LMFDB - Embedded newform 684.3.t.a.265.10

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [684,3,Mod(265,684)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(684, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 2, 3]))

N = Newforms(chi, 3, names="a")

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

chi := DirichletCharacter("684.265");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 684 = 2^{2} \cdot 3^{2} \cdot 19 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	684.t (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:	$18.6376500822$
Analytic rank:	$0$
Dimension:	$80$
Relative dimension:	$40$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			265.10
Character	$\chi$	$=$	684.265
Dual form			684.3.t.a.493.10

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.19396 - 2.04610i) q^{3} +(2.17299 - 3.76373i) q^{5} +(1.82107 + 3.15419i) q^{7} +(0.626916 + 8.97814i) q^{9} +O(q^{10})$	\(q+(-2.19396 - 2.04610i) q^{3} +(2.17299 - 3.76373i) q^{5} +(1.82107 + 3.15419i) q^{7} +(0.626916 + 8.97814i) q^{9} +(5.82645 + 10.0917i) q^{11} +(-7.74715 - 4.47282i) q^{13} +(-12.4684 + 3.81130i) q^{15} -11.2516 q^{17} +(-18.8669 + 2.24510i) q^{19} +(2.45844 - 10.6463i) q^{21} +(-4.84901 + 8.39872i) q^{23} +(3.05624 + 5.29357i) q^{25} +(16.9948 - 20.9804i) q^{27} +(-48.9465 + 28.2593i) q^{29} +(-5.90658 - 3.41017i) q^{31} +(7.86568 - 34.0623i) q^{33} +15.8287 q^{35} -2.74588i q^{37} +(7.84508 + 25.6647i) q^{39} +(-3.15940 - 1.82408i) q^{41} +(32.1823 + 55.7414i) q^{43} +(35.1535 + 17.1499i) q^{45} +(11.6161 + 20.1197i) q^{47} +(17.8674 - 30.9472i) q^{49} +(24.6855 + 23.0219i) q^{51} +65.9323i q^{53} +50.6432 q^{55} +(45.9869 + 33.6780i) q^{57} +(-32.0067 - 18.4791i) q^{59} +(35.6842 + 61.8068i) q^{61} +(-27.1771 + 18.3273i) q^{63} +(-33.6689 + 19.4388i) q^{65} +(93.2170 + 53.8189i) q^{67} +(27.8232 - 8.50489i) q^{69} -71.3923i q^{71} -133.609 q^{73} +(4.12592 - 17.8673i) q^{75} +(-21.2208 + 36.7555i) q^{77} +(4.39592 - 2.53799i) q^{79} +(-80.2140 + 11.2571i) q^{81} +(48.9086 + 84.7122i) q^{83} +(-24.4496 + 42.3479i) q^{85} +(165.208 + 38.1499i) q^{87} -22.7245i q^{89} -32.5813i q^{91} +(5.98124 + 19.5672i) q^{93} +(-32.5476 + 75.8884i) q^{95} +(-62.3412 + 35.9927i) q^{97} +(-86.9520 + 58.6373i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 80 q + 2 q^{7} + 4 q^{9}+O(q^{10}) $ 80 * q + 2 * q^7 + 4 * q^9	$ 80 q + 2 q^{7} + 4 q^{9} + 12 q^{11} - 12 q^{17} - 2 q^{19} - 48 q^{23} - 200 q^{25} - 216 q^{35} + 102 q^{39} + 28 q^{43} + 2 q^{45} - 174 q^{47} - 306 q^{49} + 213 q^{57} + 14 q^{61} + 62 q^{63} + 220 q^{73} - 60 q^{77} + 340 q^{81} + 150 q^{83} - 252 q^{87} - 252 q^{93} + 360 q^{95} + 542 q^{99}+O(q^{100}) $ 80 * q + 2 * q^7 + 4 * q^9 + 12 * q^11 - 12 * q^17 - 2 * q^19 - 48 * q^23 - 200 * q^25 - 216 * q^35 + 102 * q^39 + 28 * q^43 + 2 * q^45 - 174 * q^47 - 306 * q^49 + 213 * q^57 + 14 * q^61 + 62 * q^63 + 220 * q^73 - 60 * q^77 + 340 * q^81 + 150 * q^83 - 252 * q^87 - 252 * q^93 + 360 * q^95 + 542 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/684\mathbb{Z}\right)^\times$.

$n$	$325$	$343$	$533$
$\chi(n)$	$-1$	$1$	$e\left(\frac{1}{3}\right)$

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
$3$	−2.19396	−	2.04610i	−0.731320	−	0.682035i
$3$	−2.19396	−	2.04610i	−0.731320	−	0.682035i
$4$		0			0
$5$	2.17299	−	3.76373i	0.434598	−	0.752745i	−0.562665	−	0.826685i	$-0.690224\pi$
$5$	2.17299	−	3.76373i	0.434598	−	0.752745i	0.997263	+	0.0739397i	$0.0235572\pi$
$6$		0			0
$7$	1.82107	+	3.15419i	0.260153	+	0.450599i	0.966282	−	0.257484i	$-0.0828936\pi$
$7$	1.82107	+	3.15419i	0.260153	+	0.450599i	−0.706129	+	0.708083i	$0.749560\pi$
$8$		0			0
$9$	0.626916	+	8.97814i	0.0696574	+	0.997571i
$10$		0			0
$11$	5.82645	+	10.0917i	0.529677	+	0.917427i	0.999401	+	0.0346139i	$0.0110202\pi$
$11$	5.82645	+	10.0917i	0.529677	+	0.917427i	−0.469724	+	0.882813i	$0.655647\pi$
$12$		0			0
$13$	−7.74715	−	4.47282i	−0.595934	−	0.344063i	0.171506	−	0.985183i	$-0.445137\pi$
$13$	−7.74715	−	4.47282i	−0.595934	−	0.344063i	−0.767441	+	0.641120i	$0.778470\pi$
$14$		0			0
$15$	−12.4684	+	3.81130i	−0.831228	+	0.254087i
$16$		0			0
$17$	−11.2516			−0.661858			−0.330929	−	0.943656i	$-0.607362\pi$
$17$	−11.2516			−0.661858			−0.330929	+	0.943656i	$0.607362\pi$
$18$		0			0
$19$	−18.8669	+	2.24510i	−0.992994	+	0.118163i
$19$	−18.8669	+	2.24510i	−0.992994	+	0.118163i
$20$		0			0
$21$	2.45844	−	10.6463i	0.117069	−	0.506965i
$22$		0			0
$23$	−4.84901	+	8.39872i	−0.210826	+	0.365162i	−0.951973	−	0.306181i	$-0.900949\pi$
$23$	−4.84901	+	8.39872i	−0.210826	+	0.365162i	0.741147	+	0.671343i	$0.234282\pi$
$24$		0			0
$25$	3.05624	+	5.29357i	0.122250	+	0.211743i
$26$		0			0
$27$	16.9948	−	20.9804i	0.629436	−	0.777052i
$28$		0			0
$29$	−48.9465	+	28.2593i	−1.68781	+	0.974457i	−0.731618	+	0.681715i	$0.761234\pi$
$29$	−48.9465	+	28.2593i	−1.68781	+	0.974457i	−0.956191	+	0.292742i	$0.905432\pi$
$30$		0			0
$31$	−5.90658	−	3.41017i	−0.190535	−	0.110005i	0.401698	−	0.915772i	$-0.368420\pi$
$31$	−5.90658	−	3.41017i	−0.190535	−	0.110005i	−0.592233	+	0.805767i	$0.701753\pi$
$32$		0			0
$33$	7.86568	−	34.0623i	0.238354	−	1.03219i
$34$		0			0
$35$	15.8287			0.452248
$36$		0			0
$37$		−	2.74588i		−	0.0742129i	−0.999311	−	0.0371064i	$-0.988186\pi$
$37$		−	2.74588i		−	0.0742129i	0.999311	−	0.0371064i	$-0.0118141\pi$
$38$		0			0
$39$	7.84508	+	25.6647i	0.201156	+	0.658068i
$40$		0			0
$41$	−3.15940	−	1.82408i	−0.0770586	−	0.0444898i	0.460976	−	0.887413i	$-0.347500\pi$
$41$	−3.15940	−	1.82408i	−0.0770586	−	0.0444898i	−0.538034	+	0.842923i	$0.680833\pi$
$42$		0			0
$43$	32.1823	+	55.7414i	0.748425	+	1.29631i	0.948577	+	0.316546i	$0.102523\pi$
$43$	32.1823	+	55.7414i	0.748425	+	1.29631i	−0.200152	+	0.979765i	$0.564144\pi$
$44$		0			0
$45$	35.1535	+	17.1499i	0.781190	+	0.381108i
$46$		0			0
$47$	11.6161	+	20.1197i	0.247151	+	0.428079i	0.962734	−	0.270449i	$-0.0871722\pi$
$47$	11.6161	+	20.1197i	0.247151	+	0.428079i	−0.715583	+	0.698528i	$0.753839\pi$
$48$		0			0
$49$	17.8674	−	30.9472i	0.364640	−	0.631576i
$50$		0			0
$51$	24.6855	+	23.0219i	0.484030	+	0.451410i
$52$		0			0
$53$			65.9323i			1.24401i	0.783015	+	0.622003i	$0.213681\pi$
$53$			65.9323i			1.24401i	−0.783015	+	0.622003i	$0.786319\pi$
$54$		0			0
$55$	50.6432			0.920785
$56$		0			0
$57$	45.9869	+	33.6780i	0.806788	+	0.590842i
$58$		0			0
$59$	−32.0067	−	18.4791i	−0.542486	−	0.313204i	0.203600	−	0.979054i	$-0.434736\pi$
$59$	−32.0067	−	18.4791i	−0.542486	−	0.313204i	−0.746086	+	0.665850i	$0.768069\pi$
$60$		0			0
$61$	35.6842	+	61.8068i	0.584986	+	1.01323i	0.994877	+	0.101091i	$0.0322335\pi$
$61$	35.6842	+	61.8068i	0.584986	+	1.01323i	−0.409891	+	0.912135i	$0.634433\pi$
$62$		0			0
$63$	−27.1771	+	18.3273i	−0.431383	+	0.290909i
$64$		0			0
$65$	−33.6689	+	19.4388i	−0.517984	+	0.299058i
$66$		0			0
$67$	93.2170	+	53.8189i	1.39130	+	0.803267i	0.993459	−	0.114188i	$-0.0364266\pi$
$67$	93.2170	+	53.8189i	1.39130	+	0.803267i	0.397840	+	0.917455i	$0.369760\pi$
$68$		0			0
$69$	27.8232	−	8.50489i	0.403235	−	0.123259i
$70$		0			0
$71$		−	71.3923i		−	1.00553i	−0.864424	−	0.502763i	$-0.832317\pi$
$71$		−	71.3923i		−	1.00553i	0.864424	−	0.502763i	$-0.167683\pi$
$72$		0			0
$73$	−133.609			−1.83026			−0.915132	−	0.403154i	$-0.867914\pi$
$73$	−133.609			−1.83026			−0.915132	+	0.403154i	$0.867914\pi$
$74$		0			0
$75$	4.12592	−	17.8673i	0.0550122	−	0.238230i
$76$		0			0
$77$	−21.2208	+	36.7555i	−0.275594	+	0.477344i
$78$		0			0
$79$	4.39592	−	2.53799i	0.0556446	−	0.0321264i	−0.471920	−	0.881642i	$-0.656439\pi$
$79$	4.39592	−	2.53799i	0.0556446	−	0.0321264i	0.527564	+	0.849515i	$0.323105\pi$
$80$		0			0
$81$	−80.2140	+	11.2571i	−0.990296	+	0.138976i
$82$		0			0
$83$	48.9086	+	84.7122i	0.589261	+	1.02063i	0.994330	+	0.106343i	$0.0339142\pi$
$83$	48.9086	+	84.7122i	0.589261	+	1.02063i	−0.405069	+	0.914286i	$0.632753\pi$
$84$		0			0
$85$	−24.4496	+	42.3479i	−0.287642	+	0.498211i
$86$		0			0
$87$	165.208	+	38.1499i	1.89894	+	0.438505i
$88$		0			0
$89$		−	22.7245i		−	0.255331i	−0.991817	−	0.127666i	$-0.959252\pi$
$89$		−	22.7245i		−	0.255331i	0.991817	−	0.127666i	$-0.0407485\pi$
$90$		0			0
$91$		−	32.5813i		−	0.358036i
$92$		0			0
$93$	5.98124	+	19.5672i	0.0643144	+	0.210400i
$94$		0			0
$95$	−32.5476	+	75.8884i	−0.342606	+	0.798825i
$96$		0			0
$97$	−62.3412	+	35.9927i	−0.642693	+	0.371059i	−0.785651	−	0.618670i	$-0.787672\pi$
$97$	−62.3412	+	35.9927i	−0.642693	+	0.371059i	0.142958	+	0.989729i	$0.454339\pi$
$98$		0			0
$99$	−86.9520	+	58.6373i	−0.878303	+	0.592296i
$100$		0			0
$101$	−32.8984	−	56.9816i	−0.325726	−	0.564175i	0.655933	−	0.754819i	$-0.272276\pi$
$101$	−32.8984	−	56.9816i	−0.325726	−	0.564175i	−0.981659	+	0.190645i	$0.938942\pi$
$102$		0			0
$103$	99.1991	+	57.2726i	0.963098	+	0.556045i	0.897125	−	0.441777i	$-0.145652\pi$
$103$	99.1991	+	57.2726i	0.963098	+	0.556045i	0.0659726	+	0.997821i	$0.478985\pi$
$104$		0			0
$105$	−34.7275	−	32.3871i	−0.330738	−	0.308449i
$106$		0			0
$107$			38.3315i			0.358238i	0.983827	+	0.179119i	$0.0573247\pi$
$107$			38.3315i			0.358238i	−0.983827	+	0.179119i	$0.942675\pi$
$108$		0			0
$109$			137.801i			1.26423i	0.774875	+	0.632114i	$0.217813\pi$
$109$			137.801i			1.26423i	−0.774875	+	0.632114i	$0.782187\pi$
$110$		0			0
$111$	−5.61835	+	6.02434i	−0.0506157	+	0.0542733i
$112$		0			0
$113$	−136.848	−	79.0091i	−1.21104	−	0.699196i	−0.248056	−	0.968746i	$-0.579792\pi$
$113$	−136.848	−	79.0091i	−1.21104	−	0.699196i	−0.962986	+	0.269550i	$0.913125\pi$
$114$		0			0
$115$	21.0737	+	36.5007i	0.183249	+	0.317397i
$116$		0			0
$117$	35.3008	−	72.3591i	0.301716	−	0.618453i
$118$		0			0
$119$	−20.4900	−	35.4897i	−0.172185	−	0.298233i
$120$		0			0
$121$	−7.39495	+	12.8084i	−0.0611153	+	0.105855i
$122$		0			0
$123$	3.19934	+	10.4664i	0.0260109	+	0.0850930i
$124$		0			0
$125$	135.214			1.08171
$126$		0			0
$127$			176.869i			1.39267i	0.717715	+	0.696337i	$0.245188\pi$
$127$			176.869i			1.39267i	−0.717715	+	0.696337i	$0.754812\pi$
$128$		0			0
$129$	43.4460	−	188.143i	0.336791	−	1.45847i
$130$		0			0
$131$	118.910	−	205.959i	0.907712	−	1.57220i	0.0904762	−	0.995899i	$-0.471161\pi$
$131$	118.910	−	205.959i	0.907712	−	1.57220i	0.817235	−	0.576304i	$-0.195506\pi$
$132$		0			0
$133$	−41.4395	−	55.4213i	−0.311575	−	0.416701i
$134$		0			0
$135$	−42.0351	−	109.554i	−0.311371	−	0.811510i
$136$		0			0
$137$	−55.4500	−	96.0422i	−0.404745	−	0.701038i	0.589547	−	0.807734i	$-0.299306\pi$
$137$	−55.4500	−	96.0422i	−0.404745	−	0.701038i	−0.994292	+	0.106696i	$0.965973\pi$
$138$		0			0
$139$	8.82535	−	15.2860i	0.0634917	−	0.109971i	−0.832532	−	0.553977i	$-0.813110\pi$
$139$	8.82535	−	15.2860i	0.0634917	−	0.109971i	0.896024	+	0.444006i	$0.146443\pi$
$140$		0			0
$141$	15.6817	−	67.9096i	0.111218	−	0.481628i
$142$		0			0
$143$		−	104.243i		−	0.728969i
$144$		0			0
$145$			245.628i			1.69399i
$146$		0			0
$147$	−102.522	+	31.3384i	−0.697425	+	0.213186i
$148$		0			0
$149$	−93.8872	+	162.617i	−0.630115	+	1.09139i	0.357412	+	0.933947i	$0.383659\pi$
$149$	−93.8872	+	162.617i	−0.630115	+	1.09139i	−0.987528	+	0.157445i	$0.949674\pi$
$150$		0			0
$151$	124.771	−	72.0363i	0.826295	−	0.477062i	−0.0262874	−	0.999654i	$-0.508369\pi$
$151$	124.771	−	72.0363i	0.826295	−	0.477062i	0.852582	+	0.522593i	$0.175035\pi$
$152$		0			0
$153$	−7.05381	−	101.018i	−0.0461033	−	0.660251i
$154$		0			0
$155$	−25.6699	+	14.8205i	−0.165612	+	0.0956161i
$156$		0			0
$157$	37.1048	−	64.2673i	0.236336	−	0.409346i	−0.723324	−	0.690509i	$-0.757387\pi$
$157$	37.1048	−	64.2673i	0.236336	−	0.409346i	0.959660	+	0.281163i	$0.0907200\pi$
$158$		0			0
$159$	134.904	−	144.653i	0.848455	−	0.909766i
$160$		0			0
$161$	−35.3216			−0.219389
$162$		0			0
$163$	57.1519			0.350625			0.175313	−	0.984513i	$-0.443906\pi$
$163$	57.1519			0.350625			0.175313	+	0.984513i	$0.443906\pi$
$164$		0			0
$165$	−111.109	−	103.621i	−0.673389	−	0.628008i
$166$		0			0
$167$	−228.112	−	131.701i	−1.36594	−	0.788627i	−0.375534	−	0.926808i	$-0.622541\pi$
$167$	−228.112	−	131.701i	−1.36594	−	0.788627i	−0.990407	+	0.138182i	$0.955874\pi$
$168$		0			0
$169$	−44.4878	−	77.0551i	−0.263241	−	0.455947i
$170$		0			0
$171$	−31.9848	−	167.982i	−0.187045	−	0.982351i
$172$		0			0
$173$	−122.071	+	70.4778i	−0.705613	+	0.407386i	−0.809435	−	0.587210i	$-0.800226\pi$
$173$	−122.071	+	70.4778i	−0.705613	+	0.407386i	0.103821	+	0.994596i	$0.466893\pi$
$174$		0			0
$175$	−11.1313	+	19.2799i	−0.0636073	+	0.110171i
$176$		0			0
$177$	32.4112	+	106.031i	0.183114	+	0.599047i
$178$		0			0
$179$			141.949i			0.793011i	0.918032	+	0.396505i	$0.129777\pi$
$179$			141.949i			0.793011i	−0.918032	+	0.396505i	$0.870223\pi$
$180$		0			0
$181$		−	140.384i		−	0.775600i	−0.921744	−	0.387800i	$-0.873235\pi$
$181$		−	140.384i		−	0.775600i	0.921744	−	0.387800i	$-0.126765\pi$
$182$		0			0
$183$	48.1735	−	208.615i	0.263243	−	1.13997i
$184$		0			0
$185$	−10.3347	−	5.96676i	−0.0558634	−	0.0322527i
$186$		0			0
$187$	−65.5568	−	113.548i	−0.350571	−	0.607207i
$188$		0			0
$189$	97.1250	+	15.3979i	0.513889	+	0.0814705i
$190$		0			0
$191$	−59.9447	−	103.827i	−0.313847	−	0.543599i	0.665345	−	0.746536i	$-0.268285\pi$
$191$	−59.9447	−	103.827i	−0.313847	−	0.543599i	−0.979192	+	0.202937i	$0.934951\pi$
$192$		0			0
$193$	289.713	+	167.266i	1.50110	+	0.866661i	0.999999	+	0.00127307i	$0.000405231\pi$
$193$	289.713	+	167.266i	1.50110	+	0.866661i	0.501102	+	0.865388i	$0.332928\pi$
$194$		0			0
$195$	113.642	+	26.2423i	0.582780	+	0.134576i
$196$		0			0
$197$	−76.4444			−0.388043			−0.194021	−	0.980997i	$-0.562153\pi$
$197$	−76.4444			−0.388043			−0.194021	+	0.980997i	$0.562153\pi$
$198$		0			0
$199$	−56.0892			−0.281855			−0.140928	−	0.990020i	$-0.545009\pi$
$199$	−56.0892			−0.281855			−0.140928	+	0.990020i	$0.545009\pi$
$200$		0			0
$201$	−94.3954	−	308.808i	−0.469629	−	1.53636i
$202$		0			0
$203$	−178.270	−	102.924i	−0.878178	−	0.507017i
$204$		0			0
$205$	−13.7307	+	7.92742i	−0.0669790	+	0.0386704i
$206$		0			0
$207$	−78.4448	−	38.2697i	−0.378961	−	0.184878i
$208$		0			0
$209$	−132.584	−	177.318i	−0.634372	−	0.848412i
$210$		0			0
$211$	9.09605	+	5.25161i	0.0431092	+	0.0248891i	0.521400	−	0.853313i	$-0.325410\pi$
$211$	9.09605	+	5.25161i	0.0431092	+	0.0248891i	−0.478290	+	0.878202i	$0.658743\pi$
$212$		0			0
$213$	−146.076	+	156.632i	−0.685803	+	0.735361i
$214$		0			0
$215$	279.727			1.30106
$216$		0			0
$217$		−	24.8406i		−	0.114473i
$218$		0			0
$219$	293.133	+	273.379i	1.33851	+	1.24830i
$220$		0			0
$221$	87.1677	+	50.3263i	0.394424	+	0.227721i
$222$		0			0
$223$	−117.143	+	67.6327i	−0.525306	+	0.303286i	−0.739103	−	0.673593i	$-0.764750\pi$
$223$	−117.143	+	67.6327i	−0.525306	+	0.303286i	0.213797	+	0.976878i	$0.431417\pi$
$224$		0			0
$225$	−45.6104	+	30.7580i	−0.202713	+	0.136702i
$226$		0			0
$227$	−289.236	+	166.990i	−1.27417	+	0.735640i	−0.975769	−	0.218801i	$-0.929785\pi$
$227$	−289.236	+	166.990i	−1.27417	+	0.735640i	−0.298397	+	0.954442i	$0.596452\pi$
$228$		0			0
$229$	8.18208	−	14.1718i	0.0357296	−	0.0618855i	−0.847608	−	0.530623i	$-0.821958\pi$
$229$	8.18208	−	14.1718i	0.0357296	−	0.0618855i	0.883337	+	0.468738i	$0.155291\pi$
$230$		0			0
$231$	121.763	−	37.2201i	0.527113	−	0.161126i
$232$		0			0
$233$	−179.264			−0.769375			−0.384687	−	0.923047i	$-0.625691\pi$
$233$	−179.264			−0.769375			−0.384687	+	0.923047i	$0.625691\pi$
$234$		0			0
$235$	100.967			0.429645
$236$		0			0
$237$	−14.8375	−	3.42627i	−0.0626053	−	0.0144569i
$238$		0			0
$239$	35.1320	−	60.8505i	0.146996	−	0.254604i	−0.783120	−	0.621871i	$-0.786373\pi$
$239$	35.1320	−	60.8505i	0.146996	−	0.254604i	0.930116	+	0.367266i	$0.119706\pi$
$240$		0			0
$241$	259.376	−	149.751i	1.07625	−	0.621373i	0.146367	−	0.989230i	$-0.453242\pi$
$241$	259.376	−	149.751i	1.07625	−	0.621373i	0.929882	+	0.367858i	$0.119909\pi$
$242$		0			0
$243$	199.019	+	139.429i	0.819010	+	0.573780i
$244$		0			0
$245$	−77.6512	−	134.496i	−0.316944	−	0.548963i
$246$		0			0
$247$	156.207	+	66.9951i	0.632415	+	0.271235i
$248$		0			0
$249$	66.0265	−	285.927i	0.265167	−	1.14830i
$250$		0			0
$251$	−0.319072			−0.00127120			−0.000635602	−	1.00000i	$-0.500202\pi$
$251$	−0.319072			−0.00127120			−0.000635602		1.00000i	$0.500202\pi$
$252$		0			0
$253$	−113.010			−0.446679
$254$		0			0
$255$	140.290	−	42.8832i	0.550155	−	0.168169i
$256$		0			0
$257$	−126.949	−	73.2938i	−0.493963	−	0.285190i	0.232254	−	0.972655i	$-0.425390\pi$
$257$	−126.949	−	73.2938i	−0.493963	−	0.285190i	−0.726217	+	0.687465i	$0.758723\pi$
$258$		0			0
$259$	8.66102	−	5.00044i	0.0334402	−	0.0193067i
$260$		0			0
$261$	−284.401	−	421.732i	−1.08966	−	1.61583i
$262$		0			0
$263$	−129.134	−	223.667i	−0.491005	−	0.850446i	0.508941	−	0.860801i	$-0.330037\pi$
$263$	−129.134	−	223.667i	−0.491005	−	0.850446i	−0.999946	+	0.0103553i	$0.996704\pi$
$264$		0			0
$265$	248.151	+	143.270i	0.936419	+	0.540642i
$266$		0			0
$267$	−46.4967	+	49.8566i	−0.174145	+	0.186729i
$268$		0			0
$269$			299.365i			1.11288i	0.830887	+	0.556441i	$0.187834\pi$
$269$			299.365i			1.11288i	−0.830887	+	0.556441i	$0.812166\pi$
$270$		0			0
$271$	−130.669			−0.482174			−0.241087	−	0.970504i	$-0.577504\pi$
$271$	−130.669			−0.482174			−0.241087	+	0.970504i	$0.577504\pi$
$272$		0			0
$273$	−66.6648	+	71.4821i	−0.244193	+	0.261839i
$274$		0			0
$275$	−35.6141	+	61.6853i	−0.129506	+	0.224310i
$276$		0			0
$277$	−44.9186	−	77.8012i	−0.162161	−	0.280871i	0.773483	−	0.633818i	$-0.218513\pi$
$277$	−44.9186	−	77.8012i	−0.162161	−	0.280871i	−0.935643	+	0.352947i	$0.885180\pi$
$278$		0			0
$279$	26.9140	−	55.1680i	0.0964660	−	0.197735i
$280$		0			0
$281$	−363.085	+	209.627i	−1.29212	+	0.746004i	−0.979029	−	0.203721i	$-0.934696\pi$
$281$	−363.085	+	209.627i	−1.29212	+	0.746004i	−0.313087	+	0.949724i	$0.601363\pi$
$282$		0			0
$283$	110.015	−	190.551i	0.388744	−	0.673324i	−0.603537	−	0.797335i	$-0.706242\pi$
$283$	110.015	−	190.551i	0.388744	−	0.673324i	0.992281	+	0.124011i	$0.0395757\pi$
$284$		0			0
$285$	226.684	−	99.9003i	0.795381	−	0.350527i
$286$		0			0
$287$		−	13.2872i		−	0.0462967i
$288$		0			0
$289$	−162.402			−0.561944
$290$		0			0
$291$	210.419	+	48.5900i	0.723089	+	0.166976i
$292$		0			0
$293$	197.037	+	113.759i	0.672481	+	0.388257i	0.797016	−	0.603958i	$-0.206411\pi$
$293$	197.037	+	113.759i	0.672481	+	0.388257i	−0.124535	+	0.992215i	$0.539744\pi$
$294$		0			0
$295$	−139.100	+	80.3095i	−0.471526	+	0.272236i
$296$		0			0
$297$	310.747	+	49.2650i	1.04629	+	0.165875i
$298$		0			0
$299$	75.1319	−	43.3774i	0.251277	−	0.145075i
$300$		0			0
$301$	−117.213	+	203.018i	−0.389411	+	0.674479i
$302$		0			0
$303$	−44.4127	+	192.329i	−0.146577	+	0.634749i
$304$		0			0
$305$	310.165			1.01693
$306$		0			0
$307$			418.165i			1.36210i	0.732236	+	0.681051i	$0.238477\pi$
$307$			418.165i			1.36210i	−0.732236	+	0.681051i	$0.761523\pi$
$308$		0			0
$309$	−100.453	−	328.625i	−0.325091	−	1.06351i
$310$		0			0
$311$	−66.7863	+	115.677i	−0.214747	+	0.371953i	−0.953194	−	0.302358i	$-0.902226\pi$
$311$	−66.7863	+	115.677i	−0.214747	+	0.371953i	0.738447	+	0.674311i	$0.235559\pi$
$312$		0			0
$313$	−198.133	−	343.176i	−0.633013	−	1.09641i	−0.986932	−	0.161134i	$-0.948485\pi$
$313$	−198.133	−	343.176i	−0.633013	−	1.09641i	0.353920	−	0.935276i	$-0.384849\pi$
$314$		0			0
$315$	9.92326	+	142.112i	0.0315024	+	0.451150i
$316$		0			0
$317$	138.791	−	80.1310i	0.437827	−	0.252779i	−0.264849	−	0.964290i	$-0.585322\pi$
$317$	138.791	−	80.1310i	0.437827	−	0.252779i	0.702675	+	0.711511i	$0.251989\pi$
$318$		0			0
$319$	−570.368	−	329.302i	−1.78799	−	1.03229i
$320$		0			0
$321$	78.4302	−	84.0977i	0.244331	−	0.261987i
$322$		0			0
$323$	212.283	−	25.2609i	0.657221	−	0.0782072i
$324$		0			0
$325$		−	54.6800i		−	0.168246i
$326$		0			0
$327$	281.955	−	302.330i	0.862248	−	0.924555i
$328$		0			0
$329$	−42.3076	+	73.2789i	−0.128594	+	0.222732i
$330$		0			0
$331$	−183.253	+	105.801i	−0.553635	+	0.319641i	−0.750587	−	0.660772i	$-0.770229\pi$
$331$	−183.253	+	105.801i	−0.553635	+	0.319641i	0.196952	+	0.980413i	$0.436896\pi$
$332$		0			0
$333$	24.6529	−	1.72143i	0.0740326	−	0.00516947i
$334$		0			0
$335$	405.119	−	233.896i	1.20931	−	0.698196i
$336$		0			0
$337$	251.413	+	145.154i	0.746034	+	0.430723i	0.824259	−	0.566213i	$-0.191592\pi$
$337$	251.413	+	145.154i	0.746034	+	0.430723i	−0.0782251	+	0.996936i	$0.524925\pi$
$338$		0			0
$339$	138.578	+	453.348i	0.408784	+	1.33731i
$340$		0			0
$341$		−	79.4766i		−	0.233069i
$342$		0			0
$343$	308.616			0.899756
$344$		0			0
$345$	28.4494	−	123.200i	0.0824620	−	0.357101i
$346$		0			0
$347$	−110.407	+	191.231i	−0.318177	+	0.551099i	−0.980108	−	0.198466i	$-0.936404\pi$
$347$	−110.407	+	191.231i	−0.318177	+	0.551099i	0.661931	+	0.749565i	$0.269737\pi$
$348$		0			0
$349$	74.6856	+	129.359i	0.213999	+	0.370657i	0.952962	−	0.303088i	$-0.0980178\pi$
$349$	74.6856	+	129.359i	0.213999	+	0.370657i	−0.738963	+	0.673745i	$0.764684\pi$
$350$		0			0
$351$	−225.503	+	86.5238i	−0.642458	+	0.246507i
$352$		0			0
$353$	−191.356	−	331.438i	−0.542085	−	0.938919i	−0.998784	−	0.0492975i	$-0.984302\pi$
$353$	−191.356	−	331.438i	−0.542085	−	0.938919i	0.456699	−	0.889621i	$-0.349032\pi$
$354$		0			0
$355$	−268.701	−	155.135i	−0.756905	−	0.436999i
$356$		0			0
$357$	−27.6614	+	119.788i	−0.0774829	+	0.335539i
$358$		0			0
$359$	319.915			0.891127			0.445563	−	0.895250i	$-0.353003\pi$
$359$	319.915			0.891127			0.445563	+	0.895250i	$0.353003\pi$
$360$		0			0
$361$	350.919	−	84.7160i	0.972075	−	0.234670i
$362$		0			0
$363$	42.4316	−	12.9703i	0.116891	−	0.0357309i
$364$		0			0
$365$	−290.331	+	502.869i	−0.795429	+	1.37772i
$366$		0			0
$367$	150.433	+	260.557i	0.409898	+	0.709964i	0.994878	−	0.101083i	$-0.0322309\pi$
$367$	150.433	+	260.557i	0.409898	+	0.709964i	−0.584980	+	0.811048i	$0.698898\pi$
$368$		0			0
$369$	14.3962	−	29.5091i	0.0390141	−	0.0799705i
$370$		0			0
$371$	−207.963	+	120.068i	−0.560547	+	0.323632i
$372$		0			0
$373$	−78.5118	−	45.3288i	−0.210487	−	0.121525i	0.391051	−	0.920369i	$-0.372112\pi$
$373$	−78.5118	−	45.3288i	−0.210487	−	0.121525i	−0.601538	+	0.798844i	$0.705445\pi$
$374$		0			0
$375$	−296.654	−	276.662i	−0.791078	−	0.737766i
$376$		0			0
$377$	505.594			1.34110
$378$		0			0
$379$			47.7140i			0.125894i	0.998017	+	0.0629472i	$0.0200500\pi$
$379$			47.7140i			0.125894i	−0.998017	+	0.0629472i	$0.979950\pi$
$380$		0			0
$381$	361.893	−	388.044i	0.949851	−	1.01849i
$382$		0			0
$383$	157.801	+	91.1066i	0.412014	+	0.237876i	0.691655	−	0.722228i	$-0.256882\pi$
$383$	157.801	+	91.1066i	0.412014	+	0.237876i	−0.279641	+	0.960105i	$0.590215\pi$
$384$		0			0
$385$	92.2250	+	159.738i	0.239545	+	0.414905i
$386$		0			0
$387$	−480.278	+	323.882i	−1.24103	+	0.836905i
$388$		0			0
$389$	−267.600	−	463.496i	−0.687917	−	1.19151i	−0.972510	−	0.232859i	$-0.925192\pi$
$389$	−267.600	−	463.496i	−0.687917	−	1.19151i	0.284593	−	0.958648i	$-0.408141\pi$
$390$		0			0
$391$	54.5590	−	94.4990i	0.139537	−	0.241685i
$392$		0			0
$393$	−682.297	+	208.562i	−1.73612	+	0.530692i
$394$		0			0
$395$		−	22.0601i		−	0.0558483i
$396$		0			0
$397$	−415.730			−1.04718			−0.523590	−	0.851971i	$-0.675408\pi$
$397$	−415.730			−1.04718			−0.523590	+	0.851971i	$0.675408\pi$
$398$		0			0
$399$	−22.4812	+	206.382i	−0.0563440	+	0.517247i
$400$		0			0
$401$	−341.091	−	196.929i	−0.850601	−	0.491095i	0.0102528	−	0.999947i	$-0.496736\pi$
$401$	−341.091	−	196.929i	−0.850601	−	0.491095i	−0.860853	+	0.508853i	$0.830070\pi$
$402$		0			0
$403$	30.5061	+	52.8381i	0.0756975	+	0.131112i
$404$		0			0
$405$	−131.935	+	326.365i	−0.325766	+	0.805839i
$406$		0			0
$407$	27.7106	−	15.9987i	0.0680849	−	0.0393088i
$408$		0			0
$409$	3.40784	+	1.96752i	0.00833213	+	0.00481056i	0.504160	−	0.863610i	$-0.331802\pi$
$409$	3.40784	+	1.96752i	0.00833213	+	0.00481056i	−0.495828	+	0.868421i	$0.665135\pi$
$410$		0			0
$411$	−74.8573	+	324.169i	−0.182135	+	0.788733i
$412$		0			0
$413$		−	134.607i		−	0.325925i
$414$		0			0
$415$	425.112			1.02437
$416$		0			0
$417$	−50.6391	+	15.4792i	−0.121437	+	0.0371203i
$418$		0			0
$419$	−257.773	+	446.476i	−0.615210	+	1.06558i	0.375137	+	0.926969i	$0.377595\pi$
$419$	−257.773	+	446.476i	−0.615210	+	1.06558i	−0.990348	+	0.138606i	$0.955738\pi$
$420$		0			0
$421$	566.357	−	326.986i	1.34527	−	0.776689i	0.357691	−	0.933840i	$-0.383564\pi$
$421$	566.357	−	326.986i	1.34527	−	0.776689i	0.987575	+	0.157151i	$0.0502309\pi$
$422$		0			0
$423$	−173.355	+	116.904i	−0.409823	+	0.276370i
$424$		0			0
$425$	−34.3876	−	59.5610i	−0.0809119	−	0.140144i
$426$		0			0
$427$	−129.967	+	225.109i	−0.304372	+	0.527188i
$428$		0			0
$429$	−213.291	+	228.704i	−0.497182	+	0.533109i
$430$		0			0
$431$		−	701.801i		−	1.62831i	−0.580649	−	0.814154i	$-0.697201\pi$
$431$		−	701.801i		−	1.62831i	0.580649	−	0.814154i	$-0.302799\pi$
$432$		0			0
$433$		−	634.175i		−	1.46461i	−0.680979	−	0.732303i	$-0.738445\pi$
$433$		−	634.175i		−	1.46461i	0.680979	−	0.732303i	$-0.261555\pi$
$434$		0			0
$435$	502.581	−	538.898i	1.15536	−	1.23885i
$436$		0			0
$437$	72.6297	−	169.344i	0.166201	−	0.387516i
$438$		0			0
$439$	−637.194	+	367.884i	−1.45147	+	0.838004i	−0.998565	−	0.0535562i	$-0.982944\pi$
$439$	−637.194	+	367.884i	−1.45147	+	0.838004i	−0.452901	+	0.891561i	$0.649611\pi$
$440$		0			0
$441$	289.050	+	141.015i	0.655442	+	0.319761i
$442$		0			0
$443$	241.376	+	418.075i	0.544867	+	0.943737i	0.998615	+	0.0526070i	$0.0167531\pi$
$443$	241.376	+	418.075i	0.544867	+	0.943737i	−0.453749	+	0.891130i	$0.649914\pi$
$444$		0			0
$445$	−85.5288	−	49.3801i	−0.192200	−	0.110966i
$446$		0			0
$447$	538.717	−	164.673i	1.20518	−	0.368396i
$448$		0			0
$449$			211.975i			0.472104i	0.971740	+	0.236052i	$0.0758536\pi$
$449$			211.975i			0.472104i	−0.971740	+	0.236052i	$0.924146\pi$
$450$		0			0
$451$		−	42.5117i		−	0.0942609i
$452$		0			0
$453$	−421.135	−	97.2488i	−0.929659	−	0.214677i
$454$		0			0
$455$	−122.627	−	70.7988i	−0.269510	−	0.155602i
$456$		0			0
$457$	122.350	+	211.916i	0.267724	+	0.463712i	0.968274	−	0.249892i	$-0.0803950\pi$
$457$	122.350	+	211.916i	0.267724	+	0.463712i	−0.700550	+	0.713604i	$0.747062\pi$
$458$		0			0
$459$	−191.218	+	236.063i	−0.416598	+	0.514298i
$460$		0			0
$461$	85.7383	+	148.503i	0.185983	+	0.322133i	0.943907	−	0.330210i	$-0.107120\pi$
$461$	85.7383	+	148.503i	0.185983	+	0.322133i	−0.757924	+	0.652343i	$0.773786\pi$
$462$		0			0
$463$	−418.250	+	724.431i	−0.903348	+	1.56465i	−0.0802290	+	0.996776i	$0.525565\pi$
$463$	−418.250	+	724.431i	−0.903348	+	1.56465i	−0.823119	+	0.567869i	$0.807768\pi$
$464$		0			0
$465$	86.6429	+	20.0076i	0.186329	+	0.0430272i
$466$		0			0
$467$	−244.116			−0.522732			−0.261366	−	0.965240i	$-0.584173\pi$
$467$	−244.116			−0.522732			−0.261366	+	0.965240i	$0.584173\pi$
$468$		0			0
$469$			392.033i			0.835890i
$470$		0			0
$471$	−212.904	+	65.0797i	−0.452025	+	0.138174i
$472$		0			0
$473$	−375.017	+	649.548i	−0.792847	+	1.37325i
$474$		0			0
$475$	−69.5463	−	93.0116i	−0.146413	−	0.195814i
$476$		0			0
$477$	−591.949	+	41.3340i	−1.24098	+	0.0866542i
$478$		0			0
$479$	271.669	+	470.545i	0.567159	+	0.982348i	0.996845	+	0.0793700i	$0.0252909\pi$
$479$	271.669	+	470.545i	0.567159	+	0.982348i	−0.429686	+	0.902978i	$0.641376\pi$
$480$		0			0
$481$	−12.2818	+	21.2727i	−0.0255339	+	0.0442260i
$482$		0			0
$483$	77.4941	+	72.2716i	0.160443	+	0.149631i
$484$		0			0
$485$			312.847i			0.645045i
$486$		0			0
$487$			494.875i			1.01617i	0.861307	+	0.508086i	$0.169647\pi$
$487$			494.875i			1.01617i	−0.861307	+	0.508086i	$0.830353\pi$
$488$		0			0
$489$	−125.389	−	116.939i	−0.256419	−	0.239139i
$490$		0			0
$491$	125.754	−	217.812i	0.256118	−	0.443609i	−0.709081	−	0.705127i	$-0.750890\pi$
$491$	125.754	−	217.812i	0.256118	−	0.443609i	0.965199	+	0.261518i	$0.0842231\pi$
$492$		0			0
$493$	550.726	−	317.962i	1.11709	−	0.644953i
$494$		0			0
$495$	31.7491	+	454.682i	0.0641395	+	0.918549i
$496$		0			0
$497$	225.185	−	130.011i	0.453089	−	0.261591i
$498$		0			0
$499$	95.5882	−	165.564i	0.191560	−	0.331791i	−0.754208	−	0.656636i	$-0.771979\pi$
$499$	95.5882	−	165.564i	0.191560	−	0.331791i	0.945767	+	0.324845i	$0.105312\pi$
$500$		0			0
$501$	230.996	+	755.687i	0.461069	+	1.50836i
$502$		0			0
$503$	243.381			0.483858			0.241929	−	0.970294i	$-0.422220\pi$
$503$	243.381			0.483858			0.241929	+	0.970294i	$0.422220\pi$
$504$		0			0
$505$	−285.951			−0.566240
$506$		0			0
$507$	−60.0584	+	260.082i	−0.118458	+	0.512983i
$508$		0			0
$509$	−117.822	−	68.0244i	−0.231477	−	0.133643i	0.379776	−	0.925078i	$-0.376001\pi$
$509$	−117.822	−	68.0244i	−0.231477	−	0.133643i	−0.611253	+	0.791435i	$0.709334\pi$
$510$		0			0
$511$	−243.312	−	421.429i	−0.476149	−	0.824715i
$512$		0			0
$513$	−273.536	+	433.990i	−0.533208	+	0.845984i
$514$		0			0
$515$	431.117	−	248.905i	0.837120	−	0.483311i
$516$		0			0
$517$	−135.361	+	234.453i	−0.261821	+	0.453487i
$518$		0			0
$519$	412.024	+	95.1448i	0.793880	+	0.183323i
$520$		0			0
$521$			575.999i			1.10556i	0.833326	+	0.552782i	$0.186434\pi$
$521$			575.999i			1.10556i	−0.833326	+	0.552782i	$0.813566\pi$
$522$		0			0
$523$		−	794.927i		−	1.51994i	−0.649960	−	0.759968i	$-0.725214\pi$
$523$		−	794.927i		−	1.51994i	0.649960	−	0.759968i	$-0.274786\pi$
$524$		0			0
$525$	63.8703	−	19.5237i	0.121658	−	0.0371879i
$526$		0			0
$527$	66.4584	+	38.3698i	0.126107	+	0.0728079i
$528$		0			0
$529$	217.474	+	376.677i	0.411105	+	0.712054i
$530$		0			0
$531$	145.842	−	298.945i	0.274655	−	0.562985i
$532$		0			0
$533$	16.3176	+	28.2629i	0.0306146	+	0.0530260i
$534$		0			0
$535$	144.269	+	83.2939i	0.269662	+	0.155689i
$536$		0			0
$537$	290.442	−	311.430i	0.540861	−	0.579945i
$538$		0			0
$539$	416.413			0.772567
$540$		0			0
$541$	534.945			0.988807			0.494403	−	0.869233i	$-0.335387\pi$
$541$	534.945			0.988807			0.494403	+	0.869233i	$0.335387\pi$
$542$		0			0
$543$	−287.239	+	307.996i	−0.528986	+	0.567211i
$544$		0			0
$545$	518.645	+	299.440i	0.951642	+	0.549431i
$546$		0			0
$547$	482.764	−	278.724i	0.882567	−	0.509550i	0.0110629	−	0.999939i	$-0.496479\pi$
$547$	482.764	−	278.724i	0.882567	−	0.509550i	0.871504	+	0.490389i	$0.163145\pi$
$548$		0			0
$549$	−532.539	+	359.125i	−0.970016	+	0.654144i
$550$		0			0
$551$	860.023	−	643.054i	1.56084	−	1.16707i
$552$		0			0
$553$	16.0106	+	9.24372i	0.0289522	+	0.0167156i
$554$		0			0
$555$	10.4654	+	34.2367i	0.0188565	+	0.0616878i
$556$		0			0
$557$	−66.6834			−0.119719			−0.0598595	−	0.998207i	$-0.519065\pi$
$557$	−66.6834			−0.119719			−0.0598595	+	0.998207i	$0.519065\pi$
$558$		0			0
$559$		−	575.782i		−	1.03002i
$560$		0			0
$561$	−88.5014	+	383.255i	−0.157757	+	0.683164i
$562$		0			0
$563$	357.589	+	206.454i	0.635150	+	0.366704i	0.782744	−	0.622344i	$-0.213820\pi$
$563$	357.589	+	206.454i	0.635150	+	0.366704i	−0.147594	+	0.989048i	$0.547153\pi$
$564$		0			0
$565$	−594.738	+	343.372i	−1.05263	+	0.607738i
$566$		0			0
$567$	−181.582	−	232.510i	−0.320251	−	0.410071i
$568$		0			0
$569$	−213.430	+	123.224i	−0.375097	+	0.216562i	−0.675683	−	0.737193i	$-0.736151\pi$
$569$	−213.430	+	123.224i	−0.375097	+	0.216562i	0.300586	+	0.953755i	$0.402818\pi$
$570$		0			0
$571$	−33.3969	+	57.8451i	−0.0584885	+	0.101305i	−0.893787	−	0.448492i	$-0.851961\pi$
$571$	−33.3969	+	57.8451i	−0.0584885	+	0.101305i	0.835299	+	0.549797i	$0.185295\pi$
$572$		0			0
$573$	−80.9252	+	350.446i	−0.141231	+	0.611599i
$574$		0			0
$575$	−59.2789			−0.103094
$576$		0			0
$577$	880.350			1.52574			0.762869	−	0.646553i	$-0.223790\pi$
$577$	880.350			1.52574			0.762869	+	0.646553i	$0.223790\pi$
$578$		0			0
$579$	−293.375	−	959.756i	−0.506692	−	1.65761i
$580$		0			0
$581$	−178.132	+	308.534i	−0.306596	+	0.531040i
$582$		0			0
$583$	−665.369	+	384.151i	−1.14128	+	0.658921i
$584$		0			0
$585$	−195.632	−	290.098i	−0.334413	−	0.495894i
$586$		0			0
$587$	−471.004	−	815.804i	−0.802393	−	1.38978i	−0.918037	−	0.396494i	$-0.870227\pi$
$587$	−471.004	−	815.804i	−0.802393	−	1.38978i	0.115645	−	0.993291i	$-0.463107\pi$
$588$		0			0
$589$	119.095	+	51.0784i	0.202199	+	0.0867205i
$590$		0			0
$591$	167.716	+	156.413i	0.283783	+	0.264659i
$592$		0			0
$593$	877.906			1.48045			0.740224	−	0.672360i	$-0.234719\pi$
$593$	877.906			1.48045			0.740224	+	0.672360i	$0.234719\pi$
$594$		0			0
$595$	−178.098			−0.299324
$596$		0			0
$597$	123.057	+	114.764i	0.206126	+	0.192235i
$598$		0			0
$599$	620.056	+	357.990i	1.03515	+	0.597645i	0.918456	−	0.395522i	$-0.129436\pi$
$599$	620.056	+	357.990i	1.03515	+	0.597645i	0.116696	+	0.993168i	$0.462770\pi$
$600$		0			0
$601$	34.6215	−	19.9887i	0.0576065	−	0.0332591i	−0.470920	−	0.882176i	$-0.656078\pi$
$601$	34.6215	−	19.9887i	0.0576065	−	0.0332591i	0.528527	+	0.848917i	$0.322745\pi$
$602$		0			0
$603$	−424.754	+	870.655i	−0.704401	+	1.44387i
$604$		0			0
$605$	32.1383	+	55.6651i	0.0531211	+	0.0920085i
$606$		0			0
$607$	−443.057	−	255.799i	−0.729912	−	0.421415i	0.0884777	−	0.996078i	$-0.471800\pi$
$607$	−443.057	−	255.799i	−0.729912	−	0.421415i	−0.818390	+	0.574663i	$0.805133\pi$
$608$		0			0
$609$	180.524	+	590.571i	0.296426	+	0.969739i
$610$		0			0
$611$		−	207.827i		−	0.340142i
$612$		0			0
$613$	−787.699			−1.28499			−0.642495	−	0.766290i	$-0.722101\pi$
$613$	−787.699			−1.28499			−0.642495	+	0.766290i	$0.722101\pi$
$614$		0			0
$615$	46.3449	+	10.7020i	0.0753576	+	0.0174016i
$616$		0			0
$617$	261.236	−	452.473i	0.423396	−	0.733344i	−0.572873	−	0.819644i	$-0.694171\pi$
$617$	261.236	−	452.473i	0.423396	−	0.733344i	0.996269	+	0.0863003i	$0.0275045\pi$
$618$		0			0
$619$	141.522	+	245.124i	0.228631	+	0.396000i	0.957403	−	0.288757i	$-0.0932418\pi$
$619$	141.522	+	245.124i	0.228631	+	0.396000i	−0.728772	+	0.684757i	$0.759908\pi$
$620$		0			0
$621$	93.8009	+	244.469i	0.151048	+	0.393669i
$622$		0			0
$623$	71.6774	−	41.3830i	0.115052	−	0.0664253i
$624$		0			0
$625$	217.413	−	376.570i	0.347860	−	0.602512i
$626$		0			0
$627$	−71.9278	+	660.309i	−0.114717	+	1.05312i
$628$		0			0
$629$			30.8955i			0.0491184i
$630$		0			0
$631$	506.286			0.802356			0.401178	−	0.916000i	$-0.368601\pi$
$631$	506.286			0.802356			0.401178	+	0.916000i	$0.368601\pi$
$632$		0			0
$633$	−9.21103	−	30.1333i	−0.0145514	−	0.0476039i
$634$		0			0
$635$	665.688	+	384.335i	1.04833	+	0.605253i
$636$		0			0
$637$	−276.843	+	159.835i	−0.434604	+	0.250919i
$638$		0			0
$639$	640.970	−	44.7570i	1.00308	−	0.0700423i
$640$		0			0
$641$	711.204	−	410.614i	1.10952	−	0.640583i	0.170817	−	0.985303i	$-0.445359\pi$
$641$	711.204	−	410.614i	1.10952	−	0.640583i	0.938706	+	0.344719i	$0.112026\pi$
$642$		0			0
$643$	197.605	−	342.262i	0.307317	−	0.532289i	−0.670457	−	0.741948i	$-0.733902\pi$
$643$	197.605	−	342.262i	0.307317	−	0.532289i	0.977775	+	0.209659i	$0.0672354\pi$
$644$		0			0
$645$	−613.710	−	572.350i	−0.951488	−	0.887365i
$646$		0			0
$647$	−30.6110			−0.0473123			−0.0236561	−	0.999720i	$-0.507531\pi$
$647$	−30.6110			−0.0473123			−0.0236561	+	0.999720i	$0.507531\pi$
$648$		0			0
$649$		−	430.669i		−	0.663588i
$650$		0			0
$651$	−50.8265	+	54.4994i	−0.0780746	+	0.0837164i
$652$		0			0
$653$	−570.679	+	988.444i	−0.873934	+	1.51370i	−0.0160393	+	0.999871i	$0.505106\pi$
$653$	−570.679	+	988.444i	−0.873934	+	1.51370i	−0.857894	+	0.513826i	$0.828228\pi$
$654$		0			0
$655$	−516.781	−	895.091i	−0.788979	−	1.36655i
$656$		0			0
$657$	−83.7618	−	1199.56i	−0.127491	−	1.82582i
$658$		0			0
$659$	805.453	−	465.028i	1.22223	−	0.705658i	0.256841	−	0.966454i	$-0.417318\pi$
$659$	805.453	−	465.028i	1.22223	−	0.705658i	0.965394	+	0.260796i	$0.0839850\pi$
$660$		0			0
$661$	−808.528	−	466.804i	−1.22319	−	0.706208i	−0.257592	−	0.966254i	$-0.582929\pi$
$661$	−808.528	−	466.804i	−1.22319	−	0.706208i	−0.965596	+	0.260045i	$0.916263\pi$
$662$		0			0
$663$	−88.2696	−	288.768i	−0.133137	−	0.435548i
$664$		0			0
$665$	−298.638	+	35.5370i	−0.449080	+	0.0534390i
$666$		0			0
$667$		−	548.117i		−	0.821765i
$668$		0			0
$669$	395.391	+	91.3039i	0.591018	+	0.136478i
$670$		0			0
$671$	−415.824	+	720.228i	−0.619707	+	1.07336i
$672$		0			0
$673$	849.446	−	490.428i	1.26218	−	0.728719i	0.288683	−	0.957425i	$-0.406783\pi$
$673$	849.446	−	490.428i	1.26218	−	0.728719i	0.973496	+	0.228706i	$0.0734495\pi$
$674$		0			0
$675$	163.001	+	25.8418i	0.241483	+	0.0382841i
$676$		0			0
$677$	−721.766	+	416.712i	−1.06612	+	0.615527i	−0.927120	−	0.374764i	$-0.877724\pi$
$677$	−721.766	+	416.712i	−1.06612	+	0.615527i	−0.139004	+	0.990292i	$0.544390\pi$
$678$		0			0
$679$	−227.056	−	131.091i	−0.334397	−	0.193064i
$680$		0			0
$681$	976.251	+	225.436i	1.43356	+	0.331037i
$682$		0			0
$683$		−	102.034i		−	0.149391i	−0.997206	−	0.0746953i	$-0.976202\pi$
$683$		−	102.034i		−	0.149391i	0.997206	−	0.0746953i	$-0.0237984\pi$
$684$		0			0
$685$	−481.969			−0.703604
$686$		0			0
$687$	−46.9481	+	14.3509i	−0.0683378	+	0.0208893i
$688$		0			0
$689$	294.903	−	510.787i	0.428016	−	0.741346i
$690$		0			0
$691$	38.7741	+	67.1587i	0.0561131	+	0.0971907i	0.892717	−	0.450617i	$-0.148796\pi$
$691$	38.7741	+	67.1587i	0.0561131	+	0.0971907i	−0.836604	+	0.547808i	$0.815463\pi$
$692$		0			0
$693$	−343.299	−	167.480i	−0.495381	−	0.241675i
$694$		0			0
$695$	−38.3548	−	66.4324i	−0.0551867	−	0.0955862i
$696$		0			0
$697$	35.5483	+	20.5238i	0.0510019	+	0.0294460i
$698$		0			0
$699$	393.299	+	366.794i	0.562659	+	0.524740i
$700$		0			0
$701$	422.018			0.602023			0.301011	−	0.953621i	$-0.402676\pi$
$701$	422.018			0.602023			0.301011	+	0.953621i	$0.402676\pi$
$702$		0			0
$703$	6.16476	+	51.8061i	0.00876922	+	0.0736929i
$704$		0			0
$705$	−221.517	−	206.588i	−0.314208	−	0.293033i
$706$		0			0
$707$	119.821	−	207.536i	0.169478	−	0.293544i
$708$		0			0
$709$	187.857	+	325.379i	0.264961	+	0.458926i	0.967553	−	0.252666i	$-0.0813075\pi$
$709$	187.857	+	325.379i	0.264961	+	0.458926i	−0.702592	+	0.711593i	$0.747974\pi$
$710$		0			0
$711$	25.5423	+	37.8761i	0.0359244	+	0.0532716i
$712$		0			0
$713$	57.2821	−	33.0718i	0.0803395	−	0.0463840i
$714$		0			0
$715$	−392.340	−	226.518i	−0.548728	−	0.316808i
$716$		0			0
$717$	−201.585	+	61.6197i	−0.281150	+	0.0859410i
$718$		0			0
$719$	−761.500			−1.05911			−0.529555	−	0.848276i	$-0.677641\pi$
$719$	−761.500			−1.05911			−0.529555	+	0.848276i	$0.677641\pi$
$720$		0			0
$721$			417.190i			0.578628i
$722$		0			0
$723$	−875.466	−	202.163i	−1.21088	−	0.279617i
$724$		0			0
$725$	−299.184	−	172.734i	−0.412668	−	0.238254i
$726$		0			0
$727$	−194.639	−	337.125i	−0.267729	−	0.463720i	0.700546	−	0.713607i	$-0.252940\pi$
$727$	−194.639	−	337.125i	−0.267729	−	0.463720i	−0.968275	+	0.249887i	$0.919607\pi$
$728$		0			0
$729$	−151.355	−	713.115i	−0.207620	−	0.978210i
$730$		0			0
$731$	−362.102	−	627.179i	−0.495351	−	0.857974i
$732$		0			0
$733$	43.0753	−	74.6086i	0.0587658	−	0.101785i	−0.835146	−	0.550029i	$-0.814617\pi$
$733$	43.0753	−	74.6086i	0.0587658	−	0.101785i	0.893912	+	0.448243i	$0.147950\pi$
$734$		0			0
$735$	−104.829	+	453.961i	−0.142624	+	0.617634i
$736$		0			0
$737$			1254.29i			1.70189i
$738$		0			0
$739$	−423.086			−0.572511			−0.286256	−	0.958153i	$-0.592411\pi$
$739$	−423.086			−0.572511			−0.286256	+	0.958153i	$0.592411\pi$
$740$		0			0
$741$	−205.632	−	466.599i	−0.277506	−	0.629689i
$742$		0			0
$743$	−620.981	−	358.523i	−0.835775	−	0.482535i	0.0200511	−	0.999799i	$-0.493617\pi$
$743$	−620.981	−	358.523i	−0.835775	−	0.482535i	−0.855826	+	0.517264i	$0.826950\pi$
$744$		0			0
$745$	408.032	+	706.732i	0.547693	+	0.948633i
$746$		0			0
$747$	−729.896	+	492.216i	−0.977104	+	0.658924i
$748$		0			0
$749$	−120.905	+	69.8044i	−0.161422	+	0.0931968i
$750$		0			0
$751$	−1193.11	−	688.841i	−1.58869	−	0.917232i	−0.993523	−	0.113631i	$-0.963752\pi$
$751$	−1193.11	−	688.841i	−1.58869	−	0.917232i	−0.595169	−	0.803600i	$-0.702915\pi$
$752$		0			0
$753$	0.700032	+	0.652855i	0.000929657	+	0.000867006i
$754$		0			0
$755$		−	626.136i		−	0.829320i
$756$		0			0
$757$	−104.619			−0.138202			−0.0691011	−	0.997610i	$-0.522013\pi$
$757$	−104.619			−0.138202			−0.0691011	+	0.997610i	$0.522013\pi$
$758$		0			0
$759$	247.939	+	231.230i	0.326665	+	0.304651i
$760$		0			0
$761$	135.264	−	234.285i	0.177745	−	0.307864i	−0.763363	−	0.645970i	$-0.776453\pi$
$761$	135.264	−	234.285i	0.177745	−	0.307864i	0.941108	+	0.338106i	$0.109786\pi$
$762$		0			0
$763$	−434.650	+	250.946i	−0.569660	+	0.328893i
$764$		0			0
$765$	−395.533	−	192.963i	−0.517037	−	0.252239i
$766$		0			0
$767$	165.307	+	286.320i	0.215524	+	0.373298i
$768$		0			0
$769$	451.785	−	782.515i	0.587497	−	1.01757i	−0.407062	−	0.913400i	$-0.633447\pi$
$769$	451.785	−	782.515i	0.587497	−	1.01757i	0.994559	−	0.104174i	$-0.0332199\pi$
$770$		0			0
$771$	128.553	+	420.553i	0.166736	+	0.545465i
$772$		0			0
$773$		−	542.519i		−	0.701836i	−0.936406	−	0.350918i	$-0.885870\pi$
$773$		−	542.519i		−	0.701836i	0.936406	−	0.350918i	$-0.114130\pi$
$774$		0			0
$775$		−	41.6892i		−	0.0537925i
$776$		0			0
$777$	−29.2333	−	6.75058i	−0.0376234	−	0.00868800i
$778$		0			0
$779$	63.7034	+	27.3216i	0.0817758	+	0.0350727i
$780$		0			0
$781$	720.470	−	415.964i	0.922497	−	0.532604i
$782$		0			0
$783$	−238.944	+	1507.18i	−0.305164	+	1.92487i
$784$		0			0
$785$	−161.256	−	279.304i	−0.205422	−	0.355802i
$786$		0			0
$787$	−1266.36	−	731.136i	−1.60910	−	0.929016i	−0.989571	−	0.144045i	$-0.953989\pi$
$787$	−1266.36	−	731.136i	−1.60910	−	0.929016i	−0.619532	−	0.784971i	$-0.712678\pi$
$788$		0			0
$789$	−174.331	+	754.939i	−0.220952	+	0.956831i
$790$		0			0
$791$		−	575.526i		−	0.727592i
$792$		0			0
$793$		−	638.435i		−	0.805088i
$794$		0			0
$795$	−251.288	−	822.072i	−0.316085	−	1.03405i
$796$		0			0
$797$	836.479	+	482.941i	1.04953	+	0.605949i	0.922519	−	0.385952i	$-0.126127\pi$
$797$	836.479	+	482.941i	1.04953	+	0.605949i	0.127015	+	0.991901i	$0.459460\pi$
$798$		0			0
$799$	−130.700	−	226.379i	−0.163579	−	0.283327i
$800$		0			0
$801$	204.024	−	14.2464i	0.254711	−	0.0177857i
$802$		0			0
$803$	−778.467	−	1348.34i	−0.969449	−	1.67913i
$804$		0			0
$805$	−76.7534	+	132.941i	−0.0953458	+	0.165144i
$806$		0			0
$807$	612.533	−	656.795i	0.759024	−	0.813873i
$808$		0			0
$809$	872.948			1.07905			0.539523	−	0.841971i	$-0.318605\pi$
$809$	872.948			1.07905			0.539523	+	0.841971i	$0.318605\pi$
$810$		0			0
$811$		−	1265.77i		−	1.56075i	−0.625312	−	0.780375i	$-0.715028\pi$
$811$		−	1265.77i		−	1.56075i	0.625312	−	0.780375i	$-0.284972\pi$
$812$		0			0
$813$	286.683	+	267.363i	0.352623	+	0.328859i
$814$		0			0
$815$	124.190	−	215.104i	0.152381	−	0.263932i
$816$		0			0
$817$	−732.324	−	979.414i	−0.896358	−	1.19879i
$818$		0			0
$819$	292.520	−	20.4258i	0.357167	−	0.0249399i
$820$		0			0
$821$	−250.001	−	433.014i	−0.304507	−	0.527422i	0.672644	−	0.739966i	$-0.265158\pi$
$821$	−250.001	−	433.014i	−0.304507	−	0.527422i	−0.977152	+	0.212544i	$0.931825\pi$
$822$		0			0
$823$	−405.788	+	702.846i	−0.493060	+	0.854004i	−0.999968	−	0.00799557i	$-0.997455\pi$
$823$	−405.788	+	702.846i	−0.493060	+	0.854004i	0.506908	+	0.862000i	$0.330788\pi$
$824$		0			0
$825$	204.350	−	62.4651i	0.247697	−	0.0757153i
$826$		0			0
$827$			138.719i			0.167738i	0.996477	+	0.0838688i	$0.0267277\pi$
$827$			138.719i			0.167738i	−0.996477	+	0.0838688i	$0.973272\pi$
$828$		0			0
$829$		−	1048.35i		−	1.26460i	−0.774724	−	0.632299i	$-0.782111\pi$
$829$		−	1048.35i		−	1.26460i	0.774724	−	0.632299i	$-0.217889\pi$
$830$		0			0
$831$	−60.6399	+	262.601i	−0.0729722	+	0.316006i
$832$		0			0
$833$	−201.036	+	348.205i	−0.241340	+	0.418014i
$834$		0			0
$835$	−991.370	+	572.368i	−1.18727	+	0.685471i
$836$		0			0
$837$	−171.928	+	65.9674i	−0.205409	+	0.0788142i
$838$		0			0
$839$	623.353	−	359.893i	0.742971	−	0.428954i	−0.0801776	−	0.996781i	$-0.525549\pi$
$839$	623.353	−	359.893i	0.742971	−	0.428954i	0.823149	+	0.567826i	$0.192215\pi$
$840$		0			0
$841$	1176.67	−	2038.05i	1.39913	−	2.42337i
$842$		0			0
$843$	1225.51	+	282.996i	1.45375	+	0.335701i
$844$		0			0
$845$	−386.686			−0.457616
$846$		0			0
$847$	−53.8670			−0.0635974
$848$		0			0
$849$	−631.254	+	192.960i	−0.743527	+	0.227279i
$850$		0			0
$851$	23.0619	+	13.3148i	0.0270997	+	0.0156460i
$852$		0			0
$853$	694.382	+	1202.71i	0.814047	+	1.40997i	0.910010	+	0.414586i	$0.136074\pi$
$853$	694.382	+	1202.71i	0.814047	+	1.40997i	−0.0959626	+	0.995385i	$0.530593\pi$
$854$		0			0
$855$	−701.741	−	244.641i	−0.820750	−	0.286130i
$856$		0			0
$857$	−676.350	+	390.491i	−0.789206	+	0.455648i	−0.839683	−	0.543077i	$-0.817259\pi$
$857$	−676.350	+	390.491i	−0.789206	+	0.455648i	0.0504770	+	0.998725i	$0.483926\pi$
$858$		0			0
$859$	295.064	−	511.066i	0.343497	−	0.594954i	−0.641583	−	0.767054i	$-0.721722\pi$
$859$	295.064	−	511.066i	0.343497	−	0.594954i	0.985080	+	0.172100i	$0.0550552\pi$
$860$		0			0
$861$	−27.1869	+	29.1515i	−0.0315760	+	0.0338577i
$862$		0			0
$863$			583.712i			0.676376i	0.941079	+	0.338188i	$0.109814\pi$
$863$			583.712i			0.676376i	−0.941079	+	0.338188i	$0.890186\pi$
$864$		0			0
$865$			612.590i			0.708196i
$866$		0			0
$867$	356.303	+	332.291i	0.410960	+	0.383265i
$868$		0			0
$869$	51.2252	+	29.5749i	0.0589473	+	0.0340332i
$870$		0			0
$871$	−481.444	−	833.886i	−0.552749	−	0.957389i
$872$		0			0
$873$	−362.230	−	537.144i	−0.414926	−	0.615285i
$874$		0			0
$875$	246.235	+	426.491i	0.281411	+	0.487419i
$876$		0			0
$877$	963.193	+	556.100i	1.09828	+	0.634093i	0.935769	−	0.352613i	$-0.114707\pi$
$877$	963.193	+	556.100i	1.09828	+	0.634093i	0.162512	+	0.986707i	$0.448040\pi$
$878$		0			0
$879$	−199.528	−	652.742i	−0.226994	−	0.742596i
$880$		0			0
$881$	1326.11			1.50523			0.752615	−	0.658461i	$-0.228792\pi$
$881$	1326.11			1.50523			0.752615	+	0.658461i	$0.228792\pi$
$882$		0			0
$883$	−234.332			−0.265382			−0.132691	−	0.991157i	$-0.542362\pi$
$883$	−234.332			−0.265382			−0.132691	+	0.991157i	$0.542362\pi$
$884$		0			0
$885$	469.502	+	108.418i	0.530511	+	0.122506i
$886$		0			0
$887$	1080.29	+	623.704i	1.21791	+	0.703162i	0.964471	−	0.264189i	$-0.0851043\pi$
$887$	1080.29	+	623.704i	1.21791	+	0.703162i	0.253441	+	0.967351i	$0.418438\pi$
$888$		0			0
$889$	−557.880	+	322.092i	−0.627537	+	0.362309i
$890$		0			0
$891$	−580.965	−	743.906i	−0.652037	−	0.834912i
$892$		0			0
$893$	−264.331	−	353.517i	−0.296003	−	0.395875i
$894$		0			0
$895$	534.257	+	308.453i	0.596935	+	0.344641i
$896$		0			0
$897$	−253.591	−	58.5594i	−0.282710	−	0.0652836i
$898$		0			0
$899$	385.475			0.428782
$900$		0			0
$901$		−	741.843i		−	0.823355i
$902$		0			0
$903$	672.556	−	205.584i	0.744802	−	0.227668i
$904$		0			0
$905$	−528.365	−	305.052i	−0.583829	−	0.337074i
$906$		0			0
$907$	1237.30	−	714.354i	1.36416	−	0.787601i	0.373989	−	0.927433i	$-0.377990\pi$
$907$	1237.30	−	714.354i	1.36416	−	0.787601i	0.990175	+	0.139832i	$0.0446564\pi$
$908$		0			0
$909$	490.965	−	331.089i	0.540115	−	0.364234i
$910$		0			0
$911$	90.4263	−	52.2076i	0.0992605	−	0.0573081i	−0.449548	−	0.893256i	$-0.648415\pi$
$911$	90.4263	−	52.2076i	0.0992605	−	0.0573081i	0.548809	+	0.835948i	$0.315082\pi$
$912$		0			0
$913$	−569.927	+	987.142i	−0.624235	+	1.08121i
$914$		0			0
$915$	−680.490	−	634.630i	−0.743705	−	0.693585i
$916$		0			0
$917$	866.177			0.944577
$918$		0			0
$919$	−866.956			−0.943369			−0.471685	−	0.881767i	$-0.656354\pi$
$919$	−866.956			−0.943369			−0.471685	+	0.881767i	$0.656354\pi$
$920$		0			0
$921$	855.610	−	917.438i	0.929001	−	0.996132i
$922$		0			0
$923$	−319.325	+	553.087i	−0.345964	+	0.599227i
$924$		0			0
$925$	14.5355	−	8.39206i	0.0157140	−	0.00907250i
$926$		0			0
$927$	−452.012	+	926.528i	−0.487607	+	0.999491i
$928$		0			0
$929$	−716.613	−	1241.21i	−0.771381	−	1.33607i	−0.936806	−	0.349849i	$-0.886233\pi$
$929$	−716.613	−	1241.21i	−0.771381	−	1.33607i	0.165425	−	0.986222i	$-0.447100\pi$
$930$		0			0
$931$	−267.622	+	623.992i	−0.287457	+	0.670238i
$932$		0			0
$933$	383.214	−	117.140i	0.410733	−	0.125552i
$934$		0			0
$935$	−569.817			−0.609430
$936$		0			0
$937$	1072.93			1.14506			0.572532	−	0.819882i	$-0.305961\pi$
$937$	1072.93			1.14506			0.572532	+	0.819882i	$0.305961\pi$
$938$		0			0
$939$	−267.479	+	1158.32i	−0.284855	+	1.23356i
$940$		0			0
$941$	−168.798	−	97.4555i	−0.179381	−	0.103566i	0.407621	−	0.913151i	$-0.366359\pi$
$941$	−168.798	−	97.4555i	−0.179381	−	0.103566i	−0.587002	+	0.809585i	$0.699692\pi$
$942$		0			0
$943$	30.6399	−	17.6900i	0.0324920	−	0.0187593i
$944$		0			0
$945$	269.005	−	332.092i	0.284661	−	0.351420i
$946$		0			0
$947$	510.794	+	884.721i	0.539381	+	0.934235i	0.998937	+	0.0460868i	$0.0146751\pi$
$947$	510.794	+	884.721i	0.539381	+	0.934235i	−0.459556	+	0.888149i	$0.651992\pi$
$948$		0			0
$949$	1035.09	+	597.610i	1.09072	+	0.629726i
$950$		0			0
$951$	−468.458	−	108.177i	−0.492595	−	0.113750i
$952$		0			0
$953$			166.198i			0.174394i	0.996191	+	0.0871971i	$0.0277910\pi$
$953$			166.198i			0.174394i	−0.996191	+	0.0871971i	$0.972209\pi$
$954$		0			0
$955$	−521.037			−0.545588
$956$		0			0
$957$	577.578	+	1889.51i	0.603530	+	1.97441i
$958$		0			0
$959$	201.957	−	349.800i	0.210591	−	0.364755i
$960$		0			0
$961$	−457.242	−	791.966i	−0.475798	−	0.824106i
$962$		0			0
$963$	−344.145	+	24.0306i	−0.357368	+	0.0249539i
$964$		0			0
$965$	1259.08	−	726.933i	1.30475	−	0.753298i
$966$		0			0
$967$	602.751	−	1043.99i	0.623320	−	1.07962i	−0.365543	−	0.930794i	$-0.619117\pi$
$967$	602.751	−	1043.99i	0.623320	−	1.07962i	0.988863	−	0.148828i	$-0.0475500\pi$
$968$		0			0
$969$	−517.426	−	378.931i	−0.533979	−	0.391053i
$970$		0			0
$971$			145.916i			0.150274i	0.997173	+	0.0751368i	$0.0239394\pi$
$971$			145.916i			0.150274i	−0.997173	+	0.0751368i	$0.976061\pi$
$972$		0			0
$973$	64.2864			0.0660703
$974$		0			0
$975$	−111.881	+	119.966i	−0.114750	+	0.123042i
$976$		0			0
$977$	324.946	+	187.608i	0.332596	+	0.192024i	0.656993	−	0.753897i	$-0.271828\pi$
$977$	324.946	+	187.608i	0.332596	+	0.192024i	−0.324397	+	0.945921i	$0.605161\pi$
$978$		0			0
$979$	229.329	−	132.403i	0.234248	−	0.135243i
$980$		0			0
$981$	−1237.20	+	86.3896i	−1.26116	+	0.0880628i
$982$		0			0
$983$	−386.037	+	222.878i	−0.392713	+	0.226733i	−0.683335	−	0.730105i	$-0.739471\pi$
$983$	−386.037	+	222.878i	−0.392713	+	0.226733i	0.290622	+	0.956838i	$0.406138\pi$
$984$		0			0
$985$	−166.113	+	287.716i	−0.168642	+	0.292097i
$986$		0			0
$987$	242.757	−	74.2052i	0.245955	−	0.0751825i
$988$		0			0
$989$	−624.208			−0.631151
$990$		0			0
$991$			1326.79i			1.33884i	0.742884	+	0.669420i	$0.233457\pi$
$991$			1326.79i			1.33884i	−0.742884	+	0.669420i	$0.766543\pi$
$992$		0			0
$993$	618.530	+	142.831i	0.622891	+	0.143838i
$994$		0			0
$995$	−121.881	+	211.105i	−0.122494	+	0.212165i
$996$		0			0
$997$	−295.318	−	511.506i	−0.296207	−	0.513046i	0.679058	−	0.734085i	$-0.262388\pi$
$997$	−295.318	−	511.506i	−0.296207	−	0.513046i	−0.975265	+	0.221039i	$0.929055\pi$
$998$		0			0
$999$	−57.6096	−	46.6656i	−0.0576673	−	0.0467123i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	684.3.t.a.265.10	✓	80
3.2	odd	2		2052.3.t.a.37.11		80
9.2	odd	6		2052.3.t.a.721.12		80
9.7	even	3	inner	684.3.t.a.493.31	yes	80
19.18	odd	2	inner	684.3.t.a.265.31	yes	80
57.56	even	2		2052.3.t.a.37.12		80
171.56	even	6		2052.3.t.a.721.11		80
171.151	odd	6	inner	684.3.t.a.493.10	yes	80

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
684.3.t.a.265.10	✓	80	1.1	even	1	trivial
684.3.t.a.265.31	yes	80	19.18	odd	2	inner
684.3.t.a.493.10	yes	80	171.151	odd	6	inner
684.3.t.a.493.31	yes	80	9.7	even	3	inner
2052.3.t.a.37.11		80	3.2	odd	2
2052.3.t.a.37.12		80	57.56	even	2
2052.3.t.a.721.11		80	171.56	even	6
2052.3.t.a.721.12		80	9.2	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 684 = 2^{2} \cdot 3^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	684.t (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-2.19396 - 2.04610i) q^{3} +(2.17299 - 3.76373i) q^{5} +(1.82107 + 3.15419i) q^{7} +(0.626916 + 8.97814i) q^{9} +O(q^{10})\)	\(q+(-2.19396 - 2.04610i) q^{3} +(2.17299 - 3.76373i) q^{5} +(1.82107 + 3.15419i) q^{7} +(0.626916 + 8.97814i) q^{9} +(5.82645 + 10.0917i) q^{11} +(-7.74715 - 4.47282i) q^{13} +(-12.4684 + 3.81130i) q^{15} -11.2516 q^{17} +(-18.8669 + 2.24510i) q^{19} +(2.45844 - 10.6463i) q^{21} +(-4.84901 + 8.39872i) q^{23} +(3.05624 + 5.29357i) q^{25} +(16.9948 - 20.9804i) q^{27} +(-48.9465 + 28.2593i) q^{29} +(-5.90658 - 3.41017i) q^{31} +(7.86568 - 34.0623i) q^{33} +15.8287 q^{35} -2.74588i q^{37} +(7.84508 + 25.6647i) q^{39} +(-3.15940 - 1.82408i) q^{41} +(32.1823 + 55.7414i) q^{43} +(35.1535 + 17.1499i) q^{45} +(11.6161 + 20.1197i) q^{47} +(17.8674 - 30.9472i) q^{49} +(24.6855 + 23.0219i) q^{51} +65.9323i q^{53} +50.6432 q^{55} +(45.9869 + 33.6780i) q^{57} +(-32.0067 - 18.4791i) q^{59} +(35.6842 + 61.8068i) q^{61} +(-27.1771 + 18.3273i) q^{63} +(-33.6689 + 19.4388i) q^{65} +(93.2170 + 53.8189i) q^{67} +(27.8232 - 8.50489i) q^{69} -71.3923i q^{71} -133.609 q^{73} +(4.12592 - 17.8673i) q^{75} +(-21.2208 + 36.7555i) q^{77} +(4.39592 - 2.53799i) q^{79} +(-80.2140 + 11.2571i) q^{81} +(48.9086 + 84.7122i) q^{83} +(-24.4496 + 42.3479i) q^{85} +(165.208 + 38.1499i) q^{87} -22.7245i q^{89} -32.5813i q^{91} +(5.98124 + 19.5672i) q^{93} +(-32.5476 + 75.8884i) q^{95} +(-62.3412 + 35.9927i) q^{97} +(-86.9520 + 58.6373i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 80 q + 2 q^{7} + 4 q^{9}+O(q^{10}) \) 80 * q + 2 * q^7 + 4 * q^9	\( 80 q + 2 q^{7} + 4 q^{9} + 12 q^{11} - 12 q^{17} - 2 q^{19} - 48 q^{23} - 200 q^{25} - 216 q^{35} + 102 q^{39} + 28 q^{43} + 2 q^{45} - 174 q^{47} - 306 q^{49} + 213 q^{57} + 14 q^{61} + 62 q^{63} + 220 q^{73} - 60 q^{77} + 340 q^{81} + 150 q^{83} - 252 q^{87} - 252 q^{93} + 360 q^{95} + 542 q^{99}+O(q^{100}) \) 80 * q + 2 * q^7 + 4 * q^9 + 12 * q^11 - 12 * q^17 - 2 * q^19 - 48 * q^23 - 200 * q^25 - 216 * q^35 + 102 * q^39 + 28 * q^43 + 2 * q^45 - 174 * q^47 - 306 * q^49 + 213 * q^57 + 14 * q^61 + 62 * q^63 + 220 * q^73 - 60 * q^77 + 340 * q^81 + 150 * q^83 - 252 * q^87 - 252 * q^93 + 360 * q^95 + 542 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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