$149$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$149$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$150$		0			0
$151$	−14.7224	−	8.50000i	−1.19809	−	0.691720i	−0.237964	−	0.971274i	$-0.576480\pi$
$151$	−14.7224	−	8.50000i	−1.19809	−	0.691720i	−0.960130	+	0.279554i	$0.909814\pi$
$152$		0			0
$153$		0			0
$154$		0			0
$155$	−25.9808			−2.08683
$156$		0			0
$157$	2.00000	−	3.46410i	0.159617	−	0.276465i	−0.775113	−	0.631822i	$-0.782307\pi$
$157$	2.00000	−	3.46410i	0.159617	−	0.276465i	0.934731	+	0.355357i	$0.115641\pi$
$158$		0			0
$159$	−2.59808	−	4.50000i	−0.206041	−	0.356873i
$160$		0			0
$161$	12.0000	+	10.3923i	0.945732	+	0.819028i
$162$		0			0
$163$	5.19615	+	9.00000i	0.406994	+	0.704934i	0.994551	−	0.104248i	$-0.0332436\pi$
$163$	5.19615	+	9.00000i	0.406994	+	0.704934i	−0.587557	+	0.809183i	$0.699910\pi$
$164$		0			0
$165$	−13.5000	−	7.79423i	−1.05097	−	0.606780i
$166$		0			0
$167$	−10.3923			−0.804181			−0.402090	−	0.915600i	$-0.631716\pi$
$167$	−10.3923			−0.804181			−0.402090	+	0.915600i	$0.631716\pi$
$168$		0			0
$169$	−9.00000			−0.692308
$170$		0			0
$171$	6.92820	+	4.00000i	0.529813	+	0.305888i
$172$		0			0
$173$	9.00000	+	15.5885i	0.684257	+	1.18517i	0.973670	+	0.227964i	$0.0732068\pi$
$173$	9.00000	+	15.5885i	0.684257	+	1.18517i	−0.289412	+	0.957205i	$0.593460\pi$
$174$		0			0
$175$	−10.3923	−	2.00000i	−0.785584	−	0.151186i
$176$		0			0
$177$	4.50000	+	7.79423i	0.338241	+	0.585850i
$178$		0			0
$179$	−5.19615	+	9.00000i	−0.388379	+	0.672692i	−0.992232	−	0.124404i	$-0.960298\pi$
$179$	−5.19615	+	9.00000i	−0.388379	+	0.672692i	0.603853	+	0.797096i	$0.293631\pi$
$180$		0			0
$181$	−10.0000			−0.743294			−0.371647	−	0.928374i	$-0.621207\pi$
$181$	−10.0000			−0.743294			−0.371647	+	0.928374i	$0.621207\pi$
$182$		0			0
$183$			8.00000i			0.591377i
$184$		0			0
$185$	18.0000	+	10.3923i	1.32339	+	0.764057i
$186$		0			0
$187$		0			0
$188$		0			0
$189$	2.50000	−	0.866025i	0.181848	−	0.0629941i
$190$		0			0
$191$	10.3923	−	6.00000i	0.751961	−	0.434145i	−0.0744412	−	0.997225i	$-0.523717\pi$
$191$	10.3923	−	6.00000i	0.751961	−	0.434145i	0.826402	+	0.563081i	$0.190384\pi$
$192$		0			0
$193$	5.50000	−	9.52628i	0.395899	−	0.685717i	−0.597317	−	0.802005i	$-0.703766\pi$
$193$	5.50000	−	9.52628i	0.395899	−	0.685717i	0.993215	+	0.116289i	$0.0370998\pi$
$194$		0			0
$195$			6.00000i			0.429669i
$196$		0			0
$197$		0			0		1.00000			$0$
$197$		0			0		−1.00000			$\pi$
$198$		0			0
$199$	−5.19615	+	9.00000i	−0.368345	+	0.637993i	−0.989307	−	0.145848i	$-0.953409\pi$
$199$	−5.19615	+	9.00000i	−0.368345	+	0.637993i	0.620962	+	0.783841i	$0.286742\pi$
$200$		0			0
$201$	−3.00000	+	1.73205i	−0.211604	+	0.122169i
$202$		0			0
$203$	−12.9904	+	4.50000i	−0.911746	+	0.315838i
$204$		0			0
$205$	−27.0000	+	15.5885i	−1.88576	+	1.08875i
$206$		0			0
$207$	5.19615	+	3.00000i	0.361158	+	0.208514i
$208$		0			0
$209$		−	41.5692i		−	2.87540i
$210$		0			0
$211$	−20.7846			−1.43087			−0.715436	−	0.698679i	$-0.753772\pi$
$211$	−20.7846			−1.43087			−0.715436	+	0.698679i	$0.753772\pi$
$212$		0			0
$213$	6.00000	−	10.3923i	0.411113	−	0.712069i
$214$		0			0
$215$	−5.19615	−	9.00000i	−0.354375	−	0.613795i
$216$		0			0
$217$	−22.5000	−	4.33013i	−1.52740	−	0.293948i
$218$		0			0
$219$	−6.92820	−	12.0000i	−0.468165	−	0.810885i
$220$		0			0
$221$		0			0
$222$		0			0
$223$	5.19615			0.347960			0.173980	−	0.984749i	$-0.444337\pi$
$223$	5.19615			0.347960			0.173980	+	0.984749i	$0.444337\pi$
$224$		0			0
$225$	−4.00000			−0.266667
$226$		0			0
$227$	2.59808	+	1.50000i	0.172440	+	0.0995585i	0.583736	−	0.811943i	$-0.301590\pi$
$227$	2.59808	+	1.50000i	0.172440	+	0.0995585i	−0.411296	+	0.911502i	$0.634924\pi$
$228$		0			0
$229$	−1.00000	−	1.73205i	−0.0660819	−	0.114457i	0.831092	−	0.556136i	$-0.187717\pi$
$229$	−1.00000	−	1.73205i	−0.0660819	−	0.114457i	−0.897173	+	0.441679i	$0.854383\pi$
$230$		0			0
$231$	−10.3923	−	9.00000i	−0.683763	−	0.592157i
$232$		0			0
$233$	12.0000	+	20.7846i	0.786146	+	1.36165i	0.928312	+	0.371802i	$0.121260\pi$
$233$	12.0000	+	20.7846i	0.786146	+	1.36165i	−0.142166	+	0.989843i	$0.545407\pi$
$234$		0			0
$235$		0			0
$236$		0			0
$237$	−5.00000			−0.324785
$238$		0			0
$239$		−	6.00000i		−	0.388108i	−0.980991	−	0.194054i	$-0.937836\pi$
$239$		−	6.00000i		−	0.388108i	0.980991	−	0.194054i	$-0.0621637\pi$
$240$		0			0
$241$	4.50000	+	2.59808i	0.289870	+	0.167357i	0.637883	−	0.770133i	$-0.279810\pi$
$241$	4.50000	+	2.59808i	0.289870	+	0.167357i	−0.348013	+	0.937490i	$0.613143\pi$
$242$		0			0
$243$	0.866025	−	0.500000i	0.0555556	−	0.0320750i
$244$		0			0
$245$	−19.5000	−	7.79423i	−1.24581	−	0.497955i
$246$		0			0
$247$	−13.8564	+	8.00000i	−0.881662	+	0.509028i
$248$		0			0
$249$	4.50000	−	7.79423i	0.285176	−	0.493939i
$250$		0			0
$251$		−	3.00000i		−	0.189358i	−0.995508	−	0.0946792i	$-0.969817\pi$
$251$		−	3.00000i		−	0.189358i	0.995508	−	0.0946792i	$-0.0301825\pi$
$252$		0			0
$253$		−	31.1769i		−	1.96008i
$254$		0			0
$255$		0			0
$256$		0			0
$257$	18.0000	−	10.3923i	1.12281	−	0.648254i	0.180693	−	0.983540i	$-0.442166\pi$
$257$	18.0000	−	10.3923i	1.12281	−	0.648254i	0.942117	+	0.335285i	$0.108833\pi$
$258$		0			0
$259$	13.8564	+	12.0000i	0.860995	+	0.745644i
$260$		0			0
$261$	−4.50000	+	2.59808i	−0.278543	+	0.160817i
$262$		0			0
$263$	5.19615	+	3.00000i	0.320408	+	0.184988i	0.651575	−	0.758585i	$-0.274109\pi$
$263$	5.19615	+	3.00000i	0.320408	+	0.184988i	−0.331166	+	0.943572i	$0.607442\pi$
$264$		0			0
$265$			15.5885i			0.957591i
$266$		0			0
$267$		0			0
$268$		0			0
$269$	7.50000	−	12.9904i	0.457283	−	0.792038i	−0.541533	−	0.840679i	$-0.682156\pi$
$269$	7.50000	−	12.9904i	0.457283	−	0.792038i	0.998816	+	0.0486418i	$0.0154893\pi$
$270$		0			0
$271$	−7.79423	−	13.5000i	−0.473466	−	0.820067i	0.526073	−	0.850439i	$-0.323664\pi$
$271$	−7.79423	−	13.5000i	−0.473466	−	0.820067i	−0.999539	+	0.0303728i	$0.990331\pi$
$272$		0			0
$273$	−1.00000	+	5.19615i	−0.0605228	+	0.314485i
$274$		0			0
$275$	10.3923	+	18.0000i	0.626680	+	1.08544i
$276$		0			0
$277$	−24.0000	−	13.8564i	−1.44202	−	0.832551i	−0.444036	−	0.896009i	$-0.646454\pi$
$277$	−24.0000	−	13.8564i	−1.44202	−	0.832551i	−0.997984	+	0.0634583i	$0.979787\pi$
$278$		0			0
$279$	−8.66025			−0.518476
$280$		0			0
$281$	−30.0000			−1.78965			−0.894825	−	0.446417i	$-0.852700\pi$
$281$	−30.0000			−1.78965			−0.894825	+	0.446417i	$0.852700\pi$
$282$		0			0
$283$	−1.73205	−	1.00000i	−0.102960	−	0.0594438i	0.447636	−	0.894216i	$-0.352266\pi$
$283$	−1.73205	−	1.00000i	−0.102960	−	0.0594438i	−0.550596	+	0.834772i	$0.685599\pi$
$284$		0			0
$285$	−12.0000	−	20.7846i	−0.710819	−	1.23117i
$286$		0			0
$287$	−25.9808	+	9.00000i	−1.53360	+	0.531253i
$288$		0			0
$289$	−8.50000	−	14.7224i	−0.500000	−	0.866025i
$290$		0			0
$291$	2.59808	−	4.50000i	0.152302	−	0.263795i
$292$		0			0
$293$	3.00000			0.175262			0.0876309	−	0.996153i	$-0.472070\pi$
$293$	3.00000			0.175262			0.0876309	+	0.996153i	$0.472070\pi$
$294$		0			0
$295$		−	27.0000i		−	1.57200i
$296$		0			0
$297$	−4.50000	−	2.59808i	−0.261116	−	0.150756i
$298$		0			0
$299$	−10.3923	+	6.00000i	−0.601003	+	0.346989i
$300$		0			0
$301$	−3.00000	−	8.66025i	−0.172917	−	0.499169i
$302$		0			0
$303$	5.19615	−	3.00000i	0.298511	−	0.172345i
$304$		0			0
$305$	12.0000	−	20.7846i	0.687118	−	1.19012i
$306$		0			0
$307$			10.0000i			0.570730i	0.958419	+	0.285365i	$0.0921148\pi$
$307$			10.0000i			0.570730i	−0.958419	+	0.285365i	$0.907885\pi$
$308$		0			0
$309$			3.46410i			0.197066i
$310$		0			0
$311$	−15.5885	+	27.0000i	−0.883940	+	1.53103i	−0.0370169	+	0.999315i	$0.511786\pi$
$311$	−15.5885	+	27.0000i	−0.883940	+	1.53103i	−0.846923	+	0.531715i	$0.821548\pi$
$312$		0			0
$313$	25.5000	−	14.7224i	1.44135	−	0.832161i	0.443406	−	0.896321i	$-0.353770\pi$
$313$	25.5000	−	14.7224i	1.44135	−	0.832161i	0.997940	+	0.0641600i	$0.0204368\pi$
$314$		0			0
$315$	−7.79423	−	1.50000i	−0.439155	−	0.0845154i
$316$		0			0
$317$	−22.5000	+	12.9904i	−1.26373	+	0.729612i	−0.973793	−	0.227435i	$-0.926966\pi$
$317$	−22.5000	+	12.9904i	−1.26373	+	0.729612i	−0.289933	+	0.957047i	$0.593633\pi$
$318$		0			0
$319$	23.3827	+	13.5000i	1.30918	+	0.755855i
$320$		0			0
$321$		−	5.19615i		−	0.290021i
$322$		0			0
$323$		0			0
$324$		0			0
$325$	4.00000	−	6.92820i	0.221880	−	0.384308i
$326$		0			0
$327$	1.73205	+	3.00000i	0.0957826	+	0.165900i
$328$		0			0
$329$		0			0
$330$		0			0
$331$	−13.8564	−	24.0000i	−0.761617	−	1.31916i	−0.942017	−	0.335566i	$-0.891072\pi$
$331$	−13.8564	−	24.0000i	−0.761617	−	1.31916i	0.180400	−	0.983593i	$-0.442261\pi$
$332$		0			0
$333$	6.00000	+	3.46410i	0.328798	+	0.189832i
$334$		0			0
$335$	10.3923			0.567792
$336$		0			0
$337$	25.0000			1.36184			0.680918	−	0.732359i	$-0.261581\pi$
$337$	25.0000			1.36184			0.680918	+	0.732359i	$0.261581\pi$
$338$		0			0
$339$	5.19615	+	3.00000i	0.282216	+	0.162938i
$340$		0			0
$341$	22.5000	+	38.9711i	1.21844	+	2.11041i
$342$		0			0
$343$	−15.5885	−	10.0000i	−0.841698	−	0.539949i
$344$		0			0
$345$	−9.00000	−	15.5885i	−0.484544	−	0.839254i
$346$		0			0
$347$	5.19615	−	9.00000i	0.278944	−	0.483145i	−0.692179	−	0.721726i	$-0.743349\pi$
$347$	5.19615	−	9.00000i	0.278944	−	0.483145i	0.971123	+	0.238581i	$0.0766823\pi$
$348$		0			0
$349$	10.0000			0.535288			0.267644	−	0.963518i	$-0.413755\pi$
$349$	10.0000			0.535288			0.267644	+	0.963518i	$0.413755\pi$
$350$		0			0
$351$			2.00000i			0.106752i
$352$		0			0
$353$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$353$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$354$		0			0
$355$	−31.1769	+	18.0000i	−1.65470	+	0.955341i
$356$		0			0
$357$		0			0
$358$		0			0
$359$	5.19615	−	3.00000i	0.274242	−	0.158334i	−0.356572	−	0.934268i	$-0.616054\pi$
$359$	5.19615	−	3.00000i	0.274242	−	0.158334i	0.630814	+	0.775934i	$0.282721\pi$
$360$		0			0
$361$	22.5000	−	38.9711i	1.18421	−	2.05111i
$362$		0			0
$363$			16.0000i			0.839782i
$364$		0			0
$365$			41.5692i			2.17583i
$366$		0			0
$367$	−4.33013	+	7.50000i	−0.226031	+	0.391497i	−0.956628	−	0.291312i	$-0.905908\pi$
$367$	−4.33013	+	7.50000i	−0.226031	+	0.391497i	0.730597	+	0.682808i	$0.239242\pi$
$368$		0			0
$369$	−9.00000	+	5.19615i	−0.468521	+	0.270501i
$370$		0			0
$371$	−2.59808	+	13.5000i	−0.134885	+	0.700885i
$372$		0			0
$373$	15.0000	−	8.66025i	0.776671	−	0.448411i	−0.0585785	−	0.998283i	$-0.518657\pi$
$373$	15.0000	−	8.66025i	0.776671	−	0.448411i	0.835249	+	0.549872i	$0.185323\pi$
$374$		0			0
$375$	−2.59808	−	1.50000i	−0.134164	−	0.0774597i
$376$		0			0
$377$		−	10.3923i		−	0.535231i
$378$		0			0
$379$	24.2487			1.24557			0.622786	−	0.782392i	$-0.286001\pi$
$379$	24.2487			1.24557			0.622786	+	0.782392i	$0.286001\pi$
$380$		0			0
$381$	−8.50000	+	14.7224i	−0.435468	+	0.754253i
$382$		0			0
$383$	−10.3923	−	18.0000i	−0.531022	−	0.919757i	−0.999345	−	0.0361995i	$-0.988475\pi$
$383$	−10.3923	−	18.0000i	−0.531022	−	0.919757i	0.468323	−	0.883558i	$-0.344859\pi$
$384$		0			0
$385$	13.5000	+	38.9711i	0.688024	+	1.98615i
$386$		0			0
$387$	−1.73205	−	3.00000i	−0.0880451	−	0.152499i
$388$		0			0
$389$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$389$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$390$		0			0
$391$		0			0
$392$		0			0
$393$	−3.00000			−0.151330
$394$		0			0
$395$	12.9904	+	7.50000i	0.653617	+	0.377366i
$396$		0			0
$397$	4.00000	+	6.92820i	0.200754	+	0.347717i	0.948772	−	0.315963i	$-0.102327\pi$
$397$	4.00000	+	6.92820i	0.200754	+	0.347717i	−0.748017	+	0.663679i	$0.768994\pi$
$398$		0			0
$399$	−6.92820	−	20.0000i	−0.346844	−	1.00125i
$400$		0			0
$401$	−6.00000	−	10.3923i	−0.299626	−	0.518967i	0.676425	−	0.736512i	$-0.263528\pi$
$401$	−6.00000	−	10.3923i	−0.299626	−	0.518967i	−0.976050	+	0.217545i	$0.930195\pi$
$402$		0			0
$403$	8.66025	−	15.0000i	0.431398	−	0.747203i
$404$		0			0
$405$	−3.00000			−0.149071
$406$		0			0
$407$		−	36.0000i		−	1.78445i
$408$		0			0
$409$	1.50000	+	0.866025i	0.0741702	+	0.0428222i	0.536626	−	0.843820i	$-0.319698\pi$
$409$	1.50000	+	0.866025i	0.0741702	+	0.0428222i	−0.462456	+	0.886642i	$0.653032\pi$
$410$		0			0
$411$	−15.5885	+	9.00000i	−0.768922	+	0.443937i
$412$		0			0
$413$	4.50000	−	23.3827i	0.221431	−	1.15059i
$414$		0			0
$415$	−23.3827	+	13.5000i	−1.14781	+	0.662689i
$416$		0			0
$417$	−10.0000	+	17.3205i	−0.489702	+	0.848189i
$418$		0			0
$419$			12.0000i			0.586238i	0.956076	+	0.293119i	$0.0946933\pi$
$419$			12.0000i			0.586238i	−0.956076	+	0.293119i	$0.905307\pi$
$420$		0			0
$421$			13.8564i			0.675320i	0.941268	+	0.337660i	$0.109635\pi$
$421$			13.8564i			0.675320i	−0.941268	+	0.337660i	$0.890365\pi$
$422$		0			0
$423$		0			0
$424$		0			0
$425$		0			0
$426$		0			0
$427$	13.8564	−	16.0000i	0.670559	−	0.774294i
$428$		0			0
$429$	9.00000	−	5.19615i	0.434524	−	0.250873i
$430$		0			0
$431$	−15.5885	−	9.00000i	−0.750870	−	0.433515i	0.0751385	−	0.997173i	$-0.476060\pi$
$431$	−15.5885	−	9.00000i	−0.750870	−	0.433515i	−0.826008	+	0.563658i	$0.809393\pi$
$432$		0			0
$433$			6.92820i			0.332948i	0.986046	+	0.166474i	$0.0532382\pi$
$433$			6.92820i			0.332948i	−0.986046	+	0.166474i	$0.946762\pi$
$434$		0			0
$435$	15.5885			0.747409
$436$		0			0
$437$	24.0000	−	41.5692i	1.14808	−	1.98853i
$438$		0			0
$439$	7.79423	+	13.5000i	0.371998	+	0.644320i	0.989873	−	0.141957i	$-0.0453394\pi$
$439$	7.79423	+	13.5000i	0.371998	+	0.644320i	−0.617875	+	0.786277i	$0.712006\pi$
$440$		0			0
$441$	−6.50000	−	2.59808i	−0.309524	−	0.123718i
$442$		0			0
$443$	−18.1865	−	31.5000i	−0.864068	−	1.49661i	−0.867969	−	0.496618i	$-0.834575\pi$
$443$	−18.1865	−	31.5000i	−0.864068	−	1.49661i	0.00390106	−	0.999992i	$-0.498758\pi$
$444$		0			0
$445$		0			0
$446$		0			0
$447$		0			0
$448$		0			0
$449$	6.00000			0.283158			0.141579	−	0.989927i	$-0.454782\pi$
$449$	6.00000			0.283158			0.141579	+	0.989927i	$0.454782\pi$
$450$		0			0
$451$	46.7654	+	27.0000i	2.20210	+	1.27138i
$452$		0			0
$453$	8.50000	+	14.7224i	0.399365	+	0.691720i
$454$		0			0
$455$	10.3923	−	12.0000i	0.487199	−	0.562569i
$456$		0			0
$457$	−11.5000	−	19.9186i	−0.537947	−	0.931752i	−0.999014	−	0.0443868i	$-0.985867\pi$
$457$	−11.5000	−	19.9186i	−0.537947	−	0.931752i	0.461067	−	0.887365i	$-0.347467\pi$
$458$		0			0
$459$		0			0
$460$		0			0
$461$	−6.00000			−0.279448			−0.139724	−	0.990190i	$-0.544622\pi$
$461$	−6.00000			−0.279448			−0.139724	+	0.990190i	$0.544622\pi$
$462$		0			0
$463$		−	20.0000i		−	0.929479i	−0.885448	−	0.464739i	$-0.846148\pi$
$463$		−	20.0000i		−	0.929479i	0.885448	−	0.464739i	$-0.153852\pi$
$464$		0			0
$465$	22.5000	+	12.9904i	1.04341	+	0.602414i
$466$		0			0
$467$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$467$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$468$		0			0
$469$	9.00000	+	1.73205i	0.415581	+	0.0799787i
$470$		0			0
$471$	−3.46410	+	2.00000i	−0.159617	+	0.0921551i
$472$		0			0
$473$	−9.00000	+	15.5885i	−0.413820	+	0.716758i
$474$		0			0
$475$			32.0000i			1.46826i
$476$		0			0
$477$			5.19615i			0.237915i
$478$		0			0
$479$	5.19615	−	9.00000i	0.237418	−	0.411220i	−0.722554	−	0.691314i	$-0.757032\pi$
$479$	5.19615	−	9.00000i	0.237418	−	0.411220i	0.959973	+	0.280094i	$0.0903655\pi$
$480$		0			0
$481$	−12.0000	+	6.92820i	−0.547153	+	0.315899i
$482$		0			0
$483$	−5.19615	−	15.0000i	−0.236433	−	0.682524i
$484$		0			0
$485$	−13.5000	+	7.79423i	−0.613003	+	0.353918i
$486$		0			0
$487$	32.0429	+	18.5000i	1.45200	+	0.838315i	0.998595	−	0.0529875i	$-0.0168744\pi$
$487$	32.0429	+	18.5000i	1.45200	+	0.838315i	0.453409	+	0.891303i	$0.350208\pi$
$488$		0			0
$489$		−	10.3923i		−	0.469956i
$490$		0			0
$491$	−15.5885			−0.703497			−0.351749	−	0.936094i	$-0.614413\pi$
$491$	−15.5885			−0.703497			−0.351749	+	0.936094i	$0.614413\pi$
$492$		0			0
$493$		0			0
$494$		0			0
$495$	7.79423	+	13.5000i	0.350325	+	0.606780i
$496$		0			0
$497$	−30.0000	+	10.3923i	−1.34568	+	0.466159i
$498$		0			0
$499$	−13.8564	−	24.0000i	−0.620298	−	1.07439i	−0.989430	−	0.145011i	$-0.953678\pi$
$499$	−13.8564	−	24.0000i	−0.620298	−	1.07439i	0.369132	−	0.929377i	$-0.379655\pi$
$500$		0			0
$501$	9.00000	+	5.19615i	0.402090	+	0.232147i
$502$		0			0
$503$	20.7846			0.926740			0.463370	−	0.886165i	$-0.346640\pi$
$503$	20.7846			0.926740			0.463370	+	0.886165i	$0.346640\pi$
$504$		0			0
$505$	−18.0000			−0.800989
$506$		0			0
$507$	7.79423	+	4.50000i	0.346154	+	0.199852i
$508$		0			0
$509$	−13.5000	−	23.3827i	−0.598377	−	1.03642i	−0.993061	−	0.117602i	$-0.962479\pi$
$509$	−13.5000	−	23.3827i	−0.598377	−	1.03642i	0.394684	−	0.918817i	$-0.370854\pi$
$510$		0			0
$511$	−6.92820	+	36.0000i	−0.306486	+	1.59255i
$512$		0			0
$513$	−4.00000	−	6.92820i	−0.176604	−	0.305888i
$514$		0			0
$515$	5.19615	−	9.00000i	0.228970	−	0.396587i
$516$		0			0
$517$		0			0
$518$		0			0
$519$		−	18.0000i		−	0.790112i
$520$		0			0
$521$	9.00000	+	5.19615i	0.394297	+	0.227648i	0.684020	−	0.729463i	$-0.260230\pi$
$521$	9.00000	+	5.19615i	0.394297	+	0.227648i	−0.289723	+	0.957110i	$0.593563\pi$
$522$		0			0
$523$	−8.66025	+	5.00000i	−0.378686	+	0.218635i	−0.677247	−	0.735756i	$-0.736827\pi$
$523$	−8.66025	+	5.00000i	−0.378686	+	0.218635i	0.298560	+	0.954391i	$0.403494\pi$
$524$		0			0
$525$	8.00000	+	6.92820i	0.349149	+	0.302372i
$526$		0			0
$527$		0			0
$528$		0			0
$529$	6.50000	−	11.2583i	0.282609	−	0.489493i
$530$		0			0
$531$		−	9.00000i		−	0.390567i
$532$		0			0
$533$		−	20.7846i		−	0.900281i
$534$		0			0
$535$	−7.79423	+	13.5000i	−0.336974	+	0.583656i
$536$		0			0
$537$	9.00000	−	5.19615i	0.388379	−	0.224231i
$538$		0			0
$539$	5.19615	+	36.0000i	0.223814	+	1.55063i
$540$		0			0
$541$	3.00000	−	1.73205i	0.128980	−	0.0744667i	−0.434122	−	0.900854i	$-0.642941\pi$
$541$	3.00000	−	1.73205i	0.128980	−	0.0744667i	0.563102	+	0.826388i	$0.309608\pi$
$542$		0			0
$543$	8.66025	+	5.00000i	0.371647	+	0.214571i
$544$		0			0
$545$		−	10.3923i		−	0.445157i
$546$		0			0
$547$		0			0			−	1.00000i	$-0.5\pi$
$547$		0			0				1.00000i	$0.5\pi$
$548$		0			0
$549$	4.00000	−	6.92820i	0.170716	−	0.295689i
$550$		0			0
$551$	20.7846	+	36.0000i	0.885454	+	1.53365i
$552$		0			0
$553$	10.0000	+	8.66025i	0.425243	+	0.368271i
$554$		0			0
$555$	−10.3923	−	18.0000i	−0.441129	−	0.764057i
$556$		0			0
$557$	−4.50000	−	2.59808i	−0.190671	−	0.110084i	0.401626	−	0.915804i	$-0.368445\pi$
$557$	−4.50000	−	2.59808i	−0.190671	−	0.110084i	−0.592297	+	0.805720i	$0.701779\pi$
$558$		0			0
$559$	6.92820			0.293032
$560$		0			0
$561$		0			0
$562$		0			0
$563$	−18.1865	−	10.5000i	−0.766471	−	0.442522i	0.0651433	−	0.997876i	$-0.479250\pi$
$563$	−18.1865	−	10.5000i	−0.766471	−	0.442522i	−0.831614	+	0.555354i	$0.812583\pi$
$564$		0			0
$565$	−9.00000	−	15.5885i	−0.378633	−	0.655811i
$566$		0			0
$567$	−2.59808	−	0.500000i	−0.109109	−	0.0209980i
$568$		0			0
$569$	18.0000	+	31.1769i	0.754599	+	1.30700i	0.945573	+	0.325409i	$0.105502\pi$
$569$	18.0000	+	31.1769i	0.754599	+	1.30700i	−0.190974	+	0.981595i	$0.561165\pi$
$570$		0			0
$571$	−3.46410	+	6.00000i	−0.144968	+	0.251092i	−0.929361	−	0.369172i	$-0.879641\pi$
$571$	−3.46410	+	6.00000i	−0.144968	+	0.251092i	0.784393	+	0.620264i	$0.212975\pi$
$572$		0			0
$573$	−12.0000			−0.501307
$574$		0			0
$575$			24.0000i			1.00087i
$576$		0			0
$577$	1.50000	+	0.866025i	0.0624458	+	0.0360531i	0.530898	−	0.847436i	$-0.321855\pi$
$577$	1.50000	+	0.866025i	0.0624458	+	0.0360531i	−0.468452	+	0.883489i	$0.655188\pi$
$578$		0			0
$579$	−9.52628	+	5.50000i	−0.395899	+	0.228572i
$580$		0			0
$581$	−22.5000	+	7.79423i	−0.933457	+	0.323359i
$582$		0			0
$583$	23.3827	−	13.5000i	0.968412	−	0.559113i
$584$		0			0
$585$	3.00000	−	5.19615i	0.124035	−	0.214834i
$586$		0			0
$587$		−	39.0000i		−	1.60970i	−0.593477	−	0.804851i	$-0.702245\pi$
$587$		−	39.0000i		−	1.60970i	0.593477	−	0.804851i	$-0.297755\pi$
$588$		0			0
$589$			69.2820i			2.85472i
$590$		0			0
$591$		0			0
$592$		0			0
$593$	−27.0000	+	15.5885i	−1.10876	+	0.640141i	−0.938507	−	0.345260i	$-0.887791\pi$
$593$	−27.0000	+	15.5885i	−1.10876	+	0.640141i	−0.170250	+	0.985401i	$0.554458\pi$
$594$		0			0
$595$		0			0
$596$		0			0
$597$	9.00000	−	5.19615i	0.368345	−	0.212664i
$598$		0			0
$599$	15.5885	+	9.00000i	0.636927	+	0.367730i	0.783430	−	0.621480i	$-0.213468\pi$
$599$	15.5885	+	9.00000i	0.636927	+	0.367730i	−0.146503	+	0.989210i	$0.546802\pi$
$600$		0			0
$601$			1.73205i			0.0706518i	0.999376	+	0.0353259i	$0.0112469\pi$
$601$			1.73205i			0.0706518i	−0.999376	+	0.0353259i	$0.988753\pi$
$602$		0			0
$603$	3.46410			0.141069
$604$		0			0
$605$	24.0000	−	41.5692i	0.975739	−	1.69003i
$606$		0			0
$607$	4.33013	+	7.50000i	0.175754	+	0.304416i	0.940422	−	0.340009i	$-0.110430\pi$
$607$	4.33013	+	7.50000i	0.175754	+	0.304416i	−0.764668	+	0.644425i	$0.777097\pi$
$608$		0			0
$609$	13.5000	+	2.59808i	0.547048	+	0.105279i
$610$		0			0
$611$		0			0
$612$		0			0
$613$	−27.0000	−	15.5885i	−1.09052	−	0.629612i	−0.156805	−	0.987630i	$-0.550119\pi$
$613$	−27.0000	−	15.5885i	−1.09052	−	0.629612i	−0.933715	+	0.358018i	$0.883453\pi$
$614$		0			0
$615$	31.1769			1.25717
$616$		0			0
$617$	−36.0000			−1.44931			−0.724653	−	0.689114i	$-0.758000\pi$
$617$	−36.0000			−1.44931			−0.724653	+	0.689114i	$0.758000\pi$
$618$		0			0
$619$	−34.6410	−	20.0000i	−1.39234	−	0.803868i	−0.398766	−	0.917053i	$-0.630561\pi$
$619$	−34.6410	−	20.0000i	−1.39234	−	0.803868i	−0.993574	+	0.113185i	$0.963895\pi$
$620$		0			0
$621$	−3.00000	−	5.19615i	−0.120386	−	0.208514i
$622$		0			0
$623$		0			0
$624$		0			0
$625$	14.5000	+	25.1147i	0.580000	+	1.00459i
$626$		0			0
$627$	−20.7846	+	36.0000i	−0.830057	+	1.43770i
$628$		0			0
$629$		0			0
$630$		0			0
$631$			7.00000i			0.278666i	0.990246	+	0.139333i	$0.0444958\pi$
$631$			7.00000i			0.278666i	−0.990246	+	0.139333i	$0.955504\pi$
$632$		0			0
$633$	18.0000	+	10.3923i	0.715436	+	0.413057i
$634$		0			0
$635$	44.1673	−	25.5000i	1.75273	−	1.01194i
$636$		0			0
$637$	11.0000	−	8.66025i	0.435836	−	0.343132i
$638$		0			0
$639$	−10.3923	+	6.00000i	−0.411113	+	0.237356i
$640$		0			0
$641$	12.0000	−	20.7846i	0.473972	−	0.820943i	−0.525584	−	0.850741i	$-0.676153\pi$
$641$	12.0000	−	20.7846i	0.473972	−	0.820943i	0.999556	+	0.0297987i	$0.00948663\pi$
$642$		0			0
$643$		−	34.0000i		−	1.34083i	−0.741987	−	0.670415i	$-0.766116\pi$
$643$		−	34.0000i		−	1.34083i	0.741987	−	0.670415i	$-0.233884\pi$
$644$		0			0
$645$			10.3923i			0.409197i
$646$		0			0
$647$	−20.7846	+	36.0000i	−0.817127	+	1.41531i	0.0906629	+	0.995882i	$0.471101\pi$
$647$	−20.7846	+	36.0000i	−0.817127	+	1.41531i	−0.907790	+	0.419424i	$0.862232\pi$
$648$		0			0
$649$	−40.5000	+	23.3827i	−1.58976	+	0.917851i
$650$		0			0
$651$	17.3205	+	15.0000i	0.678844	+	0.587896i
$652$		0			0
$653$	−31.5000	+	18.1865i	−1.23269	+	0.711694i	−0.967590	−	0.252527i	$-0.918738\pi$
$653$	−31.5000	+	18.1865i	−1.23269	+	0.711694i	−0.265100	+	0.964221i	$0.585405\pi$
$654$		0			0
$655$	7.79423	+	4.50000i	0.304546	+	0.175830i
$656$		0			0
$657$			13.8564i			0.540590i
$658$		0			0
$659$	31.1769			1.21448			0.607240	−	0.794518i	$-0.292277\pi$
$659$	31.1769			1.21448			0.607240	+	0.794518i	$0.292277\pi$
$660$		0			0
$661$	−17.0000	+	29.4449i	−0.661223	+	1.14527i	0.319071	+	0.947731i	$0.396629\pi$
$661$	−17.0000	+	29.4449i	−0.661223	+	1.14527i	−0.980294	+	0.197542i	$0.936704\pi$
$662$		0			0
$663$		0			0
$664$		0			0
$665$	−12.0000	+	62.3538i	−0.465340	+	2.41798i
$666$		0			0
$667$	15.5885	+	27.0000i	0.603587	+	1.04544i
$668$		0			0
$669$	−4.50000	−	2.59808i	−0.173980	−	0.100447i
$670$		0			0
$671$	−41.5692			−1.60476
$672$		0			0
$673$	−31.0000			−1.19496			−0.597481	−	0.801883i	$-0.703832\pi$
$673$	−31.0000			−1.19496			−0.597481	+	0.801883i	$0.703832\pi$
$674$		0			0
$675$	3.46410	+	2.00000i	0.133333	+	0.0769800i
$676$		0			0
$677$	22.5000	+	38.9711i	0.864745	+	1.49778i	0.867300	+	0.497786i	$0.165853\pi$
$677$	22.5000	+	38.9711i	0.864745	+	1.49778i	−0.00255466	+	0.999997i	$0.500813\pi$
$678$		0			0
$679$	−12.9904	+	4.50000i	−0.498525	+	0.172694i
$680$		0			0
$681$	−1.50000	−	2.59808i	−0.0574801	−	0.0995585i
$682$		0			0
$683$	12.9904	−	22.5000i	0.497063	−	0.860939i	−0.502931	−	0.864326i	$-0.667745\pi$
$683$	12.9904	−	22.5000i	0.497063	−	0.860939i	0.999994	+	0.00338791i	$0.00107841\pi$
$684$		0			0
$685$	54.0000			2.06323
$686$		0			0
$687$			2.00000i			0.0763048i
$688$		0			0
$689$	−9.00000	−	5.19615i	−0.342873	−	0.197958i
$690$		0			0
$691$	−12.1244	+	7.00000i	−0.461232	+	0.266293i	−0.712562	−	0.701609i	$-0.752465\pi$
$691$	−12.1244	+	7.00000i	−0.461232	+	0.266293i	0.251330	+	0.967901i	$0.419132\pi$
$692$		0			0
$693$	4.50000	+	12.9904i	0.170941	+	0.493464i
$694$		0			0
$695$	51.9615	−	30.0000i	1.97101	−	1.13796i
$696$		0			0
$697$		0			0
$698$		0			0
$699$		−	24.0000i		−	0.907763i
$700$		0			0
$701$		−	46.7654i		−	1.76630i	−0.469087	−	0.883152i	$-0.655417\pi$
$701$		−	46.7654i		−	1.76630i	0.469087	−	0.883152i	$-0.344583\pi$
$702$		0			0
$703$	27.7128	−	48.0000i	1.04521	−	1.81035i
$704$		0			0
$705$		0			0
$706$		0			0
$707$	−15.5885	−	3.00000i	−0.586264	−	0.112827i
$708$		0			0
$709$	18.0000	−	10.3923i	0.676004	−	0.390291i	−0.122344	−	0.992488i	$-0.539041\pi$
$709$	18.0000	−	10.3923i	0.676004	−	0.390291i	0.798348	+	0.602197i	$0.205708\pi$
$710$		0			0
$711$	4.33013	+	2.50000i	0.162392	+	0.0937573i
$712$		0			0
$713$			51.9615i			1.94597i
$714$		0			0
$715$	−31.1769			−1.16595
$716$		0			0
$717$	−3.00000	+	5.19615i	−0.112037	+	0.194054i
$718$		0			0
$719$	−10.3923	−	18.0000i	−0.387568	−	0.671287i	0.604554	−	0.796564i	$-0.293351\pi$
$719$	−10.3923	−	18.0000i	−0.387568	−	0.671287i	−0.992122	+	0.125277i	$0.960018\pi$
$720$		0			0
$721$	6.00000	−	6.92820i	0.223452	−	0.258020i
$722$		0			0
$723$	−2.59808	−	4.50000i	−0.0966235	−	0.167357i
$724$		0			0
$725$	−18.0000	−	10.3923i	−0.668503	−	0.385961i
$726$		0			0
$727$	8.66025			0.321191			0.160596	−	0.987020i	$-0.448659\pi$
$727$	8.66025			0.321191			0.160596	+	0.987020i	$0.448659\pi$
$728$		0			0
$729$	−1.00000			−0.0370370
$730$		0			0
$731$		0			0
$732$		0			0
$733$	1.00000	+	1.73205i	0.0369358	+	0.0639748i	0.883902	−	0.467671i	$-0.154907\pi$
$733$	1.00000	+	1.73205i	0.0369358	+	0.0639748i	−0.846967	+	0.531646i	$0.821574\pi$
$734$		0			0
$735$	12.9904	+	16.5000i	0.479157	+	0.608612i
$736$		0			0
$737$	−9.00000	−	15.5885i	−0.331519	−	0.574208i
$738$		0			0
$739$	13.8564	−	24.0000i	0.509716	−	0.882854i	−0.490221	−	0.871598i	$-0.663084\pi$
$739$	13.8564	−	24.0000i	0.509716	−	0.882854i	0.999937	−	0.0112558i	$-0.00358291\pi$
$740$		0			0
$741$	16.0000			0.587775
$742$		0			0
$743$		−	18.0000i		−	0.660356i	−0.943919	−	0.330178i	$-0.892891\pi$
$743$		−	18.0000i		−	0.660356i	0.943919	−	0.330178i	$-0.107109\pi$
$744$		0			0
$745$		0			0
$746$		0			0
$747$	−7.79423	+	4.50000i	−0.285176	+	0.164646i
$748$		0			0
$749$	−9.00000	+	10.3923i	−0.328853	+	0.379727i
$750$		0			0
$751$	6.06218	−	3.50000i	0.221212	−	0.127717i	−0.385299	−	0.922792i	$-0.625902\pi$
$751$	6.06218	−	3.50000i	0.221212	−	0.127717i	0.606511	+	0.795075i	$0.292568\pi$
$752$		0			0
$753$	−1.50000	+	2.59808i	−0.0546630	+	0.0946792i
$754$		0			0
$755$		−	51.0000i		−	1.85608i
$756$		0			0
$757$		0			0		1.00000			$0$
$757$		0			0		−1.00000			$\pi$
$758$		0			0
$759$	−15.5885	+	27.0000i	−0.565825	+	0.980038i
$760$		0			0
$761$	27.0000	−	15.5885i	0.978749	−	0.565081i	0.0768569	−	0.997042i	$-0.475512\pi$
$761$	27.0000	−	15.5885i	0.978749	−	0.565081i	0.901892	+	0.431961i	$0.142178\pi$
$762$		0			0
$763$	1.73205	−	9.00000i	0.0627044	−	0.325822i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	15.5885	+	9.00000i	0.562867	+	0.324971i
$768$		0			0
$769$		−	1.73205i		−	0.0624593i	−0.999512	−	0.0312297i	$-0.990058\pi$
$769$		−	1.73205i		−	0.0624593i	0.999512	−	0.0312297i	$-0.00994233\pi$
$770$		0			0
$771$	−20.7846			−0.748539
$772$		0			0
$773$	3.00000	−	5.19615i	0.107903	−	0.186893i	−0.807018	−	0.590527i	$-0.798920\pi$
$773$	3.00000	−	5.19615i	0.107903	−	0.186893i	0.914920	+	0.403634i	$0.132253\pi$
$774$		0			0
$775$	−17.3205	−	30.0000i	−0.622171	−	1.07763i
$776$		0			0
$777$	−6.00000	−	17.3205i	−0.215249	−	0.621370i
$778$		0			0
$779$	41.5692	+	72.0000i	1.48937	+	2.57967i
$780$		0			0
$781$	54.0000	+	31.1769i	1.93227	+	1.11560i
$782$		0			0
$783$	5.19615			0.185695
$784$		0			0
$785$	12.0000			0.428298
$786$		0			0
$787$	−3.46410	−	2.00000i	−0.123482	−	0.0712923i	0.436987	−	0.899468i	$-0.356046\pi$
$787$	−3.46410	−	2.00000i	−0.123482	−	0.0712923i	−0.560469	+	0.828176i	$0.689379\pi$
$788$		0			0
$789$	−3.00000	−	5.19615i	−0.106803	−	0.184988i
$790$		0			0
$791$	−5.19615	−	15.0000i	−0.184754	−	0.533339i
$792$		0			0
$793$	8.00000	+	13.8564i	0.284088	+	0.492055i
$794$		0			0
$795$	7.79423	−	13.5000i	0.276433	−	0.478796i
$796$		0			0
$797$	33.0000			1.16892			0.584460	−	0.811423i	$-0.301306\pi$
$797$	33.0000			1.16892			0.584460	+	0.811423i	$0.301306\pi$
$798$		0			0
$799$		0			0
$800$		0			0
$801$		0			0
$802$		0			0
$803$	62.3538	−	36.0000i	2.20042	−	1.27041i
$804$		0			0
$805$	−9.00000	+	46.7654i	−0.317208	+	1.64826i
$806$		0			0
$807$	−12.9904	+	7.50000i	−0.457283	+	0.264013i
$808$		0			0
$809$	−18.0000	+	31.1769i	−0.632846	+	1.09612i	0.354121	+	0.935200i	$0.384780\pi$
$809$	−18.0000	+	31.1769i	−0.632846	+	1.09612i	−0.986967	+	0.160922i	$0.948553\pi$
$810$		0			0
$811$			2.00000i			0.0702295i	0.999383	+	0.0351147i	$0.0111797\pi$
$811$			2.00000i			0.0702295i	−0.999383	+	0.0351147i	$0.988820\pi$
$812$		0			0
$813$			15.5885i			0.546711i
$814$		0			0
$815$	−15.5885	+	27.0000i	−0.546040	+	0.945769i
$816$		0			0
$817$	−24.0000	+	13.8564i	−0.839654	+	0.484774i
$818$		0			0
$819$	3.46410	−	4.00000i	0.121046	−	0.139771i
$820$		0			0
$821$	−4.50000	+	2.59808i	−0.157051	+	0.0906735i	−0.576466	−	0.817121i	$-0.695569\pi$
$821$	−4.50000	+	2.59808i	−0.157051	+	0.0906735i	0.419415	+	0.907795i	$0.362235\pi$
$822$		0			0
$823$	27.7128	+	16.0000i	0.966008	+	0.557725i	0.898017	−	0.439961i	$-0.145008\pi$
$823$	27.7128	+	16.0000i	0.966008	+	0.557725i	0.0679910	+	0.997686i	$0.478341\pi$
$824$		0			0
$825$		−	20.7846i		−	0.723627i
$826$		0			0
$827$	36.3731			1.26482			0.632408	−	0.774636i	$-0.282067\pi$
$827$	36.3731			1.26482			0.632408	+	0.774636i	$0.282067\pi$
$828$		0			0
$829$	14.0000	−	24.2487i	0.486240	−	0.842193i	−0.513635	−	0.858009i	$-0.671701\pi$
$829$	14.0000	−	24.2487i	0.486240	−	0.842193i	0.999875	+	0.0158163i	$0.00503471\pi$
$830$		0			0
$831$	13.8564	+	24.0000i	0.480673	+	0.832551i
$832$		0			0
$833$		0			0
$834$		0			0
$835$	−15.5885	−	27.0000i	−0.539461	−	0.934374i
$836$		0			0
$837$	7.50000	+	4.33013i	0.259238	+	0.149671i
$838$		0			0
$839$	−41.5692			−1.43513			−0.717564	−	0.696492i	$-0.754743\pi$
$839$	−41.5692			−1.43513			−0.717564	+	0.696492i	$0.754743\pi$
$840$		0			0
$841$	2.00000			0.0689655
$842$		0			0
$843$	25.9808	+	15.0000i	0.894825	+	0.516627i
$844$		0			0
$845$	−13.5000	−	23.3827i	−0.464414	−	0.804389i
$846$		0			0
$847$	27.7128	−	32.0000i	0.952224	−	1.09953i
$848$		0			0
$849$	1.00000	+	1.73205i	0.0343199	+	0.0594438i
$850$		0			0
$851$	20.7846	−	36.0000i	0.712487	−	1.23406i
$852$		0			0
$853$	−22.0000			−0.753266			−0.376633	−	0.926363i	$-0.622918\pi$
$853$	−22.0000			−0.753266			−0.376633	+	0.926363i	$0.622918\pi$
$854$		0			0
$855$			24.0000i			0.820783i
$856$		0			0
$857$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$857$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$858$		0			0
$859$	−12.1244	+	7.00000i	−0.413678	+	0.238837i	−0.692369	−	0.721544i	$-0.743433\pi$
$859$	−12.1244	+	7.00000i	−0.413678	+	0.238837i	0.278691	+	0.960381i	$0.410099\pi$
$860$		0			0
$861$	27.0000	+	5.19615i	0.920158	+	0.177084i
$862$		0			0
$863$	41.5692	−	24.0000i	1.41503	−	0.816970i	0.419176	−	0.907905i	$-0.362319\pi$
$863$	41.5692	−	24.0000i	1.41503	−	0.816970i	0.995857	+	0.0909355i	$0.0289857\pi$
$864$		0			0
$865$	−27.0000	+	46.7654i	−0.918028	+	1.59007i
$866$		0			0
$867$			17.0000i			0.577350i
$868$		0			0
$869$		−	25.9808i		−	0.881337i
$870$		0			0
$871$	−3.46410	+	6.00000i	−0.117377	+	0.203302i
$872$		0			0
$873$	−4.50000	+	2.59808i	−0.152302	+	0.0879316i
$874$		0			0
$875$	2.59808	+	7.50000i	0.0878310	+	0.253546i
$876$		0			0
$877$	−18.0000	+	10.3923i	−0.607817	+	0.350923i	−0.772111	−	0.635488i	$-0.780799\pi$
$877$	−18.0000	+	10.3923i	−0.607817	+	0.350923i	0.164294	+	0.986411i	$0.447466\pi$
$878$		0			0
$879$	−2.59808	−	1.50000i	−0.0876309	−	0.0505937i
$880$		0			0
$881$		−	31.1769i		−	1.05038i	−0.850986	−	0.525188i	$-0.823995\pi$
$881$		−	31.1769i		−	1.05038i	0.850986	−	0.525188i	$-0.176005\pi$
$882$		0			0
$883$	−24.2487			−0.816034			−0.408017	−	0.912974i	$-0.633780\pi$
$883$	−24.2487			−0.816034			−0.408017	+	0.912974i	$0.633780\pi$
$884$		0			0
$885$	−13.5000	+	23.3827i	−0.453798	+	0.786000i
$886$		0			0
$887$	−25.9808	−	45.0000i	−0.872349	−	1.51095i	−0.859561	−	0.511034i	$-0.829263\pi$
$887$	−25.9808	−	45.0000i	−0.872349	−	1.51095i	−0.0127881	−	0.999918i	$-0.504071\pi$
$888$		0			0
$889$	42.5000	−	14.7224i	1.42540	−	0.493775i
$890$		0			0
$891$	2.59808	+	4.50000i	0.0870388	+	0.150756i
$892$		0			0
$893$		0			0
$894$		0			0
$895$	−31.1769			−1.04213
$896$		0			0
$897$	12.0000			0.400668
$898$		0			0
$899$	−38.9711	−	22.5000i	−1.29976	−	0.750417i
$900$		0			0
$901$		0			0
$902$		0			0
$903$	−1.73205	+	9.00000i	−0.0576390	+	0.299501i
$904$		0			0
$905$	−15.0000	−	25.9808i	−0.498617	−	0.863630i
$906$		0			0
$907$	−22.5167	+	39.0000i	−0.747653	+	1.29497i	0.201291	+	0.979531i	$0.435486\pi$
$907$	−22.5167	+	39.0000i	−0.747653	+	1.29497i	−0.948945	+	0.315442i	$0.897847\pi$
$908$		0			0
$909$	−6.00000			−0.199007
$910$		0			0
$911$			12.0000i			0.397578i	0.980042	+	0.198789i	$0.0637008\pi$
$911$			12.0000i			0.397578i	−0.980042	+	0.198789i	$0.936299\pi$
$912$		0			0
$913$	40.5000	+	23.3827i	1.34035	+	0.773854i
$914$		0			0
$915$	−20.7846	+	12.0000i	−0.687118	+	0.396708i
$916$		0			0
$917$	6.00000	+	5.19615i	0.198137	+	0.171592i
$918$		0			0
$919$	6.92820	−	4.00000i	0.228540	−	0.131948i	−0.381358	−	0.924427i	$-0.624544\pi$
$919$	6.92820	−	4.00000i	0.228540	−	0.131948i	0.609898	+	0.792480i	$0.291210\pi$
$920$		0			0
$921$	5.00000	−	8.66025i	0.164756	−	0.285365i
$922$		0			0
$923$		−	24.0000i		−	0.789970i
$924$		0			0
$925$			27.7128i			0.911192i
$926$		0			0
$927$	1.73205	−	3.00000i	0.0568880	−	0.0985329i
$928$		0			0
$929$	−9.00000	+	5.19615i	−0.295280	+	0.170480i	−0.640321	−	0.768108i	$-0.721199\pi$
$929$	−9.00000	+	5.19615i	−0.295280	+	0.170480i	0.345040	+	0.938588i	$0.387865\pi$
$930$		0			0
$931$	−20.7846	+	52.0000i	−0.681188	+	1.70423i
$932$		0			0
$933$	27.0000	−	15.5885i	0.883940	−	0.510343i
$934$		0			0
$935$		0			0
$936$		0			0
$937$		−	53.6936i		−	1.75409i	−0.480406	−	0.877046i	$-0.659511\pi$
$937$		−	53.6936i		−	1.75409i	0.480406	−	0.877046i	$-0.340489\pi$
$938$		0			0
$939$	−29.4449			−0.960897
$940$		0			0
$941$	−28.5000	+	49.3634i	−0.929073	+	1.60920i	−0.144198	+	0.989549i	$0.546060\pi$
$941$	−28.5000	+	49.3634i	−0.929073	+	1.60920i	−0.784875	+	0.619654i	$0.787273\pi$
$942$		0			0
$943$	31.1769	+	54.0000i	1.01526	+	1.75848i
$944$		0			0
$945$	6.00000	+	5.19615i	0.195180	+	0.169031i
$946$		0			0
$947$	15.5885	+	27.0000i	0.506557	+	0.877382i	0.999971	+	0.00758776i	$0.00241528\pi$
$947$	15.5885	+	27.0000i	0.506557	+	0.877382i	−0.493414	+	0.869794i	$0.664251\pi$
$948$		0			0
$949$	−24.0000	−	13.8564i	−0.779073	−	0.449798i
$950$		0			0
$951$	25.9808			0.842484
$952$		0			0
$953$	54.0000			1.74923			0.874616	−	0.484817i	$-0.161114\pi$
$953$	54.0000			1.74923			0.874616	+	0.484817i	$0.161114\pi$
$954$		0			0
$955$	31.1769	+	18.0000i	1.00886	+	0.582466i
$956$		0			0
$957$	−13.5000	−	23.3827i	−0.436393	−	0.755855i
$958$		0			0
$959$	46.7654	+	9.00000i	1.51013	+	0.290625i
$960$		0			0
$961$	−22.0000	−	38.1051i	−0.709677	−	1.22920i
$962$		0			0
$963$	−2.59808	+	4.50000i	−0.0837218	+	0.145010i
$964$		0			0
$965$	33.0000			1.06231
$966$		0			0
$967$			29.0000i			0.932577i	0.884633	+	0.466289i	$0.154409\pi$
$967$			29.0000i			0.932577i	−0.884633	+	0.466289i	$0.845591\pi$
$968$		0			0
$969$		0			0
$970$		0			0
$971$	12.9904	−	7.50000i	0.416881	−	0.240686i	−0.276861	−	0.960910i	$-0.589294\pi$
$971$	12.9904	−	7.50000i	0.416881	−	0.240686i	0.693742	+	0.720224i	$0.255961\pi$
$972$		0			0
$973$	50.0000	−	17.3205i	1.60293	−	0.555270i
$974$		0			0
$975$	−6.92820	+	4.00000i	−0.221880	+	0.128103i
$976$		0			0
$977$	9.00000	−	15.5885i	0.287936	−	0.498719i	−0.685381	−	0.728184i	$-0.740364\pi$
$977$	9.00000	−	15.5885i	0.287936	−	0.498719i	0.973317	+	0.229465i	$0.0736978\pi$
$978$		0			0
$979$		0			0
$980$		0			0
$981$		−	3.46410i		−	0.110600i
$982$		0			0
$983$	−5.19615	+	9.00000i	−0.165732	+	0.287055i	−0.936915	−	0.349558i	$-0.886332\pi$
$983$	−5.19615	+	9.00000i	−0.165732	+	0.287055i	0.771183	+	0.636613i	$0.219665\pi$
$984$		0			0
$985$		0			0
$986$		0			0
$987$		0			0
$988$		0			0
$989$	−18.0000	+	10.3923i	−0.572367	+	0.330456i
$990$		0			0
$991$	14.7224	+	8.50000i	0.467673	+	0.270011i	0.715265	−	0.698853i	$-0.246306\pi$
$991$	14.7224	+	8.50000i	0.467673	+	0.270011i	−0.247592	+	0.968864i	$0.579639\pi$
$992$		0			0
$993$			27.7128i			0.879440i
$994$		0			0
$995$	−31.1769			−0.988375
$996$		0			0
$997$	−7.00000	+	12.1244i	−0.221692	+	0.383982i	−0.955322	−	0.295567i	$-0.904491\pi$
$997$	−7.00000	+	12.1244i	−0.221692	+	0.383982i	0.733630	+	0.679549i	$0.237825\pi$
$998$		0			0
$999$	−3.46410	−	6.00000i	−0.109599	−	0.189832i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1344.2.bb.d.31.1	yes	4
4.3	odd	2	inner	1344.2.bb.d.31.2	yes	4
7.5	odd	6		1344.2.bb.a.607.1	yes	4
8.3	odd	2		1344.2.bb.a.31.1	✓	4
8.5	even	2		1344.2.bb.a.31.2	yes	4
28.19	even	6		1344.2.bb.a.607.2	yes	4
56.5	odd	6	inner	1344.2.bb.d.607.2	yes	4
56.19	even	6	inner	1344.2.bb.d.607.1	yes	4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1344.2.bb.a.31.1	✓	4	8.3	odd	2
1344.2.bb.a.31.2	yes	4	8.5	even	2
1344.2.bb.a.607.1	yes	4	7.5	odd	6
1344.2.bb.a.607.2	yes	4	28.19	even	6
1344.2.bb.d.31.1	yes	4	1.1	even	1	trivial
1344.2.bb.d.31.2	yes	4	4.3	odd	2	inner
1344.2.bb.d.607.1	yes	4	56.19	even	6	inner
1344.2.bb.d.607.2	yes	4	56.5	odd	6	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 1344 = 2^{6} \cdot 3 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1344.bb (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.866025 - 0.500000i) q^{3} +(1.50000 + 2.59808i) q^{5} +(0.866025 + 2.50000i) q^{7} +(0.500000 + 0.866025i) q^{9} +O(q^{10})\)	\(q+(-0.866025 - 0.500000i) q^{3} +(1.50000 + 2.59808i) q^{5} +(0.866025 + 2.50000i) q^{7} +(0.500000 + 0.866025i) q^{9} +(2.59808 - 4.50000i) q^{11} -2.00000 q^{13} -3.00000i q^{15} +(6.92820 - 4.00000i) q^{19} +(0.500000 - 2.59808i) q^{21} +(5.19615 - 3.00000i) q^{23} +(-2.00000 + 3.46410i) q^{25} -1.00000i q^{27} +5.19615i q^{29} +(-4.33013 + 7.50000i) q^{31} +(-4.50000 + 2.59808i) q^{33} +(-5.19615 + 6.00000i) q^{35} +(6.00000 - 3.46410i) q^{37} +(1.73205 + 1.00000i) q^{39} +10.3923i q^{41} -3.46410 q^{43} +(-1.50000 + 2.59808i) q^{45} +(-5.50000 + 4.33013i) q^{49} +(4.50000 + 2.59808i) q^{53} +15.5885 q^{55} -8.00000 q^{57} +(-7.79423 - 4.50000i) q^{59} +(-4.00000 - 6.92820i) q^{61} +(-1.73205 + 2.00000i) q^{63} +(-3.00000 - 5.19615i) q^{65} +(1.73205 - 3.00000i) q^{67} -6.00000 q^{69} +12.0000i q^{71} +(12.0000 + 6.92820i) q^{73} +(3.46410 - 2.00000i) q^{75} +(13.5000 + 2.59808i) q^{77} +(4.33013 - 2.50000i) q^{79} +(-0.500000 + 0.866025i) q^{81} +9.00000i q^{83} +(2.59808 - 4.50000i) q^{87} +(-1.73205 - 5.00000i) q^{91} +(7.50000 - 4.33013i) q^{93} +(20.7846 + 12.0000i) q^{95} +5.19615i q^{97} +5.19615 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 6 q^{5} + 2 q^{9}+O(q^{10}) \) 4 * q + 6 * q^5 + 2 * q^9	\( 4 q + 6 q^{5} + 2 q^{9} - 8 q^{13} + 2 q^{21} - 8 q^{25} - 18 q^{33} + 24 q^{37} - 6 q^{45} - 22 q^{49} + 18 q^{53} - 32 q^{57} - 16 q^{61} - 12 q^{65} - 24 q^{69} + 48 q^{73} + 54 q^{77} - 2 q^{81} + 30 q^{93}+O(q^{100}) \) 4 * q + 6 * q^5 + 2 * q^9 - 8 * q^13 + 2 * q^21 - 8 * q^25 - 18 * q^33 + 24 * q^37 - 6 * q^45 - 22 * q^49 + 18 * q^53 - 32 * q^57 - 16 * q^61 - 12 * q^65 - 24 * q^69 + 48 * q^73 + 54 * q^77 - 2 * q^81 + 30 * q^93

Introduction

L-functions

Modular forms

Varieties

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Database

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