LMFDB - Embedded newform 672.2.q.l.193.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [672,2,Mod(193,672)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(672, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 0, 0, 4]))

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

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

chi := DirichletCharacter("672.193");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 672 = 2^{5} \cdot 3 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	672.q (of order $3$, 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:	$5.36594701583$
Analytic rank:	$0$
Dimension:	$6$
Relative dimension:	$3$ over $\Q(\zeta_{3})$
Coefficient field:	6.0.1156923.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - 3x^{5} + 12x^{4} - 19x^{3} + 27x^{2} - 18x + 4 $ x^6 - 3x^5 + 12x^4 - 19x^3 + 27x^2 - 18*x + 4
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			193.1
Root			$0.500000 + 0.0585812i$ of defining polynomial
Character	$\chi$	$=$	672.193
Dual form			672.2.q.l.289.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.500000 - 0.866025i) q^{3} +(-1.37328 - 2.37860i) q^{5} +(2.64510 + 0.0585812i) q^{7} +(-0.500000 - 0.866025i) q^{9} +O(q^{10})$	\(q+(0.500000 - 0.866025i) q^{3} +(-1.37328 - 2.37860i) q^{5} +(2.64510 + 0.0585812i) q^{7} +(-0.500000 - 0.866025i) q^{9} +(0.771819 - 1.33683i) q^{11} +6.03677 q^{13} -2.74657 q^{15} +(-3.74657 + 6.48925i) q^{17} +(-3.01839 - 5.22800i) q^{19} +(1.37328 - 2.26144i) q^{21} +(-3.74657 - 6.48925i) q^{23} +(-1.27182 + 2.20285i) q^{25} -1.00000 q^{27} +1.25343 q^{29} +(2.64510 - 4.58145i) q^{31} +(-0.771819 - 1.33683i) q^{33} +(-3.49314 - 6.37208i) q^{35} +(-2.47475 - 4.28639i) q^{37} +(3.01839 - 5.22800i) q^{39} -5.08727 q^{41} -3.45636 q^{43} +(-1.37328 + 2.37860i) q^{45} +(4.74657 + 8.22130i) q^{47} +(6.99314 + 0.309906i) q^{49} +(3.74657 + 6.48925i) q^{51} +(1.91692 - 3.32021i) q^{53} -4.23970 q^{55} -6.03677 q^{57} +(2.77182 - 4.80093i) q^{59} +(7.29021 + 12.6270i) q^{61} +(-1.27182 - 2.32002i) q^{63} +(-8.29021 - 14.3591i) q^{65} +(-2.01839 + 3.49595i) q^{67} -7.49314 q^{69} +5.49314 q^{71} +(-6.27182 + 10.8631i) q^{73} +(1.27182 + 2.20285i) q^{75} +(2.11985 - 3.49084i) q^{77} +(-3.89853 - 6.75246i) q^{79} +(-0.500000 + 0.866025i) q^{81} +6.52991 q^{83} +20.5804 q^{85} +(0.626716 - 1.08550i) q^{87} +(4.74657 + 8.22130i) q^{89} +(15.9679 + 0.353641i) q^{91} +(-2.64510 - 4.58145i) q^{93} +(-8.29021 + 14.3591i) q^{95} +1.54364 q^{97} -1.54364 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q + 3 q^{3} + 3 q^{7} - 3 q^{9}+O(q^{10}) $ 6 * q + 3 * q^3 + 3 * q^7 - 3 * q^9	$ 6 q + 3 q^{3} + 3 q^{7} - 3 q^{9} - 6 q^{13} - 6 q^{17} + 3 q^{19} - 6 q^{23} - 3 q^{25} - 6 q^{27} + 24 q^{29} + 3 q^{31} + 12 q^{35} - 3 q^{37} - 3 q^{39} - 12 q^{41} - 30 q^{43} + 12 q^{47} + 9 q^{49} + 6 q^{51} - 6 q^{53} + 24 q^{55} + 6 q^{57} + 12 q^{59} + 18 q^{61} - 3 q^{63} - 24 q^{65} + 9 q^{67} - 12 q^{69} - 33 q^{73} + 3 q^{75} - 12 q^{77} - 27 q^{79} - 3 q^{81} - 36 q^{83} + 72 q^{85} + 12 q^{87} + 12 q^{89} + 51 q^{91} - 3 q^{93} - 24 q^{95}+O(q^{100}) $ 6 * q + 3 * q^3 + 3 * q^7 - 3 * q^9 - 6 * q^13 - 6 * q^17 + 3 * q^19 - 6 * q^23 - 3 * q^25 - 6 * q^27 + 24 * q^29 + 3 * q^31 + 12 * q^35 - 3 * q^37 - 3 * q^39 - 12 * q^41 - 30 * q^43 + 12 * q^47 + 9 * q^49 + 6 * q^51 - 6 * q^53 + 24 * q^55 + 6 * q^57 + 12 * q^59 + 18 * q^61 - 3 * q^63 - 24 * q^65 + 9 * q^67 - 12 * q^69 - 33 * q^73 + 3 * q^75 - 12 * q^77 - 27 * q^79 - 3 * q^81 - 36 * q^83 + 72 * q^85 + 12 * q^87 + 12 * q^89 + 51 * q^91 - 3 * q^93 - 24 * q^95

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/672\mathbb{Z}\right)^\times$.

$n$	$127$	$421$	$449$	$577$
$\chi(n)$	$1$	$1$	$1$	$e\left(\frac{2}{3}\right)$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	0.500000	−	0.866025i	0.288675	−	0.500000i
$3$	0.500000	−	0.866025i	0.288675	−	0.500000i
$4$		0			0
$5$	−1.37328	−	2.37860i	−0.614151	−	1.06374i	−0.990533	−	0.137277i	$-0.956165\pi$
$5$	−1.37328	−	2.37860i	−0.614151	−	1.06374i	0.376381	−	0.926465i	$-0.377168\pi$
$6$		0			0
$7$	2.64510	+	0.0585812i	0.999755	+	0.0221416i
$7$	2.64510	+	0.0585812i	0.999755	+	0.0221416i
$8$		0			0
$9$	−0.500000	−	0.866025i	−0.166667	−	0.288675i
$10$		0			0
$11$	0.771819	−	1.33683i	0.232712	−	0.403069i	−0.725893	−	0.687807i	$-0.758573\pi$
$11$	0.771819	−	1.33683i	0.232712	−	0.403069i	0.958605	+	0.284738i	$0.0919067\pi$
$12$		0			0
$13$	6.03677			1.67430			0.837150	−	0.546974i	$-0.184220\pi$
$13$	6.03677			1.67430			0.837150	+	0.546974i	$0.184220\pi$
$14$		0			0
$15$	−2.74657			−0.709161
$16$		0			0
$17$	−3.74657	+	6.48925i	−0.908676	+	1.57387i	−0.0927713	+	0.995687i	$0.529573\pi$
$17$	−3.74657	+	6.48925i	−0.908676	+	1.57387i	−0.815905	+	0.578186i	$0.803761\pi$
$18$		0			0
$19$	−3.01839	−	5.22800i	−0.692465	−	1.19939i	−0.971028	−	0.238967i	$-0.923191\pi$
$19$	−3.01839	−	5.22800i	−0.692465	−	1.19939i	0.278562	−	0.960418i	$-0.410142\pi$
$20$		0			0
$21$	1.37328	−	2.26144i	0.299675	−	0.493486i
$22$		0			0
$23$	−3.74657	−	6.48925i	−0.781213	−	1.35310i	−0.931235	−	0.364419i	$-0.881268\pi$
$23$	−3.74657	−	6.48925i	−0.781213	−	1.35310i	0.150022	−	0.988683i	$-0.452066\pi$
$24$		0			0
$25$	−1.27182	+	2.20285i	−0.254364	+	0.440571i
$26$		0			0
$27$	−1.00000			−0.192450
$28$		0			0
$29$	1.25343			0.232756			0.116378	−	0.993205i	$-0.462872\pi$
$29$	1.25343			0.232756			0.116378	+	0.993205i	$0.462872\pi$
$30$		0			0
$31$	2.64510	−	4.58145i	0.475074	−	0.822853i	−0.524518	−	0.851399i	$-0.675754\pi$
$31$	2.64510	−	4.58145i	0.475074	−	0.822853i	0.999592	+	0.0285462i	$0.00908778\pi$
$32$		0			0
$33$	−0.771819	−	1.33683i	−0.134356	−	0.232712i
$34$		0			0
$35$	−3.49314	−	6.37208i	−0.590448	−	1.07708i
$36$		0			0
$37$	−2.47475	−	4.28639i	−0.406846	−	0.704679i	0.587688	−	0.809088i	$-0.300038\pi$
$37$	−2.47475	−	4.28639i	−0.406846	−	0.704679i	−0.994534	+	0.104409i	$0.966705\pi$
$38$		0			0
$39$	3.01839	−	5.22800i	0.483329	−	0.837150i
$40$		0			0
$41$	−5.08727			−0.794499			−0.397249	−	0.917711i	$-0.630035\pi$
$41$	−5.08727			−0.794499			−0.397249	+	0.917711i	$0.630035\pi$
$42$		0			0
$43$	−3.45636			−0.527090			−0.263545	−	0.964647i	$-0.584892\pi$
$43$	−3.45636			−0.527090			−0.263545	+	0.964647i	$0.584892\pi$
$44$		0			0
$45$	−1.37328	+	2.37860i	−0.204717	+	0.354580i
$46$		0			0
$47$	4.74657	+	8.22130i	0.692358	+	1.19920i	0.971063	+	0.238823i	$0.0767615\pi$
$47$	4.74657	+	8.22130i	0.692358	+	1.19920i	−0.278705	+	0.960377i	$0.589905\pi$
$48$		0			0
$49$	6.99314	+	0.309906i	0.999019	+	0.0442723i
$50$		0			0
$51$	3.74657	+	6.48925i	0.524624	+	0.908676i
$52$		0			0
$53$	1.91692	−	3.32021i	0.263309	−	0.456065i	−0.703810	−	0.710388i	$-0.748519\pi$
$53$	1.91692	−	3.32021i	0.263309	−	0.456065i	0.967119	+	0.254323i	$0.0818527\pi$
$54$		0			0
$55$	−4.23970			−0.571682
$56$		0			0
$57$	−6.03677			−0.799590
$58$		0			0
$59$	2.77182	−	4.80093i	0.360860	−	0.625028i	−0.627243	−	0.778824i	$-0.715817\pi$
$59$	2.77182	−	4.80093i	0.360860	−	0.625028i	0.988103	+	0.153796i	$0.0491499\pi$
$60$		0			0
$61$	7.29021	+	12.6270i	0.933415	+	1.61672i	0.777436	+	0.628962i	$0.216520\pi$
$61$	7.29021	+	12.6270i	0.933415	+	1.61672i	0.155979	+	0.987760i	$0.450147\pi$
$62$		0			0
$63$	−1.27182	−	2.32002i	−0.160234	−	0.292295i
$64$		0			0
$65$	−8.29021	−	14.3591i	−1.02827	−	1.78102i
$66$		0			0
$67$	−2.01839	+	3.49595i	−0.246585	+	0.427098i	−0.962576	−	0.271012i	$-0.912642\pi$
$67$	−2.01839	+	3.49595i	−0.246585	+	0.427098i	0.715991	+	0.698110i	$0.245975\pi$
$68$		0			0
$69$	−7.49314			−0.902068
$70$		0			0
$71$	5.49314			0.651915			0.325958	−	0.945384i	$-0.394313\pi$
$71$	5.49314			0.651915			0.325958	+	0.945384i	$0.394313\pi$
$72$		0			0
$73$	−6.27182	+	10.8631i	−0.734061	+	1.27143i	0.221073	+	0.975257i	$0.429044\pi$
$73$	−6.27182	+	10.8631i	−0.734061	+	1.27143i	−0.955134	+	0.296173i	$0.904289\pi$
$74$		0			0
$75$	1.27182	+	2.20285i	0.146857	+	0.254364i
$76$		0			0
$77$	2.11985	−	3.49084i	0.241580	−	0.397818i
$78$		0			0
$79$	−3.89853	−	6.75246i	−0.438619	−	0.759711i	0.558964	−	0.829192i	$-0.311199\pi$
$79$	−3.89853	−	6.75246i	−0.438619	−	0.759711i	−0.997583	+	0.0694809i	$0.977866\pi$
$80$		0			0
$81$	−0.500000	+	0.866025i	−0.0555556	+	0.0962250i
$82$		0			0
$83$	6.52991			0.716751			0.358375	−	0.933578i	$-0.383331\pi$
$83$	6.52991			0.716751			0.358375	+	0.933578i	$0.383331\pi$
$84$		0			0
$85$	20.5804			2.23226
$86$		0			0
$87$	0.626716	−	1.08550i	0.0671910	−	0.116378i
$88$		0			0
$89$	4.74657	+	8.22130i	0.503135	+	0.871456i	0.999993	+	0.00362404i	$0.00115357\pi$
$89$	4.74657	+	8.22130i	0.503135	+	0.871456i	−0.496858	+	0.867832i	$0.665513\pi$
$90$		0			0
$91$	15.9679	+	0.353641i	1.67389	+	0.0370717i
$92$		0			0
$93$	−2.64510	−	4.58145i	−0.274284	−	0.475074i
$94$		0			0
$95$	−8.29021	+	14.3591i	−0.850557	+	1.47321i
$96$		0			0
$97$	1.54364			0.156733			0.0783663	−	0.996925i	$-0.475030\pi$
$97$	1.54364			0.156733			0.0783663	+	0.996925i	$0.475030\pi$
$98$		0			0
$99$	−1.54364			−0.155141
$100$		0			0
$101$	1.29021	−	2.23470i	0.128380	−	0.222361i	−0.794669	−	0.607043i	$-0.792356\pi$
$101$	1.29021	−	2.23470i	0.128380	−	0.222361i	0.923049	+	0.384682i	$0.125689\pi$
$102$		0			0
$103$	3.27182	+	5.66696i	0.322382	+	0.558382i	0.980979	−	0.194114i	$-0.0621832\pi$
$103$	3.27182	+	5.66696i	0.322382	+	0.558382i	−0.658597	+	0.752496i	$0.728850\pi$
$104$		0			0
$105$	−7.26496	−	0.160897i	−0.708987	−	0.0157020i
$106$		0			0
$107$	−2.26496	−	3.92302i	−0.218961	−	0.379252i	0.735529	−	0.677493i	$-0.236934\pi$
$107$	−2.26496	−	3.92302i	−0.218961	−	0.379252i	−0.954491	+	0.298241i	$0.903600\pi$
$108$		0			0
$109$	3.22132	−	5.57949i	0.308546	−	0.534418i	−0.669498	−	0.742814i	$-0.733491\pi$
$109$	3.22132	−	5.57949i	0.308546	−	0.534418i	0.978045	+	0.208396i	$0.0668242\pi$
$110$		0			0
$111$	−4.94950			−0.469786
$112$		0			0
$113$	8.00000			0.752577			0.376288	−	0.926503i	$-0.377200\pi$
$113$	8.00000			0.752577			0.376288	+	0.926503i	$0.377200\pi$
$114$		0			0
$115$	−10.2902	+	17.8232i	−0.959567	+	1.66202i
$116$		0			0
$117$	−3.01839	−	5.22800i	−0.279050	−	0.483329i
$118$		0			0
$119$	−10.2902	+	16.9452i	−0.943302	+	1.55337i
$120$		0			0
$121$	4.30859	+	7.46270i	0.391690	+	0.678427i
$122$		0			0
$123$	−2.54364	+	4.40571i	−0.229352	+	0.397249i
$124$		0			0
$125$	−6.74657			−0.603431
$126$		0			0
$127$	−3.79707			−0.336935			−0.168468	−	0.985707i	$-0.553882\pi$
$127$	−3.79707			−0.336935			−0.168468	+	0.985707i	$0.553882\pi$
$128$		0			0
$129$	−1.72818	+	2.99330i	−0.152158	+	0.263545i
$130$		0			0
$131$	0.771819	+	1.33683i	0.0674341	+	0.116799i	0.897771	−	0.440462i	$-0.145185\pi$
$131$	0.771819	+	1.33683i	0.0674341	+	0.116799i	−0.830337	+	0.557262i	$0.811852\pi$
$132$		0			0
$133$	−7.67768	−	14.0054i	−0.665739	−	1.21442i
$134$		0			0
$135$	1.37328	+	2.37860i	0.118193	+	0.204717i
$136$		0			0
$137$	−0.746568	+	1.29309i	−0.0637836	+	0.110476i	−0.896154	−	0.443744i	$-0.853650\pi$
$137$	−0.746568	+	1.29309i	−0.0637836	+	0.110476i	0.832370	+	0.554220i	$0.186983\pi$
$138$		0			0
$139$	2.94950			0.250173			0.125087	−	0.992146i	$-0.460079\pi$
$139$	2.94950			0.250173			0.125087	+	0.992146i	$0.460079\pi$
$140$		0			0
$141$	9.49314			0.799466
$142$		0			0
$143$	4.65929	−	8.07013i	0.389630	−	0.674858i
$144$		0			0
$145$	−1.72132	−	2.98141i	−0.142948	−	0.247593i
$146$		0			0
$147$	3.76496	−	5.90128i	0.310528	−	0.486729i
$148$		0			0
$149$	0.746568	+	1.29309i	0.0611613	+	0.105934i	0.894985	−	0.446097i	$-0.147186\pi$
$149$	0.746568	+	1.29309i	0.0611613	+	0.105934i	−0.833823	+	0.552031i	$0.813853\pi$
$150$		0			0
$151$	4.86642	−	8.42889i	0.396024	−	0.685933i	−0.597208	−	0.802087i	$-0.703723\pi$
$151$	4.86642	−	8.42889i	0.396024	−	0.685933i	0.993231	+	0.116154i	$0.0370565\pi$
$152$		0			0
$153$	7.49314			0.605784
$154$		0			0
$155$	−14.5299			−1.16707
$156$		0			0
$157$	−4.54364	+	7.86981i	−0.362622	+	0.628079i	−0.988391	−	0.151929i	$-0.951452\pi$
$157$	−4.54364	+	7.86981i	−0.362622	+	0.628079i	0.625770	+	0.780008i	$0.284785\pi$
$158$		0			0
$159$	−1.91692	−	3.32021i	−0.152022	−	0.263309i
$160$		0			0
$161$	−9.52991	−	17.3842i	−0.751062	−	1.37007i
$162$		0			0
$163$	9.78334	+	16.9452i	0.766290	+	1.32725i	0.939562	+	0.342380i	$0.111233\pi$
$163$	9.78334	+	16.9452i	0.766290	+	1.32725i	−0.173271	+	0.984874i	$0.555434\pi$
$164$		0			0
$165$	−2.11985	+	3.67169i	−0.165030	+	0.285841i
$166$		0			0
$167$	11.8990			0.920772			0.460386	−	0.887719i	$-0.347711\pi$
$167$	11.8990			0.920772			0.460386	+	0.887719i	$0.347711\pi$
$168$		0			0
$169$	23.4426			1.80328
$170$		0			0
$171$	−3.01839	+	5.22800i	−0.230822	+	0.399795i
$172$		0			0
$173$	−1.29021	−	2.23470i	−0.0980925	−	0.169901i	0.812803	−	0.582539i	$-0.197941\pi$
$173$	−1.29021	−	2.23470i	−0.0980925	−	0.169901i	−0.910895	+	0.412638i	$0.864607\pi$
$174$		0			0
$175$	−3.49314	+	5.75227i	−0.264056	+	0.434831i
$176$		0			0
$177$	−2.77182	−	4.80093i	−0.208343	−	0.360860i
$178$		0			0
$179$	−1.49314	+	2.58619i	−0.111602	+	0.193301i	−0.916416	−	0.400226i	$-0.868932\pi$
$179$	−1.49314	+	2.58619i	−0.111602	+	0.193301i	0.804814	+	0.593527i	$0.202265\pi$
$180$		0			0
$181$	−10.5436			−0.783702			−0.391851	−	0.920029i	$-0.628165\pi$
$181$	−10.5436			−0.783702			−0.391851	+	0.920029i	$0.628165\pi$
$182$		0			0
$183$	14.5804			1.07781
$184$		0			0
$185$	−6.79707	+	11.7729i	−0.499730	+	0.865559i
$186$		0			0
$187$	5.78334	+	10.0170i	0.422920	+	0.732519i
$188$		0			0
$189$	−2.64510	−	0.0585812i	−0.192403	−	0.00426115i
$190$		0			0
$191$	8.58041	+	14.8617i	0.620857	+	1.07536i	0.989327	+	0.145716i	$0.0465485\pi$
$191$	8.58041	+	14.8617i	0.620857	+	1.07536i	−0.368470	+	0.929640i	$0.620118\pi$
$192$		0			0
$193$	−5.44950	+	9.43881i	−0.392264	+	0.679420i	−0.992748	−	0.120216i	$-0.961641\pi$
$193$	−5.44950	+	9.43881i	−0.392264	+	0.679420i	0.600484	+	0.799637i	$0.294975\pi$
$194$		0			0
$195$	−16.5804			−1.18735
$196$		0			0
$197$	5.41959			0.386130			0.193065	−	0.981186i	$-0.438157\pi$
$197$	5.41959			0.386130			0.193065	+	0.981186i	$0.438157\pi$
$198$		0			0
$199$	−11.4931	+	19.9067i	−0.814727	+	1.41115i	0.0947970	+	0.995497i	$0.469780\pi$
$199$	−11.4931	+	19.9067i	−0.814727	+	1.41115i	−0.909524	+	0.415652i	$0.863554\pi$
$200$		0			0
$201$	2.01839	+	3.49595i	0.142366	+	0.246585i
$202$		0			0
$203$	3.31546	+	0.0734275i	0.232699	+	0.00515360i
$204$		0			0
$205$	6.98627	+	12.1006i	0.487942	+	0.845141i
$206$		0			0
$207$	−3.74657	+	6.48925i	−0.260404	+	0.451034i
$208$		0			0
$209$	−9.31859			−0.644580
$210$		0			0
$211$	−3.08727			−0.212537			−0.106268	−	0.994337i	$-0.533890\pi$
$211$	−3.08727			−0.212537			−0.106268	+	0.994337i	$0.533890\pi$
$212$		0			0
$213$	2.74657	−	4.75720i	0.188192	−	0.325958i
$214$		0			0
$215$	4.74657	+	8.22130i	0.323713	+	0.560688i
$216$		0			0
$217$	7.26496	−	11.9635i	0.493177	−	0.812132i
$218$		0			0
$219$	6.27182	+	10.8631i	0.423810	+	0.734061i
$220$		0			0
$221$	−22.6172	+	39.1741i	−1.52140	+	2.63514i
$222$		0			0
$223$	22.7466			1.52322			0.761611	−	0.648034i	$-0.224409\pi$
$223$	22.7466			1.52322			0.761611	+	0.648034i	$0.224409\pi$
$224$		0			0
$225$	2.54364			0.169576
$226$		0			0
$227$	11.3017	−	19.5752i	0.750122	−	1.29925i	−0.197641	−	0.980274i	$-0.563328\pi$
$227$	11.3017	−	19.5752i	0.750122	−	1.29925i	0.947763	−	0.318975i	$-0.103339\pi$
$228$		0			0
$229$	5.67768	+	9.83403i	0.375192	+	0.649851i	0.990356	−	0.138548i	$-0.0442435\pi$
$229$	5.67768	+	9.83403i	0.375192	+	0.649851i	−0.615164	+	0.788399i	$0.710910\pi$
$230$		0			0
$231$	−1.96323	−	3.58126i	−0.129171	−	0.235630i
$232$		0			0
$233$	−1.70979	−	2.96145i	−0.112012	−	0.194011i	0.804569	−	0.593859i	$-0.202396\pi$
$233$	−1.70979	−	2.96145i	−0.112012	−	0.194011i	−0.916582	+	0.399848i	$0.869063\pi$
$234$		0			0
$235$	13.0368	−	22.5804i	0.850425	−	1.47298i
$236$		0			0
$237$	−7.79707			−0.506474
$238$		0			0
$239$	7.49314			0.484691			0.242345	−	0.970190i	$-0.422083\pi$
$239$	7.49314			0.484691			0.242345	+	0.970190i	$0.422083\pi$
$240$		0			0
$241$	9.30173	−	16.1111i	0.599177	−	1.03781i	−0.393766	−	0.919211i	$-0.628828\pi$
$241$	9.30173	−	16.1111i	0.599177	−	1.03781i	0.992943	−	0.118594i	$-0.0378388\pi$
$242$		0			0
$243$	0.500000	+	0.866025i	0.0320750	+	0.0555556i
$244$		0			0
$245$	−8.86642	−	17.0594i	−0.566455	−	1.08989i
$246$		0			0
$247$	−18.2213	−	31.5602i	−1.15939	−	2.00813i
$248$		0			0
$249$	3.26496	−	5.65507i	0.206908	−	0.358375i
$250$		0			0
$251$	−24.5299			−1.54831			−0.774157	−	0.632994i	$-0.781826\pi$
$251$	−24.5299			−1.54831			−0.774157	+	0.632994i	$0.781826\pi$
$252$		0			0
$253$	−11.5667			−0.727191
$254$		0			0
$255$	10.2902	−	17.8232i	0.644398	−	1.11613i
$256$		0			0
$257$	8.74657	+	15.1495i	0.545596	+	0.945000i	0.998569	+	0.0534758i	$0.0170300\pi$
$257$	8.74657	+	15.1495i	0.545596	+	0.945000i	−0.452973	+	0.891524i	$0.649637\pi$
$258$		0			0
$259$	−6.29487	−	11.4829i	−0.391144	−	0.713514i
$260$		0			0
$261$	−0.626716	−	1.08550i	−0.0387927	−	0.0671910i
$262$		0			0
$263$	−6.74657	+	11.6854i	−0.416011	+	0.720553i	−0.995534	−	0.0944035i	$-0.969906\pi$
$263$	−6.74657	+	11.6854i	−0.416011	+	0.720553i	0.579523	+	0.814956i	$0.303239\pi$
$264$		0			0
$265$	−10.5299			−0.646847
$266$		0			0
$267$	9.49314			0.580971
$268$		0			0
$269$	−3.17035	+	5.49121i	−0.193300	+	0.334805i	−0.946342	−	0.323167i	$-0.895252\pi$
$269$	−3.17035	+	5.49121i	−0.193300	+	0.334805i	0.753042	+	0.657972i	$0.228586\pi$
$270$		0			0
$271$	−10.1199	−	17.5281i	−0.614737	−	1.06476i	−0.990431	−	0.138012i	$-0.955929\pi$
$271$	−10.1199	−	17.5281i	−0.614737	−	1.06476i	0.375693	−	0.926744i	$-0.377405\pi$
$272$		0			0
$273$	8.29021	−	13.6518i	0.501746	−	0.826243i
$274$		0			0
$275$	1.96323	+	3.40041i	0.118387	+	0.205052i
$276$		0			0
$277$	1.27182	−	2.20285i	0.0764162	−	0.132357i	−0.825285	−	0.564716i	$-0.808986\pi$
$277$	1.27182	−	2.20285i	0.0764162	−	0.132357i	0.901701	+	0.432360i	$0.142319\pi$
$278$		0			0
$279$	−5.29021			−0.316716
$280$		0			0
$281$	26.5804			1.58565			0.792827	−	0.609447i	$-0.208608\pi$
$281$	26.5804			1.58565			0.792827	+	0.609447i	$0.208608\pi$
$282$		0			0
$283$	−10.2718	+	17.7913i	−0.610596	+	1.05758i	0.380544	+	0.924763i	$0.375737\pi$
$283$	−10.2718	+	17.7913i	−0.610596	+	1.05758i	−0.991140	+	0.132821i	$0.957597\pi$
$284$		0			0
$285$	8.29021	+	14.3591i	0.491069	+	0.850557i
$286$		0			0
$287$	−13.4564	−	0.298018i	−0.794304	−	0.0175915i
$288$		0			0
$289$	−19.5735	−	33.9024i	−1.15139	−	1.99426i
$290$		0			0
$291$	0.771819	−	1.33683i	0.0452448	−	0.0783663i
$292$		0			0
$293$	5.25343			0.306909			0.153454	−	0.988156i	$-0.450960\pi$
$293$	5.25343			0.306909			0.153454	+	0.988156i	$0.450960\pi$
$294$		0			0
$295$	−15.2260			−0.886491
$296$		0			0
$297$	−0.771819	+	1.33683i	−0.0447855	+	0.0775707i
$298$		0			0
$299$	−22.6172	−	39.1741i	−1.30799	−	2.26550i
$300$		0			0
$301$	−9.14243	−	0.202478i	−0.526961	−	0.0116706i
$302$		0			0
$303$	−1.29021	−	2.23470i	−0.0741204	−	0.128380i
$304$		0			0
$305$	20.0230	−	34.6809i	1.14652	−	1.98582i
$306$		0			0
$307$	−14.8485			−0.847449			−0.423724	−	0.905791i	$-0.639277\pi$
$307$	−14.8485			−0.847449			−0.423724	+	0.905791i	$0.639277\pi$
$308$		0			0
$309$	6.54364			0.372255
$310$		0			0
$311$	−0.949499	+	1.64458i	−0.0538412	+	0.0932556i	−0.891690	−	0.452647i	$-0.850480\pi$
$311$	−0.949499	+	1.64458i	−0.0538412	+	0.0932556i	0.837849	+	0.545903i	$0.183813\pi$
$312$		0			0
$313$	0.0436371	+	0.0755817i	0.00246652	+	0.00427213i	0.867256	−	0.497862i	$-0.165882\pi$
$313$	0.0436371	+	0.0755817i	0.00246652	+	0.00427213i	−0.864790	+	0.502135i	$0.832548\pi$
$314$		0			0
$315$	−3.77182	+	6.21119i	−0.212518	+	0.349961i
$316$		0			0
$317$	−4.11985	−	7.13579i	−0.231394	−	0.400786i	0.726825	−	0.686823i	$-0.240995\pi$
$317$	−4.11985	−	7.13579i	−0.231394	−	0.400786i	−0.958219	+	0.286037i	$0.907662\pi$
$318$		0			0
$319$	0.967422	−	1.67562i	0.0541652	−	0.0938169i
$320$		0			0
$321$	−4.52991			−0.252835
$322$		0			0
$323$	45.2344			2.51691
$324$		0			0
$325$	−7.67768	+	13.2981i	−0.425881	+	0.737648i
$326$		0			0
$327$	−3.22132	−	5.57949i	−0.178139	−	0.308546i
$328$		0			0
$329$	12.0735	+	22.0242i	0.665636	+	1.21424i
$330$		0			0
$331$	−2.76496	−	4.78904i	−0.151976	−	0.263230i	0.779978	−	0.625807i	$-0.215230\pi$
$331$	−2.76496	−	4.78904i	−0.151976	−	0.263230i	−0.931954	+	0.362577i	$0.881897\pi$
$332$		0			0
$333$	−2.47475	+	4.28639i	−0.135615	+	0.234893i
$334$		0			0
$335$	11.0873			0.605763
$336$		0			0
$337$	7.17455			0.390823			0.195411	−	0.980721i	$-0.437396\pi$
$337$	7.17455			0.390823			0.195411	+	0.980721i	$0.437396\pi$
$338$		0			0
$339$	4.00000	−	6.92820i	0.217250	−	0.376288i
$340$		0			0
$341$	−4.08308	−	7.07210i	−0.221111	−	0.382976i
$342$		0			0
$343$	18.4794	+	1.22940i	0.997794	+	0.0663814i
$344$		0			0
$345$	10.2902	+	17.8232i	0.554006	+	0.959567i
$346$		0			0
$347$	12.0368	−	20.8483i	0.646168	−	1.11920i	−0.337863	−	0.941195i	$-0.609704\pi$
$347$	12.0368	−	20.8483i	0.646168	−	1.11920i	0.984030	−	0.178000i	$-0.0569627\pi$
$348$		0			0
$349$	−31.1608			−1.66800			−0.834000	−	0.551764i	$-0.813955\pi$
$349$	−31.1608			−1.66800			−0.834000	+	0.551764i	$0.813955\pi$
$350$		0			0
$351$	−6.03677			−0.322219
$352$		0			0
$353$	5.08727	−	8.81142i	0.270768	−	0.468984i	−0.698290	−	0.715814i	$-0.746056\pi$
$353$	5.08727	−	8.81142i	0.270768	−	0.468984i	0.969059	+	0.246830i	$0.0793889\pi$
$354$		0			0
$355$	−7.54364	−	13.0660i	−0.400375	−	0.693469i
$356$		0			0
$357$	9.52991	+	17.3842i	0.504376	+	0.920070i
$358$		0			0
$359$	−16.1240	−	27.9277i	−0.850995	−	1.47397i	−0.880312	−	0.474396i	$-0.842667\pi$
$359$	−16.1240	−	27.9277i	−0.850995	−	1.47397i	0.0293169	−	0.999570i	$-0.490667\pi$
$360$		0			0
$361$	−8.72132	+	15.1058i	−0.459017	+	0.795040i
$362$		0			0
$363$	8.61718			0.452285
$364$		0			0
$365$	34.4520			1.80330
$366$		0			0
$367$	1.93531	−	3.35205i	0.101022	−	0.174976i	−0.811084	−	0.584930i	$-0.801122\pi$
$367$	1.93531	−	3.35205i	0.101022	−	0.174976i	0.912106	+	0.409954i	$0.134455\pi$
$368$		0			0
$369$	2.54364	+	4.40571i	0.132416	+	0.229352i
$370$		0			0
$371$	5.26496	−	8.66999i	0.273343	−	0.450123i
$372$		0			0
$373$	−17.3454	−	30.0431i	−0.898109	−	1.55557i	−0.829909	−	0.557899i	$-0.811608\pi$
$373$	−17.3454	−	30.0431i	−0.898109	−	1.55557i	−0.0682000	−	0.997672i	$-0.521726\pi$
$374$		0			0
$375$	−3.37328	+	5.84270i	−0.174196	+	0.301716i
$376$		0			0
$377$	7.56668			0.389704
$378$		0			0
$379$	−13.4564			−0.691207			−0.345603	−	0.938381i	$-0.612326\pi$
$379$	−13.4564			−0.691207			−0.345603	+	0.938381i	$0.612326\pi$
$380$		0			0
$381$	−1.89853	+	3.28836i	−0.0972649	+	0.168468i
$382$		0			0
$383$	2.08727	+	3.61527i	0.106655	+	0.184731i	0.914413	−	0.404782i	$-0.132653\pi$
$383$	2.08727	+	3.61527i	0.106655	+	0.184731i	−0.807758	+	0.589514i	$0.799319\pi$
$384$		0			0
$385$	−11.2145	−	0.248367i	−0.571542	−	0.0126579i
$386$		0			0
$387$	1.72818	+	2.99330i	0.0878484	+	0.152158i
$388$		0			0
$389$	9.32698	−	16.1548i	0.472897	−	0.819081i	−0.526622	−	0.850099i	$-0.676542\pi$
$389$	9.32698	−	16.1548i	0.472897	−	0.819081i	0.999519	+	0.0310185i	$0.00987507\pi$
$390$		0			0
$391$	56.1471			2.83948
$392$		0			0
$393$	1.54364			0.0778662
$394$		0			0
$395$	−10.7076	+	18.5461i	−0.538757	+	0.933155i
$396$		0			0
$397$	0.728181	+	1.26125i	0.0365464	+	0.0633002i	0.883720	−	0.468016i	$-0.155031\pi$
$397$	0.728181	+	1.26125i	0.0365464	+	0.0633002i	−0.847174	+	0.531316i	$0.821698\pi$
$398$		0			0
$399$	−15.9679	−	0.353641i	−0.799394	−	0.0177042i
$400$		0			0
$401$	14.6172	+	25.3177i	0.729947	+	1.26431i	0.956905	+	0.290401i	$0.0937888\pi$
$401$	14.6172	+	25.3177i	0.729947	+	1.26431i	−0.226958	+	0.973905i	$0.572878\pi$
$402$		0			0
$403$	15.9679	−	27.6572i	0.795417	−	1.37770i
$404$		0			0
$405$	2.74657			0.136478
$406$		0			0
$407$	−7.64023			−0.378712
$408$		0			0
$409$	−13.0299	+	22.5685i	−0.644288	+	1.11594i	0.340178	+	0.940361i	$0.389513\pi$
$409$	−13.0299	+	22.5685i	−0.644288	+	1.11594i	−0.984466	+	0.175578i	$0.943821\pi$
$410$		0			0
$411$	0.746568	+	1.29309i	0.0368255	+	0.0637836i
$412$		0			0
$413$	7.61299	−	12.5366i	0.374611	−	0.616885i
$414$		0			0
$415$	−8.96742	−	15.5320i	−0.440193	−	0.762437i
$416$		0			0
$417$	1.47475	−	2.55434i	0.0722188	−	0.125087i
$418$		0			0
$419$	−32.8853			−1.60655			−0.803275	−	0.595608i	$-0.796911\pi$
$419$	−32.8853			−1.60655			−0.803275	+	0.595608i	$0.796911\pi$
$420$		0			0
$421$	−17.1976			−0.838160			−0.419080	−	0.907949i	$-0.637647\pi$
$421$	−17.1976			−0.838160			−0.419080	+	0.907949i	$0.637647\pi$
$422$		0			0
$423$	4.74657	−	8.22130i	0.230786	−	0.399733i
$424$		0			0
$425$	−9.52991	−	16.5063i	−0.462269	−	0.800673i
$426$		0			0
$427$	18.5436	+	33.8268i	0.897389	+	1.63699i
$428$		0			0
$429$	−4.65929	−	8.07013i	−0.224953	−	0.389630i
$430$		0			0
$431$	1.49314	−	2.58619i	0.0719219	−	0.124572i	−0.827822	−	0.560991i	$-0.810420\pi$
$431$	1.49314	−	2.58619i	0.0719219	−	0.124572i	0.899744	+	0.436419i	$0.143753\pi$
$432$		0			0
$433$	18.4426			0.886297			0.443148	−	0.896448i	$-0.353862\pi$
$433$	18.4426			0.886297			0.443148	+	0.896448i	$0.353862\pi$
$434$		0			0
$435$	−3.44264			−0.165062
$436$		0			0
$437$	−22.6172	+	39.1741i	−1.08193	+	1.87395i
$438$		0			0
$439$	0.286010	+	0.495384i	0.0136505	+	0.0236434i	0.872770	−	0.488132i	$-0.162321\pi$
$439$	0.286010	+	0.495384i	0.0136505	+	0.0236434i	−0.859119	+	0.511775i	$0.828988\pi$
$440$		0			0
$441$	−3.22818	−	6.21119i	−0.153723	−	0.295771i
$442$		0			0
$443$	18.2650	+	31.6358i	0.867794	+	1.50306i	0.864246	+	0.503070i	$0.167796\pi$
$443$	18.2650	+	31.6358i	0.867794	+	1.50306i	0.00354850	+	0.999994i	$0.498870\pi$
$444$		0			0
$445$	13.0368	−	22.5804i	0.618002	−	1.07041i
$446$		0			0
$447$	1.49314			0.0706229
$448$		0			0
$449$	−22.5530			−1.06434			−0.532170	−	0.846638i	$-0.678623\pi$
$449$	−22.5530			−1.06434			−0.532170	+	0.846638i	$0.678623\pi$
$450$		0			0
$451$	−3.92645	+	6.80082i	−0.184889	+	0.320238i
$452$		0			0
$453$	−4.86642	−	8.42889i	−0.228644	−	0.396024i
$454$		0			0
$455$	−21.0873	−	38.4668i	−0.988587	−	1.80335i
$456$		0			0
$457$	−10.1172	−	17.5235i	−0.473262	−	0.819714i	0.526270	−	0.850318i	$-0.323590\pi$
$457$	−10.1172	−	17.5235i	−0.473262	−	0.819714i	−0.999532	+	0.0306040i	$0.990257\pi$
$458$		0			0
$459$	3.74657	−	6.48925i	0.174875	−	0.302892i
$460$		0			0
$461$	25.4931			1.18733			0.593667	−	0.804711i	$-0.297680\pi$
$461$	25.4931			1.18733			0.593667	+	0.804711i	$0.297680\pi$
$462$		0			0
$463$	7.70446			0.358057			0.179028	−	0.983844i	$-0.442705\pi$
$463$	7.70446			0.358057			0.179028	+	0.983844i	$0.442705\pi$
$464$		0			0
$465$	−7.26496	+	12.5833i	−0.336904	+	0.583535i
$466$		0			0
$467$	18.0735	+	31.3043i	0.836344	+	1.44859i	0.892931	+	0.450193i	$0.148645\pi$
$467$	18.0735	+	31.3043i	0.836344	+	1.44859i	−0.0565874	+	0.998398i	$0.518022\pi$
$468$		0			0
$469$	−5.54364	+	9.12890i	−0.255981	+	0.421534i
$470$		0			0
$471$	4.54364	+	7.86981i	0.209360	+	0.362622i
$472$		0			0
$473$	−2.66769	+	4.62057i	−0.122660	+	0.212454i
$474$		0			0
$475$	15.3554			0.704552
$476$		0			0
$477$	−3.83384			−0.175540
$478$		0			0
$479$	13.2902	−	23.0193i	0.607245	−	1.05178i	−0.384447	−	0.923147i	$-0.625608\pi$
$479$	13.2902	−	23.0193i	0.607245	−	1.05178i	0.991692	−	0.128632i	$-0.0410587\pi$
$480$		0			0
$481$	−14.9395	−	25.8760i	−0.681183	−	1.17984i
$482$		0			0
$483$	−19.8201	−	0.438957i	−0.901846	−	0.0199732i
$484$		0			0
$485$	−2.11985	−	3.67169i	−0.0962575	−	0.166723i
$486$		0			0
$487$	−20.2118	+	35.0078i	−0.915883	+	1.58636i	−0.110281	+	0.993900i	$0.535175\pi$
$487$	−20.2118	+	35.0078i	−0.915883	+	1.58636i	−0.805603	+	0.592456i	$0.798158\pi$
$488$		0			0
$489$	19.5667			0.884836
$490$		0			0
$491$	−14.6309			−0.660284			−0.330142	−	0.943931i	$-0.607097\pi$
$491$	−14.6309			−0.660284			−0.330142	+	0.943931i	$0.607097\pi$
$492$		0			0
$493$	−4.69607	+	8.13383i	−0.211500	+	0.366329i
$494$		0			0
$495$	2.11985	+	3.67169i	0.0952803	+	0.165030i
$496$		0			0
$497$	14.5299	+	0.321794i	0.651756	+	0.0144344i
$498$		0			0
$499$	−18.0552	−	31.2725i	−0.808260	−	1.39995i	−0.914068	−	0.405561i	$-0.867076\pi$
$499$	−18.0552	−	31.2725i	−0.808260	−	1.39995i	0.105808	−	0.994387i	$-0.466257\pi$
$500$		0			0
$501$	5.94950	−	10.3048i	0.265804	−	0.460386i
$502$		0			0
$503$	−19.4931			−0.869156			−0.434578	−	0.900634i	$-0.643102\pi$
$503$	−19.4931			−0.869156			−0.434578	+	0.900634i	$0.643102\pi$
$504$		0			0
$505$	−7.08727			−0.315380
$506$		0			0
$507$	11.7213	−	20.3019i	0.520562	−	0.901640i
$508$		0			0
$509$	11.9537	+	20.7044i	0.529838	+	0.917707i	0.999394	+	0.0348040i	$0.0110807\pi$
$509$	11.9537	+	20.7044i	0.529838	+	0.917707i	−0.469556	+	0.882903i	$0.655586\pi$
$510$		0			0
$511$	−17.2260	+	28.3666i	−0.762032	+	1.25487i
$512$		0			0
$513$	3.01839	+	5.22800i	0.133265	+	0.230822i
$514$		0			0
$515$	8.98627	−	15.5647i	0.395982	−	0.685862i
$516$		0			0
$517$	14.6540			0.644480
$518$		0			0
$519$	−2.58041			−0.113267
$520$		0			0
$521$	3.54364	−	6.13776i	0.155250	−	0.268900i	−0.777900	−	0.628388i	$-0.783715\pi$
$521$	3.54364	−	6.13776i	0.155250	−	0.268900i	0.933150	+	0.359488i	$0.117048\pi$
$522$		0			0
$523$	−14.3737	−	24.8961i	−0.628520	−	1.08863i	−0.987849	−	0.155418i	$-0.950328\pi$
$523$	−14.3737	−	24.8961i	−0.628520	−	1.08863i	0.359329	−	0.933211i	$-0.383006\pi$
$524$		0			0
$525$	3.23504	+	5.90128i	0.141189	+	0.257553i
$526$		0			0
$527$	19.8201	+	34.3294i	0.863378	+	1.49541i
$528$		0			0
$529$	−16.5735	+	28.7062i	−0.720589	+	1.24810i
$530$		0			0
$531$	−5.54364			−0.240573
$532$		0			0
$533$	−30.7107			−1.33023
$534$		0			0
$535$	−6.22085	+	10.7748i	−0.268951	+	0.465837i
$536$		0			0
$537$	1.49314	+	2.58619i	0.0644336	+	0.111602i
$538$		0			0
$539$	5.81172	−	9.10944i	0.250329	−	0.392371i
$540$		0			0
$541$	3.51152	+	6.08214i	0.150972	+	0.261491i	0.931585	−	0.363523i	$-0.118426\pi$
$541$	3.51152	+	6.08214i	0.150972	+	0.261491i	−0.780613	+	0.625015i	$0.785093\pi$
$542$		0			0
$543$	−5.27182	+	9.13106i	−0.226235	+	0.391851i
$544$		0			0
$545$	−17.6951			−0.757976
$546$		0			0
$547$	−5.59414			−0.239188			−0.119594	−	0.992823i	$-0.538159\pi$
$547$	−5.59414			−0.239188			−0.119594	+	0.992823i	$0.538159\pi$
$548$		0			0
$549$	7.29021	−	12.6270i	0.311138	−	0.538907i
$550$		0			0
$551$	−3.78334	−	6.55294i	−0.161176	−	0.279165i
$552$		0			0
$553$	−9.91646	−	18.0893i	−0.421691	−	0.769237i
$554$		0			0
$555$	6.79707	+	11.7729i	0.288520	+	0.499730i
$556$		0			0
$557$	−14.3228	+	24.8078i	−0.606876	+	1.05114i	0.384876	+	0.922968i	$0.374244\pi$
$557$	−14.3228	+	24.8078i	−0.606876	+	1.05114i	−0.991752	+	0.128172i	$0.959089\pi$
$558$		0			0
$559$	−20.8653			−0.882507
$560$		0			0
$561$	11.5667			0.488346
$562$		0			0
$563$	−9.94637	+	17.2276i	−0.419189	+	0.726057i	−0.995858	−	0.0909207i	$-0.971019\pi$
$563$	−9.94637	+	17.2276i	−0.419189	+	0.726057i	0.576669	+	0.816978i	$0.304352\pi$
$564$		0			0
$565$	−10.9863	−	19.0288i	−0.462196	−	0.800547i
$566$		0			0
$567$	−1.37328	+	2.26144i	−0.0576725	+	0.0949714i
$568$		0			0
$569$	−17.8201	−	30.8653i	−0.747058	−	1.29394i	−0.949227	−	0.314592i	$-0.898132\pi$
$569$	−17.8201	−	30.8653i	−0.747058	−	1.29394i	0.202169	−	0.979351i	$-0.435201\pi$
$570$		0			0
$571$	−13.8385	+	23.9690i	−0.579123	+	1.00307i	0.416457	+	0.909155i	$0.363272\pi$
$571$	−13.8385	+	23.9690i	−0.579123	+	1.00307i	−0.995580	+	0.0939155i	$0.970062\pi$
$572$		0			0
$573$	17.1608			0.716904
$574$		0			0
$575$	19.0598			0.794849
$576$		0			0
$577$	3.00686	−	5.20804i	0.125177	−	0.216814i	−0.796625	−	0.604474i	$-0.793383\pi$
$577$	3.00686	−	5.20804i	0.125177	−	0.216814i	0.921802	+	0.387660i	$0.126717\pi$
$578$		0			0
$579$	5.44950	+	9.43881i	0.226473	+	0.392264i
$580$		0			0
$581$	17.2723	+	0.382530i	0.716575	+	0.0158700i
$582$		0			0
$583$	−2.95903	−	5.12519i	−0.122551	−	0.212264i
$584$		0			0
$585$	−8.29021	+	14.3591i	−0.342758	+	0.593674i
$586$		0			0
$587$	−15.5436			−0.641555			−0.320777	−	0.947155i	$-0.603944\pi$
$587$	−15.5436			−0.641555			−0.320777	+	0.947155i	$0.603944\pi$
$588$		0			0
$589$	−31.9358			−1.31589
$590$		0			0
$591$	2.70979	−	4.69350i	0.111466	−	0.193065i
$592$		0			0
$593$	24.3270	+	42.1356i	0.998989	+	1.73030i	0.538421	+	0.842676i	$0.319021\pi$
$593$	24.3270	+	42.1356i	0.998989	+	1.73030i	0.460568	+	0.887624i	$0.347646\pi$
$594$		0			0
$595$	54.4373	+	1.20562i	2.23171	+	0.0494258i
$596$		0			0
$597$	11.4931	+	19.9067i	0.470383	+	0.814727i
$598$		0			0
$599$	−10.4564	+	18.1110i	−0.427235	+	0.739993i	−0.996626	−	0.0820735i	$-0.973846\pi$
$599$	−10.4564	+	18.1110i	−0.427235	+	0.739993i	0.569391	+	0.822067i	$0.307179\pi$
$600$		0			0
$601$	−7.98627			−0.325767			−0.162883	−	0.986645i	$-0.552079\pi$
$601$	−7.98627			−0.325767			−0.162883	+	0.986645i	$0.552079\pi$
$602$		0			0
$603$	4.03677			0.164390
$604$		0			0
$605$	11.8338	−	20.4968i	0.481114	−	0.833314i
$606$		0			0
$607$	1.35490	+	2.34675i	0.0549936	+	0.0952517i	0.892212	−	0.451618i	$-0.149153\pi$
$607$	1.35490	+	2.34675i	0.0549936	+	0.0952517i	−0.837218	+	0.546869i	$0.815819\pi$
$608$		0			0
$609$	1.72132	−	2.83456i	0.0697513	−	0.114862i
$610$		0			0
$611$	28.6540	+	49.6301i	1.15922	+	2.00782i
$612$		0			0
$613$	8.25343	−	14.2954i	0.333353	−	0.577384i	−0.649814	−	0.760093i	$-0.725153\pi$
$613$	8.25343	−	14.2954i	0.333353	−	0.577384i	0.983167	+	0.182709i	$0.0584866\pi$
$614$		0			0
$615$	13.9725			0.563427
$616$		0			0
$617$	−23.1608			−0.932420			−0.466210	−	0.884674i	$-0.654381\pi$
$617$	−23.1608			−0.932420			−0.466210	+	0.884674i	$0.654381\pi$
$618$		0			0
$619$	−14.7145	+	25.4862i	−0.591424	+	1.02438i	0.402617	+	0.915369i	$0.368101\pi$
$619$	−14.7145	+	25.4862i	−0.591424	+	1.02438i	−0.994041	+	0.109008i	$0.965233\pi$
$620$		0			0
$621$	3.74657	+	6.48925i	0.150345	+	0.260404i
$622$		0			0
$623$	12.0735	+	22.0242i	0.483716	+	0.882382i
$624$		0			0
$625$	15.6240	+	27.0616i	0.624962	+	1.08247i
$626$		0			0
$627$	−4.65929	+	8.07013i	−0.186074	+	0.322290i
$628$		0			0
$629$	37.0873			1.47877
$630$		0			0
$631$	35.7054			1.42141			0.710705	−	0.703491i	$-0.248376\pi$
$631$	35.7054			1.42141			0.710705	+	0.703491i	$0.248376\pi$
$632$		0			0
$633$	−1.54364	+	2.67366i	−0.0613541	+	0.106268i
$634$		0			0
$635$	5.21445	+	9.03170i	0.206929	+	0.358412i
$636$		0			0
$637$	42.2160	+	1.87083i	1.67266	+	0.0741252i
$638$		0			0
$639$	−2.74657	−	4.75720i	−0.108653	−	0.188192i
$640$		0			0
$641$	1.68141	−	2.91229i	0.0664118	−	0.115029i	−0.830908	−	0.556410i	$-0.812178\pi$
$641$	1.68141	−	2.91229i	0.0664118	−	0.115029i	0.897319	+	0.441382i	$0.145512\pi$
$642$		0			0
$643$	−10.2113			−0.402695			−0.201348	−	0.979520i	$-0.564532\pi$
$643$	−10.2113			−0.402695			−0.201348	+	0.979520i	$0.564532\pi$
$644$		0			0
$645$	9.49314			0.373792
$646$		0			0
$647$	−10.2765	+	17.7994i	−0.404010	+	0.699766i	−0.994206	−	0.107494i	$-0.965717\pi$
$647$	−10.2765	+	17.7994i	−0.404010	+	0.699766i	0.590196	+	0.807260i	$0.299051\pi$
$648$		0			0
$649$	−4.27868	−	7.41089i	−0.167953	−	0.290903i
$650$		0			0
$651$	−6.72818	−	12.2734i	−0.263698	−	0.481031i
$652$		0			0
$653$	5.67722	+	9.83323i	0.222167	+	0.384804i	0.955466	−	0.295102i	$-0.0953538\pi$
$653$	5.67722	+	9.83323i	0.222167	+	0.384804i	−0.733299	+	0.679906i	$0.762020\pi$
$654$		0			0
$655$	2.11985	−	3.67169i	0.0828295	−	0.143465i
$656$		0			0
$657$	12.5436			0.489374
$658$		0			0
$659$	−21.2344			−0.827174			−0.413587	−	0.910465i	$-0.635724\pi$
$659$	−21.2344			−0.827174			−0.413587	+	0.910465i	$0.635724\pi$
$660$		0			0
$661$	14.4610	−	25.0472i	0.562469	−	0.974224i	−0.434812	−	0.900521i	$-0.643185\pi$
$661$	14.4610	−	25.0472i	0.562469	−	0.974224i	0.997280	−	0.0737028i	$-0.0234816\pi$
$662$		0			0
$663$	22.6172	+	39.1741i	0.878379	+	1.52140i
$664$		0			0
$665$	−22.7696	+	37.4955i	−0.882968	+	1.45401i
$666$		0			0
$667$	−4.69607	−	8.13383i	−0.181832	−	0.314943i
$668$		0			0
$669$	11.3733	−	19.6991i	0.439717	−	0.761611i
$670$		0			0
$671$	22.5069			0.868868
$672$		0			0
$673$	−34.2618			−1.32070			−0.660348	−	0.750960i	$-0.729591\pi$
$673$	−34.2618			−1.32070			−0.660348	+	0.750960i	$0.729591\pi$
$674$		0			0
$675$	1.27182	−	2.20285i	0.0489523	−	0.0847879i
$676$		0			0
$677$	−17.3733	−	30.0914i	−0.667710	−	1.15651i	−0.978543	−	0.206042i	$-0.933941\pi$
$677$	−17.3733	−	30.0914i	−0.667710	−	1.15651i	0.310833	−	0.950464i	$-0.399392\pi$
$678$		0			0
$679$	4.08308	+	0.0904281i	0.156694	+	0.00347031i
$680$		0			0
$681$	−11.3017	−	19.5752i	−0.433083	−	0.750122i
$682$		0			0
$683$	0.140907	−	0.244058i	0.00539166	−	0.00933863i	−0.863317	−	0.504662i	$-0.831617\pi$
$683$	0.140907	−	0.244058i	0.00539166	−	0.00933863i	0.868709	+	0.495323i	$0.164950\pi$
$684$		0			0
$685$	4.10100			0.156691
$686$		0			0
$687$	11.3554			0.433234
$688$		0			0
$689$	11.5720	−	20.0433i	0.440859	−	0.763590i
$690$		0			0
$691$	17.2076	+	29.8044i	0.654608	+	1.13381i	0.981992	+	0.188922i	$0.0604995\pi$
$691$	17.2076	+	29.8044i	0.654608	+	1.13381i	−0.327384	+	0.944891i	$0.606167\pi$
$692$		0			0
$693$	−4.08308	−	0.0904281i	−0.155103	−	0.00343508i
$694$		0			0
$695$	−4.05050	−	7.01567i	−0.153644	−	0.266120i
$696$		0			0
$697$	19.0598	−	33.0126i	0.721942	−	1.25044i
$698$		0			0
$699$	−3.41959			−0.129341
$700$		0			0
$701$	−0.498472			−0.0188270			−0.00941352	−	0.999956i	$-0.502996\pi$
$701$	−0.498472			−0.0188270			−0.00941352	+	0.999956i	$0.502996\pi$
$702$		0			0
$703$	−14.9395	+	25.8760i	−0.563454	+	0.975931i
$704$		0			0
$705$	−13.0368	−	22.5804i	−0.490993	−	0.850425i
$706$		0			0
$707$	3.54364	−	5.83543i	0.133272	−	0.219464i
$708$		0			0
$709$	2.08727	+	3.61527i	0.0783892	+	0.135774i	0.902555	−	0.430574i	$-0.141689\pi$
$709$	2.08727	+	3.61527i	0.0783892	+	0.135774i	−0.824166	+	0.566348i	$0.808356\pi$
$710$		0			0
$711$	−3.89853	+	6.75246i	−0.146206	+	0.253237i
$712$		0			0
$713$	−39.6402			−1.48454
$714$		0			0
$715$	−25.5941			−0.957166
$716$		0			0
$717$	3.74657	−	6.48925i	0.139918	−	0.242345i
$718$		0			0
$719$	−0.493136	−	0.854137i	−0.0183909	−	0.0318540i	0.856683	−	0.515842i	$-0.172521\pi$
$719$	−0.493136	−	0.854137i	−0.0183909	−	0.0318540i	−0.875074	+	0.483988i	$0.839188\pi$
$720$		0			0
$721$	8.32232	+	15.1813i	0.309939	+	0.565383i
$722$		0			0
$723$	−9.30173	−	16.1111i	−0.345935	−	0.599177i
$724$		0			0
$725$	−1.59414	+	2.76113i	−0.0592048	+	0.102546i
$726$		0			0
$727$	34.9304			1.29550			0.647749	−	0.761854i	$-0.275711\pi$
$727$	34.9304			1.29550			0.647749	+	0.761854i	$0.275711\pi$
$728$		0			0
$729$	1.00000			0.0370370
$730$		0			0
$731$	12.9495	−	22.4292i	0.478955	−	0.829574i
$732$		0			0
$733$	−2.56202	−	4.43756i	−0.0946305	−	0.163905i	0.814824	−	0.579709i	$-0.196834\pi$
$733$	−2.56202	−	4.43756i	−0.0946305	−	0.163905i	−0.909454	+	0.415804i	$0.863500\pi$
$734$		0			0
$735$	−19.2071	−	0.851179i	−0.708466	−	0.0313962i
$736$		0			0
$737$	3.11566	+	5.39648i	0.114767	+	0.198782i
$738$		0			0
$739$	−8.46102	+	14.6549i	−0.311244	+	0.539090i	−0.978632	−	0.205620i	$-0.934079\pi$
$739$	−8.46102	+	14.6549i	−0.311244	+	0.539090i	0.667388	+	0.744710i	$0.267412\pi$
$740$		0			0
$741$	−36.4426			−1.33875
$742$		0			0
$743$	−6.81172			−0.249898			−0.124949	−	0.992163i	$-0.539877\pi$
$743$	−6.81172			−0.249898			−0.124949	+	0.992163i	$0.539877\pi$
$744$		0			0
$745$	2.05050	−	3.55157i	0.0751245	−	0.130120i
$746$		0			0
$747$	−3.26496	−	5.65507i	−0.119458	−	0.206908i
$748$		0			0
$749$	−5.76122	−	10.5095i	−0.210511	−	0.384008i
$750$		0			0
$751$	−13.0877	−	22.6686i	−0.477578	−	0.827190i	0.522091	−	0.852890i	$-0.325152\pi$
$751$	−13.0877	−	22.6686i	−0.477578	−	0.827190i	−0.999670	+	0.0256996i	$0.991819\pi$
$752$		0			0
$753$	−12.2650	+	21.2435i	−0.446960	+	0.774157i
$754$		0			0
$755$	−26.7319			−0.972874
$756$		0			0
$757$	49.7138			1.80688			0.903439	−	0.428717i	$-0.141034\pi$
$757$	49.7138			1.80688			0.903439	+	0.428717i	$0.141034\pi$
$758$		0			0
$759$	−5.78334	+	10.0170i	−0.209922	+	0.363596i
$760$		0			0
$761$	6.32698	+	10.9586i	0.229353	+	0.397251i	0.957616	−	0.288046i	$-0.0930057\pi$
$761$	6.32698	+	10.9586i	0.229353	+	0.397251i	−0.728264	+	0.685297i	$0.759672\pi$
$762$		0			0
$763$	8.84757	−	14.5696i	0.320304	−	0.527455i
$764$		0			0
$765$	−10.2902	−	17.8232i	−0.372043	−	0.644398i
$766$		0			0
$767$	16.7328	−	28.9821i	0.604188	−	1.04648i
$768$		0			0
$769$	−20.2344			−0.729670			−0.364835	−	0.931072i	$-0.618875\pi$
$769$	−20.2344			−0.729670			−0.364835	+	0.931072i	$0.618875\pi$
$770$		0			0
$771$	17.4931			0.630000
$772$		0			0
$773$	9.87062	−	17.0964i	0.355021	−	0.614915i	−0.632100	−	0.774887i	$-0.717807\pi$
$773$	9.87062	−	17.0964i	0.355021	−	0.614915i	0.987122	+	0.159972i	$0.0511402\pi$
$774$		0			0
$775$	6.72818	+	11.6536i	0.241683	+	0.418608i
$776$		0			0
$777$	−13.0919	−	0.289947i	−0.469671	−	0.0104018i
$778$		0			0
$779$	15.3554	+	26.5963i	0.550163	+	0.952910i
$780$		0			0
$781$	4.23970	−	7.34338i	0.151709	−	0.262767i
$782$		0			0
$783$	−1.25343			−0.0447940
$784$		0			0
$785$	24.9588			0.890818
$786$		0			0
$787$	−8.45636	+	14.6469i	−0.301437	+	0.522104i	−0.976462	−	0.215691i	$-0.930800\pi$
$787$	−8.45636	+	14.6469i	−0.301437	+	0.522104i	0.675025	+	0.737795i	$0.264133\pi$
$788$		0			0
$789$	6.74657	+	11.6854i	0.240184	+	0.416011i
$790$		0			0
$791$	21.1608	+	0.468649i	0.752392	+	0.0166633i
$792$		0			0
$793$	44.0093	+	76.2264i	1.56282	+	2.70688i
$794$		0			0
$795$	−5.26496	+	9.11917i	−0.186729	+	0.323424i
$796$		0			0
$797$	3.48475			0.123436			0.0617180	−	0.998094i	$-0.480342\pi$
$797$	3.48475			0.123436			0.0617180	+	0.998094i	$0.480342\pi$
$798$		0			0
$799$	−71.1334			−2.51652
$800$		0			0
$801$	4.74657	−	8.22130i	0.167712	−	0.290485i
$802$		0			0
$803$	9.68141	+	16.7687i	0.341650	+	0.591754i
$804$		0			0
$805$	−28.2628	+	46.5413i	−0.996131	+	1.64036i
$806$		0			0
$807$	3.17035	+	5.49121i	0.111602	+	0.193300i
$808$		0			0
$809$	9.59414	−	16.6175i	0.337312	−	0.584241i	−0.646614	−	0.762817i	$-0.723816\pi$
$809$	9.59414	−	16.6175i	0.337312	−	0.584241i	0.983926	+	0.178576i	$0.0571490\pi$
$810$		0			0
$811$	48.8285			1.71460			0.857300	−	0.514817i	$-0.172140\pi$
$811$	48.8285			1.71460			0.857300	+	0.514817i	$0.172140\pi$
$812$		0			0
$813$	−20.2397			−0.709837
$814$		0			0
$815$	26.8706	−	46.5413i	0.941237	−	1.63027i
$816$		0			0
$817$	10.4326	+	18.0699i	0.364992	+	0.632184i
$818$		0			0
$819$	−7.67768	−	14.0054i	−0.268280	−	0.489389i
$820$		0			0
$821$	13.2723	+	22.9883i	0.463206	+	0.802296i	0.999119	−	0.0419773i	$-0.0133657\pi$
$821$	13.2723	+	22.9883i	0.463206	+	0.802296i	−0.535913	+	0.844273i	$0.680032\pi$
$822$		0			0
$823$	8.47941	−	14.6868i	0.295574	−	0.511949i	−0.679545	−	0.733634i	$-0.737823\pi$
$823$	8.47941	−	14.6868i	0.295574	−	0.511949i	0.975118	+	0.221686i	$0.0711559\pi$
$824$		0			0
$825$	3.92645			0.136702
$826$		0			0
$827$	−42.4289			−1.47540			−0.737699	−	0.675130i	$-0.764088\pi$
$827$	−42.4289			−1.47540			−0.737699	+	0.675130i	$0.764088\pi$
$828$		0			0
$829$	15.9679	−	27.6572i	0.554588	−	0.960574i	−0.443348	−	0.896350i	$-0.646209\pi$
$829$	15.9679	−	27.6572i	0.554588	−	0.960574i	0.997935	−	0.0642243i	$-0.0204573\pi$
$830$		0			0
$831$	−1.27182	−	2.20285i	−0.0441189	−	0.0764162i
$832$		0			0
$833$	−28.2113	+	44.2191i	−0.977464	+	1.53210i
$834$		0			0
$835$	−16.3407	−	28.3029i	−0.565493	−	0.979463i
$836$		0			0
$837$	−2.64510	+	4.58145i	−0.0914281	+	0.158358i
$838$		0			0
$839$	−49.5392			−1.71028			−0.855142	−	0.518394i	$-0.826530\pi$
$839$	−49.5392			−1.71028			−0.855142	+	0.518394i	$0.826530\pi$
$840$		0			0
$841$	−27.4289			−0.945824
$842$		0			0
$843$	13.2902	−	23.0193i	0.457739	−	0.792827i
$844$		0			0
$845$	−32.1934	−	55.7606i	−1.10749	−	1.91822i
$846$		0			0
$847$	10.9595	+	19.9920i	0.376573	+	0.686934i
$848$		0			0
$849$	10.2718	+	17.7913i	0.352528	+	0.610596i
$850$		0			0
$851$	−18.5436	+	32.1185i	−0.635668	+	1.10101i
$852$		0			0
$853$	11.4564			0.392258			0.196129	−	0.980578i	$-0.437163\pi$
$853$	11.4564			0.392258			0.196129	+	0.980578i	$0.437163\pi$
$854$		0			0
$855$	16.5804			0.567038
$856$		0			0
$857$	16.1240	−	27.9277i	0.550787	−	0.953991i	−0.447431	−	0.894318i	$-0.647661\pi$
$857$	16.1240	−	27.9277i	0.550787	−	0.953991i	0.998218	−	0.0596726i	$-0.0190057\pi$
$858$		0			0
$859$	−1.54364	−	2.67366i	−0.0526682	−	0.0912240i	0.838489	−	0.544918i	$-0.183439\pi$
$859$	−1.54364	−	2.67366i	−0.0526682	−	0.0912240i	−0.891158	+	0.453694i	$0.850106\pi$
$860$		0			0
$861$	−6.98627	+	11.5045i	−0.238092	+	0.392074i
$862$		0			0
$863$	−9.07355	−	15.7158i	−0.308867	−	0.534974i	0.669248	−	0.743039i	$-0.266617\pi$
$863$	−9.07355	−	15.7158i	−0.308867	−	0.534974i	−0.978115	+	0.208066i	$0.933283\pi$
$864$		0			0
$865$	−3.54364	+	6.13776i	−0.120487	+	0.208690i
$866$		0			0
$867$	−39.1471			−1.32951
$868$		0			0
$869$	−12.0358			−0.408288
$870$		0			0
$871$	−12.1845	+	21.1042i	−0.412858	+	0.715090i
$872$		0			0
$873$	−0.771819	−	1.33683i	−0.0261221	−	0.0452448i
$874$		0			0
$875$	−17.8454	−	0.395222i	−0.603283	−	0.0133609i
$876$		0			0
$877$	−4.44264	−	7.69487i	−0.150017	−	0.259837i	0.781216	−	0.624260i	$-0.214600\pi$
$877$	−4.44264	−	7.69487i	−0.150017	−	0.259837i	−0.931234	+	0.364423i	$0.881266\pi$
$878$		0			0
$879$	2.62672	−	4.54961i	0.0885969	−	0.153454i
$880$		0			0
$881$	−41.5667			−1.40042			−0.700209	−	0.713938i	$-0.746910\pi$
$881$	−41.5667			−1.40042			−0.700209	+	0.713938i	$0.746910\pi$
$882$		0			0
$883$	28.7182			0.966444			0.483222	−	0.875498i	$-0.339466\pi$
$883$	28.7182			0.966444			0.483222	+	0.875498i	$0.339466\pi$
$884$		0			0
$885$	−7.61299	+	13.1861i	−0.255908	+	0.443245i
$886$		0			0
$887$	−20.9074	−	36.2127i	−0.702001	−	1.21590i	−0.967763	−	0.251863i	$-0.918957\pi$
$887$	−20.9074	−	36.2127i	−0.702001	−	1.21590i	0.265761	−	0.964039i	$-0.414377\pi$
$888$		0			0
$889$	−10.0436	−	0.222437i	−0.336853	−	0.00746029i
$890$		0			0
$891$	0.771819	+	1.33683i	0.0258569	+	0.0447855i
$892$		0			0
$893$	28.6540	−	49.6301i	0.958868	−	1.66081i
$894$		0			0
$895$	8.20200			0.274163
$896$		0			0
$897$	−45.2344			−1.51033
$898$		0			0
$899$	3.31546	−	5.74254i	0.110577	−	0.191524i
$900$		0			0
$901$	14.3638	+	24.8787i	0.478526	+	0.828831i
$902$		0			0
$903$	−4.74657	+	7.81634i	−0.157956	+	0.260112i
$904$		0			0
$905$	14.4794	+	25.0791i	0.481312	+	0.833657i
$906$		0			0
$907$	28.5851	−	49.5108i	0.949152	−	1.64398i	0.201935	−	0.979399i	$-0.435277\pi$
$907$	28.5851	−	49.5108i	0.949152	−	1.64398i	0.747217	−	0.664580i	$-0.231389\pi$
$908$		0			0
$909$	−2.58041			−0.0855868
$910$		0			0
$911$	−24.4059			−0.808602			−0.404301	−	0.914626i	$-0.632485\pi$
$911$	−24.4059			−0.808602			−0.404301	+	0.914626i	$0.632485\pi$
$912$		0			0
$913$	5.03991	−	8.72937i	0.166797	−	0.288900i
$914$		0			0
$915$	−20.0230	−	34.6809i	−0.661942	−	1.14652i
$916$		0			0
$917$	1.96323	+	3.58126i	0.0648314	+	0.118264i
$918$		0			0
$919$	−23.8522	−	41.3133i	−0.786812	−	1.36280i	−0.927910	−	0.372803i	$-0.878397\pi$
$919$	−23.8522	−	41.3133i	−0.786812	−	1.36280i	0.141098	−	0.989996i	$-0.454937\pi$
$920$		0			0
$921$	−7.42425	+	12.8592i	−0.244637	+	0.423724i
$922$		0			0
$923$	33.1608			1.09150
$924$		0			0
$925$	12.5897			0.413948
$926$		0			0
$927$	3.27182	−	5.66696i	0.107461	−	0.186127i
$928$		0			0
$929$	−19.6172	−	33.9780i	−0.643619	−	1.11478i	−0.984619	−	0.174717i	$-0.944099\pi$
$929$	−19.6172	−	33.9780i	−0.643619	−	1.11478i	0.341000	−	0.940063i	$-0.389234\pi$
$930$		0			0
$931$	−19.4878	−	37.4955i	−0.638687	−	1.22887i
$932$		0			0
$933$	0.949499	+	1.64458i	0.0310852	+	0.0538412i
$934$		0			0
$935$	15.8843	−	27.5125i	0.519474	−	0.899755i
$936$		0			0
$937$	15.3491			0.501433			0.250717	−	0.968061i	$-0.419334\pi$
$937$	15.3491			0.501433			0.250717	+	0.968061i	$0.419334\pi$
$938$		0			0
$939$	0.0872743			0.00284809
$940$		0			0
$941$	6.08308	−	10.5362i	0.198303	−	0.343470i	−0.749676	−	0.661806i	$-0.769790\pi$
$941$	6.08308	−	10.5362i	0.198303	−	0.343470i	0.947978	+	0.318335i	$0.103124\pi$
$942$		0			0
$943$	19.0598	+	33.0126i	0.620673	+	1.07504i
$944$		0			0
$945$	3.49314	+	6.37208i	0.113632	+	0.207284i
$946$		0			0
$947$	9.52991	+	16.5063i	0.309680	+	0.536382i	0.978292	−	0.207229i	$-0.0664446\pi$
$947$	9.52991	+	16.5063i	0.309680	+	0.536382i	−0.668612	+	0.743611i	$0.733111\pi$
$948$		0			0
$949$	−37.8615	+	65.5781i	−1.22904	+	2.12876i
$950$		0			0
$951$	−8.23970			−0.267191
$952$		0			0
$953$	17.1334			0.555004			0.277502	−	0.960725i	$-0.410493\pi$
$953$	17.1334			0.555004			0.277502	+	0.960725i	$0.410493\pi$
$954$		0			0
$955$	23.5667	−	40.8187i	0.762600	−	1.32086i
$956$		0			0
$957$	−0.967422	−	1.67562i	−0.0312723	−	0.0541652i
$958$		0			0
$959$	−2.05050	+	3.37663i	−0.0662141	+	0.109037i
$960$		0			0
$961$	1.50686	+	2.60996i	0.0486085	+	0.0841924i
$962$		0			0
$963$	−2.26496	+	3.92302i	−0.0729872	+	0.126417i
$964$		0			0
$965$	29.9348			0.963637
$966$		0			0
$967$	26.7833			0.861294			0.430647	−	0.902520i	$-0.358285\pi$
$967$	26.7833			0.861294			0.430647	+	0.902520i	$0.358285\pi$
$968$		0			0
$969$	22.6172	−	39.1741i	0.726569	−	1.25845i
$970$		0			0
$971$	−5.75809	−	9.97331i	−0.184786	−	0.320059i	0.758718	−	0.651419i	$-0.225826\pi$
$971$	−5.75809	−	9.97331i	−0.184786	−	0.320059i	−0.943504	+	0.331360i	$0.892493\pi$
$972$		0			0
$973$	7.80173	+	0.172785i	0.250112	+	0.00553924i
$974$		0			0
$975$	7.67768	+	13.2981i	0.245883	+	0.425881i
$976$		0			0
$977$	−10.6677	+	18.4770i	−0.341289	+	0.591131i	−0.984672	−	0.174414i	$-0.944197\pi$
$977$	−10.6677	+	18.4770i	−0.341289	+	0.591131i	0.643383	+	0.765544i	$0.277530\pi$
$978$		0			0
$979$	14.6540			0.468343
$980$		0			0
$981$	−6.44264			−0.205698
$982$		0			0
$983$	25.1976	−	43.6435i	0.803678	−	1.39201i	−0.113501	−	0.993538i	$-0.536207\pi$
$983$	25.1976	−	43.6435i	0.803678	−	1.39201i	0.917180	−	0.398474i	$-0.130460\pi$
$984$		0			0
$985$	−7.44264	−	12.8910i	−0.237142	−	0.410742i
$986$		0			0
$987$	25.1103	+	0.556119i	0.799270	+	0.0177015i
$988$		0			0
$989$	12.9495	+	22.4292i	0.411770	+	0.713207i
$990$		0			0
$991$	−6.34117	+	10.9832i	−0.201434	+	0.348894i	−0.948991	−	0.315304i	$-0.897893\pi$
$991$	−6.34117	+	10.9832i	−0.201434	+	0.348894i	0.747557	+	0.664198i	$0.231227\pi$
$992$		0			0
$993$	−5.52991			−0.175486
$994$		0			0
$995$	63.1334			2.00146
$996$		0			0
$997$	20.1708	−	34.9369i	0.638816	−	1.10646i	−0.346877	−	0.937911i	$-0.612758\pi$
$997$	20.1708	−	34.9369i	0.638816	−	1.10646i	0.985693	−	0.168551i	$-0.0539089\pi$
$998$		0			0
$999$	2.47475	+	4.28639i	0.0782976	+	0.135615i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	672.2.q.l.193.1	yes	6
3.2	odd	2		2016.2.s.v.865.3		6
4.3	odd	2		672.2.q.k.193.1	✓	6
7.2	even	3	inner	672.2.q.l.289.1	yes	6
7.3	odd	6		4704.2.a.bv.1.1		3
7.4	even	3		4704.2.a.bs.1.3		3
8.3	odd	2		1344.2.q.z.193.3		6
8.5	even	2		1344.2.q.y.193.3		6
12.11	even	2		2016.2.s.u.865.3		6
21.2	odd	6		2016.2.s.v.289.3		6
28.3	even	6		4704.2.a.bt.1.1		3
28.11	odd	6		4704.2.a.bu.1.3		3
28.23	odd	6		672.2.q.k.289.1	yes	6
56.3	even	6		9408.2.a.ei.1.3		3
56.11	odd	6		9408.2.a.eh.1.1		3
56.37	even	6		1344.2.q.y.961.3		6
56.45	odd	6		9408.2.a.eg.1.3		3
56.51	odd	6		1344.2.q.z.961.3		6
56.53	even	6		9408.2.a.ej.1.1		3
84.23	even	6		2016.2.s.u.289.3		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
672.2.q.k.193.1	✓	6	4.3	odd	2
672.2.q.k.289.1	yes	6	28.23	odd	6
672.2.q.l.193.1	yes	6	1.1	even	1	trivial
672.2.q.l.289.1	yes	6	7.2	even	3	inner
1344.2.q.y.193.3		6	8.5	even	2
1344.2.q.y.961.3		6	56.37	even	6
1344.2.q.z.193.3		6	8.3	odd	2
1344.2.q.z.961.3		6	56.51	odd	6
2016.2.s.u.289.3		6	84.23	even	6
2016.2.s.u.865.3		6	12.11	even	2
2016.2.s.v.289.3		6	21.2	odd	6
2016.2.s.v.865.3		6	3.2	odd	2
4704.2.a.bs.1.3		3	7.4	even	3
4704.2.a.bt.1.1		3	28.3	even	6
4704.2.a.bu.1.3		3	28.11	odd	6
4704.2.a.bv.1.1		3	7.3	odd	6
9408.2.a.eg.1.3		3	56.45	odd	6
9408.2.a.eh.1.1		3	56.11	odd	6
9408.2.a.ei.1.3		3	56.3	even	6
9408.2.a.ej.1.1		3	56.53	even	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:	\( N \)	\(=\)	\( 672 = 2^{5} \cdot 3 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	672.q (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.500000 - 0.866025i) q^{3} +(-1.37328 - 2.37860i) q^{5} +(2.64510 + 0.0585812i) q^{7} +(-0.500000 - 0.866025i) q^{9} +O(q^{10})\)	\(q+(0.500000 - 0.866025i) q^{3} +(-1.37328 - 2.37860i) q^{5} +(2.64510 + 0.0585812i) q^{7} +(-0.500000 - 0.866025i) q^{9} +(0.771819 - 1.33683i) q^{11} +6.03677 q^{13} -2.74657 q^{15} +(-3.74657 + 6.48925i) q^{17} +(-3.01839 - 5.22800i) q^{19} +(1.37328 - 2.26144i) q^{21} +(-3.74657 - 6.48925i) q^{23} +(-1.27182 + 2.20285i) q^{25} -1.00000 q^{27} +1.25343 q^{29} +(2.64510 - 4.58145i) q^{31} +(-0.771819 - 1.33683i) q^{33} +(-3.49314 - 6.37208i) q^{35} +(-2.47475 - 4.28639i) q^{37} +(3.01839 - 5.22800i) q^{39} -5.08727 q^{41} -3.45636 q^{43} +(-1.37328 + 2.37860i) q^{45} +(4.74657 + 8.22130i) q^{47} +(6.99314 + 0.309906i) q^{49} +(3.74657 + 6.48925i) q^{51} +(1.91692 - 3.32021i) q^{53} -4.23970 q^{55} -6.03677 q^{57} +(2.77182 - 4.80093i) q^{59} +(7.29021 + 12.6270i) q^{61} +(-1.27182 - 2.32002i) q^{63} +(-8.29021 - 14.3591i) q^{65} +(-2.01839 + 3.49595i) q^{67} -7.49314 q^{69} +5.49314 q^{71} +(-6.27182 + 10.8631i) q^{73} +(1.27182 + 2.20285i) q^{75} +(2.11985 - 3.49084i) q^{77} +(-3.89853 - 6.75246i) q^{79} +(-0.500000 + 0.866025i) q^{81} +6.52991 q^{83} +20.5804 q^{85} +(0.626716 - 1.08550i) q^{87} +(4.74657 + 8.22130i) q^{89} +(15.9679 + 0.353641i) q^{91} +(-2.64510 - 4.58145i) q^{93} +(-8.29021 + 14.3591i) q^{95} +1.54364 q^{97} -1.54364 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q + 3 q^{3} + 3 q^{7} - 3 q^{9}+O(q^{10}) \) 6 * q + 3 * q^3 + 3 * q^7 - 3 * q^9	\( 6 q + 3 q^{3} + 3 q^{7} - 3 q^{9} - 6 q^{13} - 6 q^{17} + 3 q^{19} - 6 q^{23} - 3 q^{25} - 6 q^{27} + 24 q^{29} + 3 q^{31} + 12 q^{35} - 3 q^{37} - 3 q^{39} - 12 q^{41} - 30 q^{43} + 12 q^{47} + 9 q^{49} + 6 q^{51} - 6 q^{53} + 24 q^{55} + 6 q^{57} + 12 q^{59} + 18 q^{61} - 3 q^{63} - 24 q^{65} + 9 q^{67} - 12 q^{69} - 33 q^{73} + 3 q^{75} - 12 q^{77} - 27 q^{79} - 3 q^{81} - 36 q^{83} + 72 q^{85} + 12 q^{87} + 12 q^{89} + 51 q^{91} - 3 q^{93} - 24 q^{95}+O(q^{100}) \) 6 * q + 3 * q^3 + 3 * q^7 - 3 * q^9 - 6 * q^13 - 6 * q^17 + 3 * q^19 - 6 * q^23 - 3 * q^25 - 6 * q^27 + 24 * q^29 + 3 * q^31 + 12 * q^35 - 3 * q^37 - 3 * q^39 - 12 * q^41 - 30 * q^43 + 12 * q^47 + 9 * q^49 + 6 * q^51 - 6 * q^53 + 24 * q^55 + 6 * q^57 + 12 * q^59 + 18 * q^61 - 3 * q^63 - 24 * q^65 + 9 * q^67 - 12 * q^69 - 33 * q^73 + 3 * q^75 - 12 * q^77 - 27 * q^79 - 3 * q^81 - 36 * q^83 + 72 * q^85 + 12 * q^87 + 12 * q^89 + 51 * q^91 - 3 * q^93 - 24 * q^95

Introduction

L-functions

Modular forms

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Database

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