LMFDB - Embedded newform 1232.2.q.k.177.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

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

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

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

chi := DirichletCharacter("1232.177");

S:= CuspForms(chi, 2);

N := Newforms(S);

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

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$9.83756952902$
Analytic rank:	$0$
Dimension:	$6$
Relative dimension:	$3$ over $\Q(\zeta_{3})$
Coefficient field:	6.0.1783323.2
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - x^{5} + 5x^{4} - 2x^{3} + 19x^{2} - 12x + 9 $ x^6 - x^5 + 5x^4 - 2x^3 + 19x^2 - 12x + 9
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 77)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			177.3
Root			$-0.956115 - 1.65604i$ of defining polynomial
Character	$\chi$	$=$	1232.177
Dual form			1232.2.q.k.529.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.956115 + 1.65604i) q^{3} +(1.78442 - 3.09071i) q^{5} +(-1.78442 - 1.95341i) q^{7} +(-0.328310 + 0.568650i) q^{9} +O(q^{10})$	\(q+(0.956115 + 1.65604i) q^{3} +(1.78442 - 3.09071i) q^{5} +(-1.78442 - 1.95341i) q^{7} +(-0.328310 + 0.568650i) q^{9} +(-0.500000 - 0.866025i) q^{11} -5.91223 q^{13} +6.82446 q^{15} +(0.828310 + 1.43468i) q^{17} +(0.740539 - 1.28265i) q^{19} +(1.52882 - 4.82277i) q^{21} +(1.67169 - 2.89545i) q^{23} +(-3.86834 - 6.70017i) q^{25} +4.48108 q^{27} +3.08007 q^{29} +(-3.54003 - 6.13152i) q^{31} +(0.956115 - 1.65604i) q^{33} +(-9.22162 + 2.02943i) q^{35} +(2.25561 - 3.90683i) q^{37} +(-5.65277 - 9.79088i) q^{39} -1.28575 q^{41} -1.59899 q^{43} +(1.17169 + 2.02943i) q^{45} +(-0.828310 + 1.43468i) q^{47} +(-0.631656 + 6.97144i) q^{49} +(-1.58392 + 2.74343i) q^{51} +(-4.61274 - 7.98949i) q^{53} -3.56885 q^{55} +2.83216 q^{57} +(4.42598 + 7.66602i) q^{59} +(3.34338 - 5.79090i) q^{61} +(1.69665 - 0.373387i) q^{63} +(-10.5499 + 18.2730i) q^{65} +(-4.91223 - 8.50823i) q^{67} +6.39331 q^{69} +8.61878 q^{71} +(-2.28057 - 3.95007i) q^{73} +(7.39716 - 12.8123i) q^{75} +(-0.799494 + 2.52206i) q^{77} +(-3.19665 + 5.53677i) q^{79} +(5.26936 + 9.12679i) q^{81} -0.167838 q^{83} +5.91223 q^{85} +(2.94490 + 5.10071i) q^{87} +(1.28442 - 2.22469i) q^{89} +(10.5499 + 11.5490i) q^{91} +(6.76936 - 11.7249i) q^{93} +(-2.64287 - 4.57759i) q^{95} +9.73669 q^{97} +0.656620 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q - q^{3} + 2 q^{5} - 2 q^{7}+O(q^{10}) $ 6 * q - q^3 + 2 * q^5 - 2 * q^7	$ 6 q - q^{3} + 2 q^{5} - 2 q^{7} - 3 q^{11} - 22 q^{13} + 14 q^{15} + 3 q^{17} - 11 q^{19} + 10 q^{21} + 12 q^{23} - 3 q^{25} - 4 q^{27} - 18 q^{29} - 3 q^{31} - q^{33} - 9 q^{35} + 4 q^{37} - 5 q^{39} - 10 q^{41} - 4 q^{43} + 9 q^{45} - 3 q^{47} - 24 q^{49} + 2 q^{51} - 17 q^{53} - 4 q^{55} + 40 q^{57} + 8 q^{59} + 24 q^{61} - 12 q^{63} - 15 q^{65} - 16 q^{67} - 6 q^{69} - 14 q^{71} + 20 q^{73} + 25 q^{75} - 2 q^{77} + 3 q^{79} + 17 q^{81} + 22 q^{83} + 22 q^{85} + 30 q^{87} - q^{89} + 15 q^{91} + 26 q^{93} - 17 q^{95} + 18 q^{97}+O(q^{100}) $ 6 * q - q^3 + 2 * q^5 - 2 * q^7 - 3 * q^11 - 22 * q^13 + 14 * q^15 + 3 * q^17 - 11 * q^19 + 10 * q^21 + 12 * q^23 - 3 * q^25 - 4 * q^27 - 18 * q^29 - 3 * q^31 - q^33 - 9 * q^35 + 4 * q^37 - 5 * q^39 - 10 * q^41 - 4 * q^43 + 9 * q^45 - 3 * q^47 - 24 * q^49 + 2 * q^51 - 17 * q^53 - 4 * q^55 + 40 * q^57 + 8 * q^59 + 24 * q^61 - 12 * q^63 - 15 * q^65 - 16 * q^67 - 6 * q^69 - 14 * q^71 + 20 * q^73 + 25 * q^75 - 2 * q^77 + 3 * q^79 + 17 * q^81 + 22 * q^83 + 22 * q^85 + 30 * q^87 - q^89 + 15 * q^91 + 26 * q^93 - 17 * q^95 + 18 * q^97

Display 100 coefficients 10 coefficients

Character values

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

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

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	0.956115	+	1.65604i	0.552013	+	0.956115i	0.998129	+	0.0611395i	$0.0194735\pi$
$3$	0.956115	+	1.65604i	0.552013	+	0.956115i	−0.446116	+	0.894975i	$0.647193\pi$
$4$		0			0
$5$	1.78442	−	3.09071i	0.798019	−	1.38221i	−0.122885	−	0.992421i	$-0.539215\pi$
$5$	1.78442	−	3.09071i	0.798019	−	1.38221i	0.920904	−	0.389789i	$-0.127452\pi$
$6$		0			0
$7$	−1.78442	−	1.95341i	−0.674449	−	0.738321i
$7$	−1.78442	−	1.95341i	−0.674449	−	0.738321i
$8$		0			0
$9$	−0.328310	+	0.568650i	−0.109437	+	0.189550i
$10$		0			0
$11$	−0.500000	−	0.866025i	−0.150756	−	0.261116i
$11$	−0.500000	−	0.866025i	−0.150756	−	0.261116i
$12$		0			0
$13$	−5.91223			−1.63976			−0.819879	−	0.572537i	$-0.805959\pi$
$13$	−5.91223			−1.63976			−0.819879	+	0.572537i	$0.805959\pi$
$14$		0			0
$15$	6.82446			1.76207
$16$		0			0
$17$	0.828310	+	1.43468i	0.200895	+	0.347960i	0.948817	−	0.315826i	$-0.102282\pi$
$17$	0.828310	+	1.43468i	0.200895	+	0.347960i	−0.747922	+	0.663786i	$0.768948\pi$
$18$		0			0
$19$	0.740539	−	1.28265i	0.169891	−	0.294261i	−0.768490	−	0.639862i	$-0.778992\pi$
$19$	0.740539	−	1.28265i	0.169891	−	0.294261i	0.938382	+	0.345601i	$0.112325\pi$
$20$		0			0
$21$	1.52882	−	4.82277i	0.333615	−	1.05241i
$22$		0			0
$23$	1.67169	−	2.89545i	0.348571	−	0.603743i	−0.637425	−	0.770513i	$-0.720000\pi$
$23$	1.67169	−	2.89545i	0.348571	−	0.603743i	0.985996	+	0.166769i	$0.0533335\pi$
$24$		0			0
$25$	−3.86834	−	6.70017i	−0.773669	−	1.34003i
$26$		0			0
$27$	4.48108			0.862384
$28$		0			0
$29$	3.08007			0.571954			0.285977	−	0.958236i	$-0.407682\pi$
$29$	3.08007			0.571954			0.285977	+	0.958236i	$0.407682\pi$
$30$		0			0
$31$	−3.54003	−	6.13152i	−0.635809	−	1.10125i	−0.986343	−	0.164703i	$-0.947333\pi$
$31$	−3.54003	−	6.13152i	−0.635809	−	1.10125i	0.350534	−	0.936550i	$-0.386000\pi$
$32$		0			0
$33$	0.956115	−	1.65604i	0.166438	−	0.288279i
$34$		0			0
$35$	−9.22162	+	2.02943i	−1.55874	+	0.343036i
$36$		0			0
$37$	2.25561	−	3.90683i	0.370820	−	0.642279i	−0.618872	−	0.785492i	$-0.712410\pi$
$37$	2.25561	−	3.90683i	0.370820	−	0.642279i	0.989692	+	0.143213i	$0.0457434\pi$
$38$		0			0
$39$	−5.65277	−	9.79088i	−0.905167	−	1.56780i
$40$		0			0
$41$	−1.28575			−0.200800			−0.100400	−	0.994947i	$-0.532012\pi$
$41$	−1.28575			−0.200800			−0.100400	+	0.994947i	$0.532012\pi$
$42$		0			0
$43$	−1.59899			−0.243843			−0.121922	−	0.992540i	$-0.538906\pi$
$43$	−1.59899			−0.243843			−0.121922	+	0.992540i	$0.538906\pi$
$44$		0			0
$45$	1.17169	+	2.02943i	0.174665	+	0.302529i
$46$		0			0
$47$	−0.828310	+	1.43468i	−0.120821	+	0.209269i	−0.920092	−	0.391703i	$-0.871886\pi$
$47$	−0.828310	+	1.43468i	−0.120821	+	0.209269i	0.799270	+	0.600972i	$0.205220\pi$
$48$		0			0
$49$	−0.631656	+	6.97144i	−0.0902366	+	0.995920i
$50$		0			0
$51$	−1.58392	+	2.74343i	−0.221793	+	0.384157i
$52$		0			0
$53$	−4.61274	−	7.98949i	−0.633608	−	1.09744i	−0.986808	−	0.161893i	$-0.948240\pi$
$53$	−4.61274	−	7.98949i	−0.633608	−	1.09744i	0.353200	−	0.935548i	$-0.385093\pi$
$54$		0			0
$55$	−3.56885			−0.481224
$56$		0			0
$57$	2.83216			0.375129
$58$		0			0
$59$	4.42598	+	7.66602i	0.576213	+	0.998030i	0.995909	+	0.0903653i	$0.0288035\pi$
$59$	4.42598	+	7.66602i	0.576213	+	0.998030i	−0.419696	+	0.907665i	$0.637863\pi$
$60$		0			0
$61$	3.34338	−	5.79090i	0.428076	−	0.741449i	−0.568626	−	0.822596i	$-0.692525\pi$
$61$	3.34338	−	5.79090i	0.428076	−	0.741449i	0.996702	+	0.0811468i	$0.0258583\pi$
$62$		0			0
$63$	1.69665	−	0.373387i	0.213758	−	0.0470424i
$64$		0			0
$65$	−10.5499	+	18.2730i	−1.30856	+	2.26649i
$66$		0			0
$67$	−4.91223	−	8.50823i	−0.600124	−	1.03945i	−0.992802	−	0.119770i	$-0.961784\pi$
$67$	−4.91223	−	8.50823i	−0.600124	−	1.03945i	0.392677	−	0.919676i	$-0.371549\pi$
$68$		0			0
$69$	6.39331			0.769664
$70$		0			0
$71$	8.61878			1.02286			0.511430	−	0.859325i	$-0.329116\pi$
$71$	8.61878			1.02286			0.511430	+	0.859325i	$0.329116\pi$
$72$		0			0
$73$	−2.28057	−	3.95007i	−0.266921	−	0.462321i	0.701144	−	0.713019i	$-0.252673\pi$
$73$	−2.28057	−	3.95007i	−0.266921	−	0.462321i	−0.968065	+	0.250699i	$0.919340\pi$
$74$		0			0
$75$	7.39716	−	12.8123i	0.854150	−	1.47943i
$76$		0			0
$77$	−0.799494	+	2.52206i	−0.0911108	+	0.287416i
$78$		0			0
$79$	−3.19665	+	5.53677i	−0.359652	+	0.622935i	−0.987903	−	0.155076i	$-0.950438\pi$
$79$	−3.19665	+	5.53677i	−0.359652	+	0.622935i	0.628251	+	0.778011i	$0.283771\pi$
$80$		0			0
$81$	5.26936	+	9.12679i	0.585484	+	1.01409i
$82$		0			0
$83$	−0.167838			−0.0184226			−0.00921130	−	0.999958i	$-0.502932\pi$
$83$	−0.167838			−0.0184226			−0.00921130	+	0.999958i	$0.502932\pi$
$84$		0			0
$85$	5.91223			0.641271
$86$		0			0
$87$	2.94490	+	5.10071i	0.315726	+	0.546854i
$88$		0			0
$89$	1.28442	−	2.22469i	0.136149	−	0.235817i	−0.789887	−	0.613252i	$-0.789861\pi$
$89$	1.28442	−	2.22469i	0.136149	−	0.235817i	0.926036	+	0.377436i	$0.123194\pi$
$90$		0			0
$91$	10.5499	+	11.5490i	1.10593	+	1.21067i
$92$		0			0
$93$	6.76936	−	11.7249i	0.701949	−	1.21581i
$94$		0			0
$95$	−2.64287	−	4.57759i	−0.271153	−	0.469651i
$96$		0			0
$97$	9.73669			0.988611			0.494305	−	0.869288i	$-0.335422\pi$
$97$	9.73669			0.988611			0.494305	+	0.869288i	$0.335422\pi$
$98$		0			0
$99$	0.656620			0.0659928
$100$		0			0
$101$	−0.927299	−	1.60613i	−0.0922697	−	0.159816i	0.816196	−	0.577775i	$-0.196079\pi$
$101$	−0.927299	−	1.60613i	−0.0922697	−	0.159816i	−0.908466	+	0.417959i	$0.862746\pi$
$102$		0			0
$103$	−1.58392	+	2.74343i	−0.156068	+	0.270318i	−0.933447	−	0.358714i	$-0.883215\pi$
$103$	−1.58392	+	2.74343i	−0.156068	+	0.270318i	0.777379	+	0.629032i	$0.216549\pi$
$104$		0			0
$105$	−12.1777	−	13.3310i	−1.18843	−	1.30097i
$106$		0			0
$107$	−2.38341	+	4.12819i	−0.230413	+	0.399087i	−0.957930	−	0.287003i	$-0.907341\pi$
$107$	−2.38341	+	4.12819i	−0.230413	+	0.399087i	0.727517	+	0.686090i	$0.240674\pi$
$108$		0			0
$109$	7.44105	+	12.8883i	0.712723	+	1.23447i	0.963831	+	0.266513i	$0.0858716\pi$
$109$	7.44105	+	12.8883i	0.712723	+	1.23447i	−0.251108	+	0.967959i	$0.580795\pi$
$110$		0			0
$111$	8.62648			0.818789
$112$		0			0
$113$	12.4432			1.17056			0.585281	−	0.810831i	$-0.300984\pi$
$113$	12.4432			1.17056			0.585281	+	0.810831i	$0.300984\pi$
$114$		0			0
$115$	−5.96601	−	10.3334i	−0.556333	−	0.963597i
$116$		0			0
$117$	1.94105	−	3.36199i	0.179450	−	0.310816i
$118$		0			0
$119$	1.32446	−	4.17810i	0.121413	−	0.383006i
$120$		0			0
$121$	−0.500000	+	0.866025i	−0.0454545	+	0.0787296i
$122$		0			0
$123$	−1.22932	−	2.12925i	−0.110844	−	0.191988i
$124$		0			0
$125$	−9.76683			−0.873571
$126$		0			0
$127$	6.62142			0.587556			0.293778	−	0.955874i	$-0.405087\pi$
$127$	6.62142			0.587556			0.293778	+	0.955874i	$0.405087\pi$
$128$		0			0
$129$	−1.52882	−	2.64799i	−0.134605	−	0.233142i
$130$		0			0
$131$	−3.02882	+	5.24606i	−0.264629	+	0.458351i	−0.967466	−	0.253000i	$-0.918583\pi$
$131$	−3.02882	+	5.24606i	−0.264629	+	0.458351i	0.702837	+	0.711351i	$0.251916\pi$
$132$		0			0
$133$	−3.82699	+	0.842215i	−0.331842	+	0.0730293i
$134$		0			0
$135$	7.99615	−	13.8497i	0.688199	−	1.19200i
$136$		0			0
$137$	3.71172	+	6.42889i	0.317114	+	0.549257i	0.979885	−	0.199565i	$-0.0639529\pi$
$137$	3.71172	+	6.42889i	0.317114	+	0.549257i	−0.662771	+	0.748822i	$0.730620\pi$
$138$		0			0
$139$	10.8245			0.918119			0.459059	−	0.888406i	$-0.348187\pi$
$139$	10.8245			0.918119			0.459059	+	0.888406i	$0.348187\pi$
$140$		0			0
$141$	−3.16784			−0.266780
$142$		0			0
$143$	2.95611	+	5.12014i	0.247203	+	0.428168i
$144$		0			0
$145$	5.49615	−	9.51961i	0.456430	−	0.790560i
$146$		0			0
$147$	−12.1489	+	5.61945i	−1.00203	+	0.463484i
$148$		0			0
$149$	0.500000	−	0.866025i	0.0409616	−	0.0709476i	−0.844818	−	0.535054i	$-0.820291\pi$
$149$	0.500000	−	0.866025i	0.0409616	−	0.0709476i	0.885779	+	0.464107i	$0.153625\pi$
$150$		0			0
$151$	8.21172	+	14.2231i	0.668261	+	1.15746i	0.978390	+	0.206767i	$0.0662942\pi$
$151$	8.21172	+	14.2231i	0.668261	+	1.15746i	−0.310130	+	0.950694i	$0.600372\pi$
$152$		0			0
$153$	−1.08777			−0.0879411
$154$		0			0
$155$	−25.2677			−2.02955
$156$		0			0
$157$	5.72547	+	9.91681i	0.456942	+	0.791447i	0.998798	−	0.0490246i	$-0.0156113\pi$
$157$	5.72547	+	9.91681i	0.456942	+	0.791447i	−0.541855	+	0.840472i	$0.682278\pi$
$158$		0			0
$159$	8.82061	−	15.2777i	0.699520	−	1.21160i
$160$		0			0
$161$	−8.63902	+	1.90121i	−0.680850	+	0.149837i
$162$		0			0
$163$	−4.46986	+	7.74203i	−0.350107	+	0.606402i	−0.986268	−	0.165154i	$-0.947188\pi$
$163$	−4.46986	+	7.74203i	−0.350107	+	0.606402i	0.636161	+	0.771556i	$0.280521\pi$
$164$		0			0
$165$	−3.41223	−	5.91015i	−0.265642	−	0.460105i
$166$		0			0
$167$	18.2178			1.40973			0.704867	−	0.709340i	$-0.251007\pi$
$167$	18.2178			1.40973			0.704867	+	0.709340i	$0.251007\pi$
$168$		0			0
$169$	21.9545			1.68880
$170$		0			0
$171$	0.486253	+	0.842215i	0.0371847	+	0.0644058i
$172$		0			0
$173$	−9.78057	+	16.9404i	−0.743603	+	1.28796i	0.207241	+	0.978290i	$0.433551\pi$
$173$	−9.78057	+	16.9404i	−0.743603	+	1.28796i	−0.950845	+	0.309669i	$0.899782\pi$
$174$		0			0
$175$	−6.18544	+	19.5124i	−0.467575	+	1.47500i
$176$		0			0
$177$	−8.46348	+	14.6592i	−0.636154	+	1.10185i
$178$		0			0
$179$	1.62395	+	2.81277i	0.121380	+	0.210236i	0.920312	−	0.391185i	$-0.127935\pi$
$179$	1.62395	+	2.81277i	0.121380	+	0.210236i	−0.798932	+	0.601421i	$0.794601\pi$
$180$		0			0
$181$	−10.3407			−0.768621			−0.384310	−	0.923204i	$-0.625561\pi$
$181$	−10.3407			−0.768621			−0.384310	+	0.923204i	$0.625561\pi$
$182$		0			0
$183$	12.7866			0.945214
$184$		0			0
$185$	−8.04993	−	13.9429i	−0.591843	−	1.02510i
$186$		0			0
$187$	0.828310	−	1.43468i	0.0605720	−	0.104914i
$188$		0			0
$189$	−7.99615	−	8.75340i	−0.581634	−	0.636716i
$190$		0			0
$191$	5.01122	−	8.67968i	0.362599	−	0.628040i	−0.625789	−	0.779993i	$-0.715223\pi$
$191$	5.01122	−	8.67968i	0.362599	−	0.628040i	0.988388	+	0.151953i	$0.0485561\pi$
$192$		0			0
$193$	−12.6627	−	21.9324i	−0.911478	−	1.57873i	−0.811977	−	0.583690i	$-0.801609\pi$
$193$	−12.6627	−	21.9324i	−0.911478	−	1.57873i	−0.0995016	−	0.995037i	$-0.531725\pi$
$194$		0			0
$195$	−40.3478			−2.88936
$196$		0			0
$197$	−24.5809			−1.75132			−0.875660	−	0.482929i	$-0.839573\pi$
$197$	−24.5809			−1.75132			−0.875660	+	0.482929i	$0.839573\pi$
$198$		0			0
$199$	2.79564	+	4.84219i	0.198178	+	0.343254i	0.947938	−	0.318456i	$-0.103164\pi$
$199$	2.79564	+	4.84219i	0.198178	+	0.343254i	−0.749760	+	0.661710i	$0.769831\pi$
$200$		0			0
$201$	9.39331	−	16.2697i	0.662553	−	1.14758i
$202$		0			0
$203$	−5.49615	−	6.01665i	−0.385754	−	0.422286i
$204$		0			0
$205$	−2.29432	+	3.97388i	−0.160242	+	0.277548i
$206$		0			0
$207$	1.09767	+	1.90121i	0.0762930	+	0.132143i
$208$		0			0
$209$	−1.48108			−0.102448
$210$		0			0
$211$	−12.0999			−0.832988			−0.416494	−	0.909138i	$-0.636741\pi$
$211$	−12.0999			−0.832988			−0.416494	+	0.909138i	$0.636741\pi$
$212$		0			0
$213$	8.24054	+	14.2730i	0.564632	+	0.977972i
$214$		0			0
$215$	−2.85327	+	4.94202i	−0.194592	+	0.337043i
$216$		0			0
$217$	−5.66047	+	17.8564i	−0.384258	+	1.21217i
$218$		0			0
$219$	4.36098	−	7.55344i	0.294688	−	0.510414i
$220$		0			0
$221$	−4.89716	−	8.48213i	−0.329419	−	0.570570i
$222$		0			0
$223$	−15.6265			−1.04643			−0.523213	−	0.852202i	$-0.675267\pi$
$223$	−15.6265			−1.04643			−0.523213	+	0.852202i	$0.675267\pi$
$224$		0			0
$225$	5.08007			0.338671
$226$		0			0
$227$	−7.83435	−	13.5695i	−0.519984	−	0.900639i	−0.999730	−	0.0232317i	$-0.992604\pi$
$227$	−7.83435	−	13.5695i	−0.519984	−	0.900639i	0.479746	−	0.877408i	$-0.340729\pi$
$228$		0			0
$229$	2.78575	−	4.82506i	0.184087	−	0.318849i	−0.759181	−	0.650879i	$-0.774400\pi$
$229$	2.78575	−	4.82506i	0.184087	−	0.318849i	0.943269	+	0.332031i	$0.107734\pi$
$230$		0			0
$231$	−4.94105	+	1.08739i	−0.325097	+	0.0715449i
$232$		0			0
$233$	9.63770	−	16.6930i	0.631387	−	1.09359i	−0.355882	−	0.934531i	$-0.615819\pi$
$233$	9.63770	−	16.6930i	0.631387	−	1.09359i	0.987268	−	0.159063i	$-0.0508472\pi$
$234$		0			0
$235$	2.95611	+	5.12014i	0.192836	+	0.334001i
$236$		0			0
$237$	−12.2255			−0.794130
$238$		0			0
$239$	22.1575			1.43325			0.716624	−	0.697459i	$-0.245686\pi$
$239$	22.1575			1.43325			0.716624	+	0.697459i	$0.245686\pi$
$240$		0			0
$241$	9.93719	+	17.2117i	0.640111	+	1.10870i	0.985408	+	0.170211i	$0.0544449\pi$
$241$	9.93719	+	17.2117i	0.640111	+	1.10870i	−0.345297	+	0.938494i	$0.612222\pi$
$242$		0			0
$243$	−3.35460	+	5.81033i	−0.215198	+	0.372733i
$244$		0			0
$245$	20.4196	+	14.3923i	1.30456	+	0.919489i
$246$		0			0
$247$	−4.37824	+	7.58333i	−0.278581	+	0.482516i
$248$		0			0
$249$	−0.160472	−	0.277946i	−0.0101695	−	0.0176141i
$250$		0			0
$251$	−22.1076			−1.39542			−0.697708	−	0.716382i	$-0.745797\pi$
$251$	−22.1076			−1.39542			−0.697708	+	0.716382i	$0.745797\pi$
$252$		0			0
$253$	−3.34338			−0.210196
$254$		0			0
$255$	5.65277	+	9.79088i	0.353990	+	0.613129i
$256$		0			0
$257$	−14.5598	+	25.2184i	−0.908217	+	1.57308i	−0.0916768	+	0.995789i	$0.529223\pi$
$257$	−14.5598	+	25.2184i	−0.908217	+	1.57308i	−0.816540	+	0.577289i	$0.804111\pi$
$258$		0			0
$259$	−11.6566	+	2.56530i	−0.724307	+	0.159400i
$260$		0			0
$261$	−1.01122	+	1.75148i	−0.0625928	+	0.108414i
$262$		0			0
$263$	−7.75176	−	13.4264i	−0.477994	−	0.827910i	0.521688	−	0.853136i	$-0.325303\pi$
$263$	−7.75176	−	13.4264i	−0.477994	−	0.827910i	−0.999682	+	0.0252268i	$0.991969\pi$
$264$		0			0
$265$	−32.9243			−2.02252
$266$		0			0
$267$	4.91223			0.300624
$268$		0			0
$269$	−0.853274	−	1.47791i	−0.0520251	−	0.0901100i	0.838840	−	0.544378i	$-0.183234\pi$
$269$	−0.853274	−	1.47791i	−0.0520251	−	0.0901100i	−0.890865	+	0.454268i	$0.849901\pi$
$270$		0			0
$271$	−10.2642	+	17.7781i	−0.623505	+	1.07994i	0.365323	+	0.930881i	$0.380958\pi$
$271$	−10.2642	+	17.7781i	−0.623505	+	1.07994i	−0.988828	+	0.149061i	$0.952375\pi$
$272$		0			0
$273$	−9.03871	+	28.5133i	−0.547048	+	1.72570i
$274$		0			0
$275$	−3.86834	+	6.70017i	−0.233270	+	0.404035i
$276$		0			0
$277$	13.3305	+	23.0891i	0.800952	+	1.38729i	0.918990	+	0.394281i	$0.129006\pi$
$277$	13.3305	+	23.0891i	0.800952	+	1.38729i	−0.118038	+	0.993009i	$0.537660\pi$
$278$		0			0
$279$	4.64892			0.278323
$280$		0			0
$281$	15.7444			0.939232			0.469616	−	0.882871i	$-0.344392\pi$
$281$	15.7444			0.939232			0.469616	+	0.882871i	$0.344392\pi$
$282$		0			0
$283$	−8.03486	−	13.9168i	−0.477623	−	0.827267i	0.522048	−	0.852916i	$-0.325168\pi$
$283$	−8.03486	−	13.9168i	−0.477623	−	0.827267i	−0.999671	+	0.0256490i	$0.991835\pi$
$284$		0			0
$285$	5.05378	−	8.75340i	0.299360	−	0.518507i
$286$		0			0
$287$	2.29432	+	2.51160i	0.135429	+	0.148255i
$288$		0			0
$289$	7.12780	−	12.3457i	0.419283	−	0.726219i
$290$		0			0
$291$	9.30939	+	16.1243i	0.545726	+	0.945225i
$292$		0			0
$293$	15.3357			0.895920			0.447960	−	0.894054i	$-0.352151\pi$
$293$	15.3357			0.895920			0.447960	+	0.894054i	$0.352151\pi$
$294$		0			0
$295$	31.5913			1.83932
$296$		0			0
$297$	−2.24054	−	3.88073i	−0.130009	−	0.225183i
$298$		0			0
$299$	−9.88341	+	17.1186i	−0.571573	+	0.989993i
$300$		0			0
$301$	2.85327	+	3.12349i	0.164460	+	0.180035i
$302$		0			0
$303$	1.77321	−	3.07129i	0.101868	−	0.176441i
$304$		0			0
$305$	−11.9320	−	20.6669i	−0.683225	−	1.18338i
$306$		0			0
$307$	16.4707			0.940034			0.470017	−	0.882657i	$-0.344248\pi$
$307$	16.4707			0.940034			0.470017	+	0.882657i	$0.344248\pi$
$308$		0			0
$309$	−6.05763			−0.344607
$310$		0			0
$311$	10.8146	+	18.7314i	0.613238	+	1.06216i	0.990691	+	0.136130i	$0.0434665\pi$
$311$	10.8146	+	18.7314i	0.613238	+	1.06216i	−0.377453	+	0.926029i	$0.623200\pi$
$312$		0			0
$313$	−8.19412	+	14.1926i	−0.463159	+	0.802215i	−0.999116	−	0.0420298i	$-0.986618\pi$
$313$	−8.19412	+	14.1926i	−0.463159	+	0.802215i	0.535957	+	0.844245i	$0.319951\pi$
$314$		0			0
$315$	1.87352	−	5.91015i	0.105561	−	0.332999i
$316$		0			0
$317$	−2.23064	+	3.86359i	−0.125285	+	0.217001i	−0.921844	−	0.387560i	$-0.873318\pi$
$317$	−2.23064	+	3.86359i	−0.125285	+	0.217001i	0.796559	+	0.604561i	$0.206651\pi$
$318$		0			0
$319$	−1.54003	−	2.66742i	−0.0862253	−	0.149347i
$320$		0			0
$321$	−9.11526			−0.508764
$322$		0			0
$323$	2.45359			0.136521
$324$		0			0
$325$	22.8705	+	39.6129i	1.26863	+	2.19733i
$326$		0			0
$327$	−14.2290	+	24.6453i	−0.786865	+	1.36289i
$328$		0			0
$329$	4.28057	−	0.942037i	0.235996	−	0.0519362i
$330$		0			0
$331$	9.51979	−	16.4888i	0.523255	−	0.906304i	−0.476379	−	0.879240i	$-0.658051\pi$
$331$	9.51979	−	16.4888i	0.523255	−	0.906304i	0.999634	−	0.0270640i	$-0.00861579\pi$
$332$		0			0
$333$	1.48108	+	2.56530i	0.0811626	+	0.140578i
$334$		0			0
$335$	−35.0620			−1.91564
$336$		0			0
$337$	27.0147			1.47159			0.735793	−	0.677206i	$-0.236810\pi$
$337$	27.0147			1.47159			0.735793	+	0.677206i	$0.236810\pi$
$338$		0			0
$339$	11.8972	+	20.6065i	0.646165	+	1.11919i
$340$		0			0
$341$	−3.54003	+	6.13152i	−0.191704	+	0.332040i
$342$		0			0
$343$	14.7453	−	11.2061i	0.796169	−	0.605074i
$344$		0			0
$345$	11.4084	−	19.7599i	0.614206	−	1.06384i
$346$		0			0
$347$	−10.1089	−	17.5091i	−0.542673	−	0.939938i	−0.998749	−	0.0499969i	$-0.984079\pi$
$347$	−10.1089	−	17.5091i	−0.542673	−	0.939938i	0.456076	−	0.889941i	$-0.349254\pi$
$348$		0			0
$349$	−12.0224			−0.643546			−0.321773	−	0.946817i	$-0.604279\pi$
$349$	−12.0224			−0.643546			−0.321773	+	0.946817i	$0.604279\pi$
$350$		0			0
$351$	−26.4932			−1.41410
$352$		0			0
$353$	5.37956	+	9.31767i	0.286325	+	0.495930i	0.972930	−	0.231101i	$-0.0742329\pi$
$353$	5.37956	+	9.31767i	0.286325	+	0.495930i	−0.686605	+	0.727031i	$0.740900\pi$
$354$		0			0
$355$	15.3796	−	26.6382i	0.816262	−	1.41381i
$356$		0			0
$357$	8.18544	−	1.80139i	0.433219	−	0.0953397i
$358$		0			0
$359$	12.1451	−	21.0359i	0.640992	−	1.11023i	−0.344220	−	0.938889i	$-0.611856\pi$
$359$	12.1451	−	21.0359i	0.640992	−	1.11023i	0.985212	−	0.171342i	$-0.0548102\pi$
$360$		0			0
$361$	8.40320	+	14.5548i	0.442274	+	0.766041i
$362$		0			0
$363$	−1.91223			−0.100366
$364$		0			0
$365$	−16.2780			−0.852032
$366$		0			0
$367$	5.42212	+	9.39139i	0.283033	+	0.490227i	0.972130	−	0.234442i	$-0.0753262\pi$
$367$	5.42212	+	9.39139i	0.283033	+	0.490227i	−0.689098	+	0.724669i	$0.741993\pi$
$368$		0			0
$369$	0.422124	−	0.731140i	0.0219749	−	0.0380616i
$370$		0			0
$371$	−7.37571	+	23.2672i	−0.382928	+	1.20797i
$372$		0			0
$373$	16.5121	−	28.5998i	0.854963	−	1.48084i	−0.0217156	−	0.999764i	$-0.506913\pi$
$373$	16.5121	−	28.5998i	0.854963	−	1.48084i	0.876679	−	0.481076i	$-0.159754\pi$
$374$		0			0
$375$	−9.33821	−	16.1742i	−0.482223	−	0.835234i
$376$		0			0
$377$	−18.2101			−0.937866
$378$		0			0
$379$	21.9320			1.12657			0.563286	−	0.826262i	$-0.309537\pi$
$379$	21.9320			1.12657			0.563286	+	0.826262i	$0.309537\pi$
$380$		0			0
$381$	6.33084	+	10.9653i	0.324339	+	0.561771i
$382$		0			0
$383$	18.2315	−	31.5779i	0.931587	−	1.61356i	0.150977	−	0.988537i	$-0.451758\pi$
$383$	18.2315	−	31.5779i	0.931587	−	1.61356i	0.780610	−	0.625018i	$-0.214909\pi$
$384$		0			0
$385$	6.36834	+	6.97144i	0.324561	+	0.355298i
$386$		0			0
$387$	0.524964	−	0.909265i	0.0266854	−	0.0462205i
$388$		0			0
$389$	−9.73801	−	16.8667i	−0.493737	−	0.855177i	0.506237	−	0.862394i	$-0.331036\pi$
$389$	−9.73801	−	16.8667i	−0.493737	−	0.855177i	−0.999974	+	0.00721718i	$0.997703\pi$
$390$		0			0
$391$	5.53871			0.280105
$392$		0			0
$393$	−11.5836			−0.584314
$394$		0			0
$395$	11.4084	+	19.7599i	0.574018	+	0.994228i
$396$		0			0
$397$	3.91993	−	6.78952i	0.196736	−	0.340756i	−0.750732	−	0.660606i	$-0.770299\pi$
$397$	3.91993	−	6.78952i	0.196736	−	0.340756i	0.947468	+	0.319850i	$0.103633\pi$
$398$		0			0
$399$	−5.05378	−	5.53239i	−0.253005	−	0.276966i
$400$		0			0
$401$	12.2229	−	21.1708i	0.610385	−	1.05722i	−0.380791	−	0.924661i	$-0.624348\pi$
$401$	12.2229	−	21.1708i	0.610385	−	1.05722i	0.991176	−	0.132556i	$-0.0423184\pi$
$402$		0			0
$403$	20.9295	+	36.2509i	1.04257	+	1.80579i
$404$		0			0
$405$	37.6111			1.86891
$406$		0			0
$407$	−4.51122			−0.223613
$408$		0			0
$409$	1.17686	+	2.03839i	0.0581922	+	0.100792i	0.893654	−	0.448757i	$-0.148133\pi$
$409$	1.17686	+	2.03839i	0.0581922	+	0.100792i	−0.835462	+	0.549549i	$0.814800\pi$
$410$		0			0
$411$	−7.09767	+	12.2935i	−0.350102	+	0.606395i
$412$		0			0
$413$	7.07708	−	22.3252i	0.348241	−	1.09855i
$414$		0			0
$415$	−0.299494	+	0.518739i	−0.0147016	+	0.0254639i
$416$		0			0
$417$	10.3494	+	17.9257i	0.506813	+	0.877827i
$418$		0			0
$419$	−9.29081			−0.453886			−0.226943	−	0.973908i	$-0.572873\pi$
$419$	−9.29081			−0.453886			−0.226943	+	0.973908i	$0.572873\pi$
$420$		0			0
$421$	−39.0319			−1.90230			−0.951149	−	0.308733i	$-0.900095\pi$
$421$	−39.0319			−1.90230			−0.951149	+	0.308733i	$0.900095\pi$
$422$		0			0
$423$	−0.543885	−	0.942037i	−0.0264446	−	0.0458034i
$424$		0			0
$425$	6.40838	−	11.0996i	0.310852	−	0.538411i
$426$		0			0
$427$	−17.2780	+	3.80243i	−0.836143	+	0.184012i
$428$		0			0
$429$	−5.65277	+	9.79088i	−0.272918	+	0.472708i
$430$		0			0
$431$	−1.90101	−	3.29265i	−0.0915685	−	0.158601i	0.816603	−	0.577200i	$-0.195855\pi$
$431$	−1.90101	−	3.29265i	−0.0915685	−	0.158601i	−0.908171	+	0.418599i	$0.862521\pi$
$432$		0			0
$433$	8.22041			0.395048			0.197524	−	0.980298i	$-0.436710\pi$
$433$	8.22041			0.395048			0.197524	+	0.980298i	$0.436710\pi$
$434$		0			0
$435$	21.0198			1.00782
$436$		0			0
$437$	−2.47590	−	4.28839i	−0.118439	−	0.205142i
$438$		0			0
$439$	2.27068	−	3.93293i	0.108374	−	0.187708i	−0.806738	−	0.590909i	$-0.798769\pi$
$439$	2.27068	−	3.93293i	0.108374	−	0.187708i	0.915112	+	0.403201i	$0.132102\pi$
$440$		0			0
$441$	−3.75693	−	2.64799i	−0.178901	−	0.126095i
$442$		0			0
$443$	6.87220	−	11.9030i	0.326508	−	0.565528i	−0.655309	−	0.755361i	$-0.727461\pi$
$443$	6.87220	−	11.9030i	0.326508	−	0.565528i	0.981816	+	0.189833i	$0.0607947\pi$
$444$		0			0
$445$	−4.58392	−	7.93958i	−0.217299	−	0.376372i
$446$		0			0
$447$	1.91223			0.0904453
$448$		0			0
$449$	21.5662			1.01777			0.508886	−	0.860834i	$-0.330057\pi$
$449$	21.5662			1.01777			0.508886	+	0.860834i	$0.330057\pi$
$450$		0			0
$451$	0.642874	+	1.11349i	0.0302717	+	0.0524322i
$452$		0			0
$453$	−15.7027	+	27.1979i	−0.737777	+	1.27787i
$454$		0			0
$455$	54.5203	−	11.9984i	2.55595	−	0.562495i
$456$		0			0
$457$	1.65277	−	2.86268i	0.0773133	−	0.133910i	−0.824777	−	0.565459i	$-0.808699\pi$
$457$	1.65277	−	2.86268i	0.0773133	−	0.133910i	0.902090	+	0.431548i	$0.142033\pi$
$458$		0			0
$459$	3.71172	+	6.42889i	0.173248	+	0.300075i
$460$		0			0
$461$	−32.1524			−1.49749			−0.748744	−	0.662859i	$-0.769343\pi$
$461$	−32.1524			−1.49749			−0.748744	+	0.662859i	$0.769343\pi$
$462$		0			0
$463$	−5.82181			−0.270563			−0.135281	−	0.990807i	$-0.543194\pi$
$463$	−5.82181			−0.270563			−0.135281	+	0.990807i	$0.543194\pi$
$464$		0			0
$465$	−24.1588	−	41.8443i	−1.12034	−	1.94048i
$466$		0			0
$467$	−3.00737	+	5.20891i	−0.139164	+	0.241040i	−0.927181	−	0.374615i	$-0.877775\pi$
$467$	−3.00737	+	5.20891i	−0.139164	+	0.241040i	0.788016	+	0.615654i	$0.211108\pi$
$468$		0			0
$469$	−7.85460	+	24.7779i	−0.362692	+	1.14414i
$470$		0			0
$471$	−10.9484	+	18.9632i	−0.504476	+	0.873778i
$472$		0			0
$473$	0.799494	+	1.38476i	0.0367608	+	0.0636715i
$474$		0			0
$475$	−11.4586			−0.525759
$476$		0			0
$477$	6.05763			0.277360
$478$		0			0
$479$	8.56753	+	14.8394i	0.391460	+	0.678029i	0.992642	−	0.121083i	$-0.0386367\pi$
$479$	8.56753	+	14.8394i	0.391460	+	0.678029i	−0.601182	+	0.799112i	$0.705303\pi$
$480$		0			0
$481$	−13.3357	+	23.0981i	−0.608054	+	1.05318i
$482$		0			0
$483$	−11.4084	−	12.4888i	−0.519099	−	0.568259i
$484$		0			0
$485$	17.3744	−	30.0933i	0.788930	−	1.36647i
$486$		0			0
$487$	2.85713	+	4.94869i	0.129469	+	0.224246i	0.923471	−	0.383669i	$-0.125339\pi$
$487$	2.85713	+	4.94869i	0.129469	+	0.224246i	−0.794002	+	0.607915i	$0.792006\pi$
$488$		0			0
$489$	−17.0948			−0.773054
$490$		0			0
$491$	−24.0673			−1.08614			−0.543071	−	0.839687i	$-0.682739\pi$
$491$	−24.0673			−1.08614			−0.543071	+	0.839687i	$0.682739\pi$
$492$		0			0
$493$	2.55125	+	4.41890i	0.114903	+	0.199017i
$494$		0			0
$495$	1.17169	−	2.02943i	0.0526635	−	0.0912159i
$496$		0			0
$497$	−15.3796	−	16.8360i	−0.689868	−	0.755200i
$498$		0			0
$499$	5.39463	−	9.34377i	0.241497	−	0.418285i	−0.719644	−	0.694343i	$-0.755695\pi$
$499$	5.39463	−	9.34377i	0.241497	−	0.418285i	0.961141	+	0.276058i	$0.0890283\pi$
$500$		0			0
$501$	17.4183	+	30.1693i	0.778191	+	1.34787i
$502$		0			0
$503$	−28.0121			−1.24900			−0.624499	−	0.781026i	$-0.714697\pi$
$503$	−28.0121			−1.24900			−0.624499	+	0.781026i	$0.714697\pi$
$504$		0			0
$505$	−6.61878			−0.294532
$506$		0			0
$507$	20.9910	+	36.3574i	0.932242	+	1.61469i
$508$		0			0
$509$	0.957437	−	1.65833i	0.0424377	−	0.0735042i	−0.844026	−	0.536302i	$-0.819821\pi$
$509$	0.957437	−	1.65833i	0.0424377	−	0.0735042i	0.886464	+	0.462797i	$0.153154\pi$
$510$		0			0
$511$	−3.64661	+	11.5035i	−0.161317	+	0.508885i
$512$		0			0
$513$	3.31842	−	5.74766i	0.146512	−	0.253766i
$514$		0			0
$515$	5.65277	+	9.79088i	0.249091	+	0.431438i
$516$		0			0
$517$	1.65662			0.0728581
$518$		0			0
$519$	−37.4054			−1.64191
$520$		0			0
$521$	−0.789599	−	1.36763i	−0.0345930	−	0.0599168i	0.848211	−	0.529659i	$-0.177680\pi$
$521$	−0.789599	−	1.36763i	−0.0345930	−	0.0599168i	−0.882804	+	0.469742i	$0.844347\pi$
$522$		0			0
$523$	−4.48493	+	7.76813i	−0.196112	+	0.339677i	−0.947265	−	0.320452i	$-0.896165\pi$
$523$	−4.48493	+	7.76813i	−0.196112	+	0.339677i	0.751152	+	0.660129i	$0.229498\pi$
$524$		0			0
$525$	−38.2273	+	8.41279i	−1.66838	+	0.367164i
$526$		0			0
$527$	5.86449	−	10.1576i	0.255461	−	0.442472i
$528$		0			0
$529$	5.91091	+	10.2380i	0.256996	+	0.445130i
$530$		0			0
$531$	−5.81237			−0.252235
$532$		0			0
$533$	7.60163			0.329263
$534$		0			0
$535$	8.50604	+	14.7329i	0.367748	+	0.636959i
$536$		0			0
$537$	−3.10537	+	5.37866i	−0.134007	+	0.232106i
$538$		0			0
$539$	6.35327	−	2.93869i	0.273655	−	0.126578i
$540$		0			0
$541$	−9.05125	+	15.6772i	−0.389144	+	0.674017i	−0.992335	−	0.123580i	$-0.960562\pi$
$541$	−9.05125	+	15.6772i	−0.389144	+	0.674017i	0.603191	+	0.797597i	$0.293896\pi$
$542$		0			0
$543$	−9.88693	−	17.1247i	−0.424289	−	0.734889i
$544$		0			0
$545$	53.1119			2.27507
$546$		0			0
$547$	−22.6885			−0.970090			−0.485045	−	0.874489i	$-0.661197\pi$
$547$	−22.6885			−0.970090			−0.485045	+	0.874489i	$0.661197\pi$
$548$		0			0
$549$	2.19533	+	3.80243i	0.0936945	+	0.162284i
$550$		0			0
$551$	2.28091	−	3.95065i	0.0971701	−	0.168304i
$552$		0			0
$553$	16.5198	−	3.63555i	0.702493	−	0.154599i
$554$		0			0
$555$	15.3933	−	26.6620i	0.653410	−	1.13174i
$556$		0			0
$557$	−19.1777	−	33.2168i	−0.812587	−	1.40744i	−0.911048	−	0.412300i	$-0.864725\pi$
$557$	−19.1777	−	33.2168i	−0.812587	−	1.40744i	0.0984613	−	0.995141i	$-0.468608\pi$
$558$		0			0
$559$	9.45359			0.399844
$560$		0			0
$561$	3.16784			0.133746
$562$		0			0
$563$	−20.8869	−	36.1772i	−0.880279	−	1.52469i	−0.851031	−	0.525116i	$-0.824022\pi$
$563$	−20.8869	−	36.1772i	−0.880279	−	1.52469i	−0.0292482	−	0.999572i	$-0.509311\pi$
$564$		0			0
$565$	22.2040	−	38.4585i	0.934130	−	1.61796i
$566$		0			0
$567$	8.42564	−	26.5793i	0.353844	−	1.11623i
$568$		0			0
$569$	5.93500	−	10.2797i	0.248808	−	0.430949i	−0.714387	−	0.699751i	$-0.753294\pi$
$569$	5.93500	−	10.2797i	0.248808	−	0.430949i	0.963195	+	0.268802i	$0.0866278\pi$
$570$		0			0
$571$	9.90067	+	17.1485i	0.414330	+	0.717641i	0.995358	−	0.0962427i	$-0.0306825\pi$
$571$	9.90067	+	17.1485i	0.414330	+	0.717641i	−0.581028	+	0.813884i	$0.697349\pi$
$572$		0			0
$573$	19.1652			0.800637
$574$		0			0
$575$	−25.8667			−1.07872
$576$		0			0
$577$	−14.3395	−	24.8368i	−0.596962	−	1.03397i	−0.993267	−	0.115850i	$-0.963041\pi$
$577$	−14.3395	−	24.8368i	−0.596962	−	1.03397i	0.396304	−	0.918119i	$-0.370293\pi$
$578$		0			0
$579$	24.2139	−	41.9397i	1.00630	−	1.74296i
$580$		0			0
$581$	0.299494	+	0.327857i	0.0124251	+	0.0136018i
$582$		0			0
$583$	−4.61274	+	7.98949i	−0.191040	+	0.330891i
$584$		0			0
$585$	−6.92730	−	11.9984i	−0.286409	−	0.496074i
$586$		0			0
$587$	−1.01209			−0.0417733			−0.0208866	−	0.999782i	$-0.506649\pi$
$587$	−1.01209			−0.0417733			−0.0208866	+	0.999782i	$0.506649\pi$
$588$		0			0
$589$	−10.4861			−0.432074
$590$		0			0
$591$	−23.5022	−	40.7070i	−0.966751	−	1.67446i
$592$		0			0
$593$	−7.11659	+	12.3263i	−0.292243	+	0.506180i	−0.974340	−	0.225082i	$-0.927735\pi$
$593$	−7.11659	+	12.3263i	−0.292243	+	0.506180i	0.682097	+	0.731262i	$0.261068\pi$
$594$		0			0
$595$	−10.5499	−	11.5490i	−0.432505	−	0.473464i
$596$		0			0
$597$	−5.34591	+	9.25939i	−0.218793	+	0.378961i
$598$		0			0
$599$	−13.2729	−	22.9893i	−0.542315	−	0.939317i	−0.998771	−	0.0495706i	$-0.984215\pi$
$599$	−13.2729	−	22.9893i	−0.542315	−	0.939317i	0.456456	−	0.889746i	$-0.349119\pi$
$600$		0			0
$601$	−12.1558			−0.495843			−0.247922	−	0.968780i	$-0.579748\pi$
$601$	−12.1558			−0.495843			−0.247922	+	0.968780i	$0.579748\pi$
$602$		0			0
$603$	6.45094			0.262703
$604$		0			0
$605$	1.78442	+	3.09071i	0.0725472	+	0.125655i
$606$		0			0
$607$	6.98361	−	12.0960i	0.283456	−	0.490960i	−0.688778	−	0.724973i	$-0.741852\pi$
$607$	6.98361	−	12.0960i	0.283456	−	0.490960i	0.972234	+	0.234013i	$0.0751857\pi$
$608$		0			0
$609$	4.70886	−	14.8544i	0.190812	−	0.601932i
$610$		0			0
$611$	4.89716	−	8.48213i	0.198118	−	0.343150i
$612$		0			0
$613$	−2.32094	−	4.01999i	−0.0937421	−	0.162366i	0.815341	−	0.578981i	$-0.196550\pi$
$613$	−2.32094	−	4.01999i	−0.0937421	−	0.162366i	−0.909083	+	0.416615i	$0.863216\pi$
$614$		0			0
$615$	−8.77453			−0.353823
$616$		0			0
$617$	−26.3960			−1.06266			−0.531331	−	0.847165i	$-0.678308\pi$
$617$	−26.3960			−1.06266			−0.531331	+	0.847165i	$0.678308\pi$
$618$		0			0
$619$	7.34073	+	12.7145i	0.295049	+	0.511040i	0.974996	−	0.222221i	$-0.0713307\pi$
$619$	7.34073	+	12.7145i	0.295049	+	0.511040i	−0.679947	+	0.733261i	$0.737997\pi$
$620$		0			0
$621$	7.49097	−	12.9747i	0.300602	−	0.520659i
$622$		0			0
$623$	−6.63770	+	1.46078i	−0.265934	+	0.0585248i
$624$		0			0
$625$	1.91355	−	3.31437i	0.0765421	−	0.132575i
$626$		0			0
$627$	−1.41608	−	2.45272i	−0.0565528	−	0.0979524i
$628$		0			0
$629$	7.47338			0.297983
$630$		0			0
$631$	30.1498			1.20024			0.600122	−	0.799908i	$-0.295119\pi$
$631$	30.1498			1.20024			0.600122	+	0.799908i	$0.295119\pi$
$632$		0			0
$633$	−11.5688	−	20.0378i	−0.459820	−	0.796432i
$634$		0			0
$635$	11.8154	−	20.4649i	0.468881	−	0.812126i
$636$		0			0
$637$	3.73450	−	41.2168i	0.147966	−	1.63307i
$638$		0			0
$639$	−2.82963	+	4.90107i	−0.111939	+	0.193883i
$640$		0			0
$641$	8.08909	+	14.0107i	0.319500	+	0.553390i	0.980384	−	0.197098i	$-0.0631517\pi$
$641$	8.08909	+	14.0107i	0.319500	+	0.553390i	−0.660884	+	0.750488i	$0.729818\pi$
$642$		0			0
$643$	2.33568			0.0921101			0.0460550	−	0.998939i	$-0.485335\pi$
$643$	2.33568			0.0921101			0.0460550	+	0.998939i	$0.485335\pi$
$644$		0			0
$645$	−10.9122			−0.429669
$646$		0			0
$647$	7.48108	+	12.9576i	0.294112	+	0.509416i	0.974778	−	0.223177i	$-0.0716429\pi$
$647$	7.48108	+	12.9576i	0.294112	+	0.509416i	−0.680666	+	0.732594i	$0.738310\pi$
$648$		0			0
$649$	4.42598	−	7.66602i	0.173735	−	0.300917i
$650$		0			0
$651$	−34.9829	+	7.69879i	−1.37109	+	0.301739i
$652$		0			0
$653$	11.4449	−	19.8231i	0.447873	−	0.775740i	−0.550374	−	0.834918i	$-0.685515\pi$
$653$	11.4449	−	19.8231i	0.447873	−	0.775740i	0.998247	+	0.0591787i	$0.0188482\pi$
$654$		0			0
$655$	10.8094	+	18.7224i	0.422358	+	0.731545i
$656$		0			0
$657$	2.99494			0.116844
$658$		0			0
$659$	2.20568			0.0859211			0.0429606	−	0.999077i	$-0.486321\pi$
$659$	2.20568			0.0859211			0.0429606	+	0.999077i	$0.486321\pi$
$660$		0			0
$661$	0.341188	+	0.590956i	0.0132707	+	0.0229855i	0.872584	−	0.488463i	$-0.162442\pi$
$661$	0.341188	+	0.590956i	0.0132707	+	0.0229855i	−0.859314	+	0.511449i	$0.829109\pi$
$662$		0			0
$663$	9.36449	−	16.2198i	0.363687	−	0.629924i
$664$		0			0
$665$	−4.22592	+	13.3310i	−0.163874	+	0.516954i
$666$		0			0
$667$	5.14892	−	8.91819i	0.199367	−	0.345314i
$668$		0			0
$669$	−14.9407	−	25.8781i	−0.577641	−	1.00050i
$670$		0			0
$671$	−6.68676			−0.258139
$672$		0			0
$673$	−10.8865			−0.419643			−0.209821	−	0.977740i	$-0.567288\pi$
$673$	−10.8865			−0.419643			−0.209821	+	0.977740i	$0.567288\pi$
$674$		0			0
$675$	−17.3344	−	30.0240i	−0.667200	−	1.15562i
$676$		0			0
$677$	−22.8327	+	39.5474i	−0.877532	+	1.51993i	−0.0234904	+	0.999724i	$0.507478\pi$
$677$	−22.8327	+	39.5474i	−0.877532	+	1.51993i	−0.854041	+	0.520205i	$0.825855\pi$
$678$		0			0
$679$	−17.3744	−	19.0198i	−0.666768	−	0.729912i
$680$		0			0
$681$	14.9811	−	25.9480i	0.574076	−	0.994329i
$682$		0			0
$683$	3.24186	+	5.61507i	0.124046	+	0.214855i	0.921360	−	0.388711i	$-0.127079\pi$
$683$	3.24186	+	5.61507i	0.124046	+	0.214855i	−0.797313	+	0.603566i	$0.793746\pi$
$684$		0			0
$685$	26.4932			1.01225
$686$		0			0
$687$	10.6540			0.406475
$688$		0			0
$689$	27.2715	+	47.2357i	1.03896	+	1.79954i
$690$		0			0
$691$	5.47338	−	9.48016i	0.208217	−	0.360642i	−0.742936	−	0.669363i	$-0.766567\pi$
$691$	5.47338	−	9.48016i	0.208217	−	0.360642i	0.951153	+	0.308720i	$0.0999006\pi$
$692$		0			0
$693$	−1.17169	−	1.28265i	−0.0445088	−	0.0487239i
$694$		0			0
$695$	19.3154	−	33.4553i	0.732676	−	1.26903i
$696$		0			0
$697$	−1.06500	−	1.84463i	−0.0403397	−	0.0698704i
$698$		0			0
$699$	36.8590			1.39413
$700$		0			0
$701$	−0.914874			−0.0345543			−0.0172772	−	0.999851i	$-0.505500\pi$
$701$	−0.914874			−0.0345543			−0.0172772	+	0.999851i	$0.505500\pi$
$702$		0			0
$703$	−3.34073	−	5.78632i	−0.125998	−	0.218235i
$704$		0			0
$705$	−5.65277	+	9.79088i	−0.212896	+	0.368746i
$706$		0			0
$707$	−1.48274	+	4.67741i	−0.0557642	+	0.175912i
$708$		0			0
$709$	−22.1562	+	38.3756i	−0.832092	+	1.44123i	0.0642838	+	0.997932i	$0.479524\pi$
$709$	−22.1562	+	38.3756i	−0.832092	+	1.44123i	−0.896376	+	0.443294i	$0.853810\pi$
$710$		0			0
$711$	−2.09899	−	3.63555i	−0.0787182	−	0.136344i
$712$		0			0
$713$	−23.6714			−0.886499
$714$		0			0
$715$	21.0999			0.789090
$716$		0			0
$717$	21.1851	+	36.6937i	0.791172	+	1.37035i
$718$		0			0
$719$	−2.60118	+	4.50537i	−0.0970076	+	0.168022i	−0.910445	−	0.413631i	$-0.864260\pi$
$719$	−2.60118	+	4.50537i	−0.0970076	+	0.168022i	0.813437	+	0.581653i	$0.197594\pi$
$720$		0			0
$721$	8.18544	−	1.80139i	0.304842	−	0.0670873i
$722$		0			0
$723$	−19.0022	+	32.9128i	−0.706699	+	1.22404i
$724$		0			0
$725$	−11.9148	−	20.6370i	−0.442503	−	0.766438i
$726$		0			0
$727$	−50.0871			−1.85763			−0.928814	−	0.370547i	$-0.879170\pi$
$727$	−50.0871			−1.85763			−0.928814	+	0.370547i	$0.879170\pi$
$728$		0			0
$729$	18.7866			0.695801
$730$		0			0
$731$	−1.32446	−	2.29403i	−0.0489869	−	0.0848477i
$732$		0			0
$733$	23.5349	−	40.7636i	0.869280	−	1.50564i	0.00654601	−	0.999979i	$-0.497916\pi$
$733$	23.5349	−	40.7636i	0.869280	−	1.50564i	0.862734	−	0.505658i	$-0.168750\pi$
$734$		0			0
$735$	−4.31071	+	47.5763i	−0.159003	+	1.75488i
$736$		0			0
$737$	−4.91223	+	8.50823i	−0.180944	+	0.313405i
$738$		0			0
$739$	23.4957	+	40.6957i	0.864303	+	1.49702i	0.867738	+	0.497023i	$0.165573\pi$
$739$	23.4957	+	40.6957i	0.864303	+	1.49702i	−0.00343444	+	0.999994i	$0.501093\pi$
$740$		0			0
$741$	−16.7444			−0.615121
$742$		0			0
$743$	5.19533			0.190598			0.0952991	−	0.995449i	$-0.469619\pi$
$743$	5.19533			0.190598			0.0952991	+	0.995449i	$0.469619\pi$
$744$		0			0
$745$	−1.78442	−	3.09071i	−0.0653763	−	0.113235i
$746$		0			0
$747$	0.0551029	−	0.0954410i	0.00201611	−	0.00349200i
$748$		0			0
$749$	12.3171	−	2.71066i	0.450057	−	0.0990452i
$750$		0			0
$751$	16.7268	−	28.9717i	0.610369	−	1.05719i	−0.380809	−	0.924654i	$-0.624354\pi$
$751$	16.7268	−	28.9717i	0.610369	−	1.05719i	0.991178	−	0.132537i	$-0.0423123\pi$
$752$		0			0
$753$	−21.1374	−	36.6110i	−0.770288	−	1.33418i
$754$		0			0
$755$	58.6128			2.13314
$756$		0			0
$757$	40.0440			1.45542			0.727711	−	0.685884i	$-0.240584\pi$
$757$	40.0440			1.45542			0.727711	+	0.685884i	$0.240584\pi$
$758$		0			0
$759$	−3.19665	−	5.53677i	−0.116031	−	0.200972i
$760$		0			0
$761$	3.77925	−	6.54585i	0.136998	−	0.237287i	−0.789361	−	0.613929i	$-0.789588\pi$
$761$	3.77925	−	6.54585i	0.136998	−	0.237287i	0.926359	+	0.376642i	$0.122921\pi$
$762$		0			0
$763$	11.8981	−	37.5336i	0.430742	−	1.35881i
$764$		0			0
$765$	−1.94105	+	3.36199i	−0.0701786	+	0.121553i
$766$		0			0
$767$	−26.1674	−	45.3232i	−0.944849	−	1.63653i
$768$		0			0
$769$	51.5407			1.85860			0.929302	−	0.369320i	$-0.120409\pi$
$769$	51.5407			1.85860			0.929302	+	0.369320i	$0.120409\pi$
$770$		0			0
$771$	−55.6834			−2.00539
$772$		0			0
$773$	7.73284	+	13.3937i	0.278131	+	0.481737i	0.970920	−	0.239403i	$-0.0769518\pi$
$773$	7.73284	+	13.3937i	0.278131	+	0.481737i	−0.692789	+	0.721140i	$0.743618\pi$
$774$		0			0
$775$	−27.3881	+	47.4376i	−0.983811	+	1.70401i
$776$		0			0
$777$	−15.3933	−	16.8511i	−0.552232	−	0.604530i
$778$		0			0
$779$	−0.952147	+	1.64917i	−0.0341142	+	0.0590875i
$780$		0			0
$781$	−4.30939	−	7.46408i	−0.154202	−	0.267086i
$782$		0			0
$783$	13.8020			0.493244
$784$		0			0
$785$	40.8667			1.45859
$786$		0			0
$787$	10.9759	+	19.0108i	0.391249	+	0.677663i	0.992615	−	0.121311i	$-0.0387099\pi$
$787$	10.9759	+	19.0108i	0.391249	+	0.677663i	−0.601366	+	0.798974i	$0.705377\pi$
$788$		0			0
$789$	14.8231	−	25.6744i	0.527718	−	0.914034i
$790$		0			0
$791$	−22.2040	−	24.3068i	−0.789484	−	0.864250i
$792$		0			0
$793$	−19.7668	+	34.2371i	−0.701941	+	1.21580i
$794$		0			0
$795$	−31.4794	−	54.5240i	−1.11646	−	1.93377i
$796$		0			0
$797$	42.6258			1.50988			0.754942	−	0.655792i	$-0.227665\pi$
$797$	42.6258			1.50988			0.754942	+	0.655792i	$0.227665\pi$
$798$		0			0
$799$	−2.74439			−0.0970896
$800$		0			0
$801$	0.843380	+	1.46078i	0.0297994	+	0.0516140i
$802$		0			0
$803$	−2.28057	+	3.95007i	−0.0804797	+	0.139395i
$804$		0			0
$805$	−9.53958	+	30.0933i	−0.336226	+	1.06065i
$806$		0			0
$807$	1.63166	−	2.82611i	0.0574370	−	0.0994838i
$808$		0			0
$809$	−1.98372	−	3.43591i	−0.0697440	−	0.120800i	0.829045	−	0.559183i	$-0.188885\pi$
$809$	−1.98372	−	3.43591i	−0.0697440	−	0.120800i	−0.898789	+	0.438382i	$0.855552\pi$
$810$		0			0
$811$	46.9217			1.64764			0.823821	−	0.566850i	$-0.191838\pi$
$811$	46.9217			1.64764			0.823821	+	0.566850i	$0.191838\pi$
$812$		0			0
$813$	−39.2549			−1.37673
$814$		0			0
$815$	15.9523	+	27.6301i	0.558783	+	0.967841i
$816$		0			0
$817$	−1.18411	+	2.05095i	−0.0414269	+	0.0717535i
$818$		0			0
$819$	−10.0310	+	2.20755i	−0.350512	+	0.0771381i
$820$		0			0
$821$	25.3000	−	43.8209i	0.882977	−	1.52936i	0.0349620	−	0.999389i	$-0.488869\pi$
$821$	25.3000	−	43.8209i	0.882977	−	1.52936i	0.848015	−	0.529972i	$-0.177798\pi$
$822$		0			0
$823$	0.199299	+	0.345196i	0.00694714	+	0.0120328i	0.869478	−	0.493972i	$-0.164455\pi$
$823$	0.199299	+	0.345196i	0.00694714	+	0.0120328i	−0.862531	+	0.506004i	$0.831122\pi$
$824$		0			0
$825$	−14.7943			−0.515072
$826$		0			0
$827$	20.4234			0.710193			0.355096	−	0.934830i	$-0.384448\pi$
$827$	20.4234			0.710193			0.355096	+	0.934830i	$0.384448\pi$
$828$		0			0
$829$	11.6317	+	20.1466i	0.403984	+	0.699721i	0.994203	−	0.107522i	$-0.0342918\pi$
$829$	11.6317	+	20.1466i	0.403984	+	0.699721i	−0.590219	+	0.807244i	$0.700958\pi$
$830$		0			0
$831$	−25.4910	+	44.1517i	−0.884272	+	1.53160i
$832$		0			0
$833$	−10.5250	+	4.86830i	−0.364668	+	0.168676i
$834$		0			0
$835$	32.5082	−	56.3059i	1.12499	−	1.94855i
$836$		0			0
$837$	−15.8632	−	27.4758i	−0.548311	−	0.949703i
$838$		0			0
$839$	16.4861			0.569165			0.284582	−	0.958652i	$-0.408145\pi$
$839$	16.4861			0.569165			0.284582	+	0.958652i	$0.408145\pi$
$840$		0			0
$841$	−19.5132			−0.672869
$842$		0			0
$843$	15.0534	+	26.0733i	0.518468	+	0.898013i
$844$		0			0
$845$	39.1761	−	67.8549i	1.34770	−	2.33428i
$846$		0			0
$847$	2.58392	−	0.568650i	0.0887845	−	0.0195390i
$848$		0			0
$849$	15.3645	−	26.6121i	0.527308	−	0.913324i
$850$		0			0
$851$	−7.54136	−	13.0620i	−0.258514	−	0.447760i
$852$		0			0
$853$	−14.8315			−0.507820			−0.253910	−	0.967228i	$-0.581717\pi$
$853$	−14.8315			−0.507820			−0.253910	+	0.967228i	$0.581717\pi$
$854$		0			0
$855$	3.47073			0.118696
$856$		0			0
$857$	2.51594	+	4.35773i	0.0859428	+	0.148857i	0.905793	−	0.423721i	$-0.139276\pi$
$857$	2.51594	+	4.35773i	0.0859428	+	0.148857i	−0.819850	+	0.572579i	$0.805943\pi$
$858$		0			0
$859$	−28.0181	+	48.5288i	−0.955966	+	1.65578i	−0.223825	+	0.974629i	$0.571854\pi$
$859$	−28.0181	+	48.5288i	−0.955966	+	1.65578i	−0.732141	+	0.681153i	$0.761479\pi$
$860$		0			0
$861$	−1.96567	+	6.20086i	−0.0669899	+	0.211325i
$862$		0			0
$863$	−18.2380	+	31.5892i	−0.620829	+	1.07531i	0.368503	+	0.929627i	$0.379871\pi$
$863$	−18.2380	+	31.5892i	−0.620829	+	1.07531i	−0.989332	+	0.145681i	$0.953463\pi$
$864$		0			0
$865$	34.9054	+	60.4579i	1.18682	+	2.05563i
$866$		0			0
$867$	27.2600			0.925798
$868$		0			0
$869$	6.39331			0.216878
$870$		0			0
$871$	29.0422	+	50.3026i	0.984058	+	1.70444i
$872$		0			0
$873$	−3.19665	+	5.53677i	−0.108190	+	0.187391i
$874$		0			0
$875$	17.4282	+	19.0787i	0.589180	+	0.644976i
$876$		0			0
$877$	3.30807	−	5.72974i	0.111705	−	0.193480i	−0.804753	−	0.593610i	$-0.797702\pi$
$877$	3.30807	−	5.72974i	0.111705	−	0.193480i	0.916458	+	0.400131i	$0.131035\pi$
$878$		0			0
$879$	14.6627	+	25.3965i	0.494559	+	0.856602i
$880$		0			0
$881$	−22.5286			−0.759008			−0.379504	−	0.925190i	$-0.623905\pi$
$881$	−22.5286			−0.759008			−0.379504	+	0.925190i	$0.623905\pi$
$882$		0			0
$883$	51.1652			1.72185			0.860923	−	0.508735i	$-0.169887\pi$
$883$	51.1652			1.72185			0.860923	+	0.508735i	$0.169887\pi$
$884$		0			0
$885$	30.2049	+	52.3164i	1.01533	+	1.75860i
$886$		0			0
$887$	−3.16904	+	5.48895i	−0.106406	+	0.184301i	−0.914312	−	0.405011i	$-0.867268\pi$
$887$	−3.16904	+	5.48895i	−0.106406	+	0.184301i	0.807906	+	0.589312i	$0.200601\pi$
$888$		0			0
$889$	−11.8154	−	12.9344i	−0.396277	−	0.433805i
$890$		0			0
$891$	5.26936	−	9.12679i	0.176530	−	0.305759i
$892$		0			0
$893$	1.22679	+	2.12487i	0.0410531	+	0.0711060i
$894$		0			0
$895$	11.5913			0.387454
$896$		0			0
$897$	−37.7987			−1.26206
$898$		0			0
$899$	−10.9035	−	18.8855i	−0.363653	−	0.629866i
$900$		0			0
$901$	7.64155	−	13.2356i	0.254577	−	0.440940i
$902$		0			0
$903$	−2.44456	+	7.71155i	−0.0813498	+	0.256624i
$904$		0			0
$905$	−18.4523	+	31.9603i	−0.613374	+	1.06239i
$906$		0			0
$907$	−3.44237	−	5.96236i	−0.114302	−	0.197977i	0.803199	−	0.595711i	$-0.203130\pi$
$907$	−3.44237	−	5.96236i	−0.114302	−	0.197977i	−0.917500	+	0.397735i	$0.869796\pi$
$908$		0			0
$909$	1.21777			0.0403908
$910$		0			0
$911$	41.0818			1.36110			0.680550	−	0.732701i	$-0.261741\pi$
$911$	41.0818			1.36110			0.680550	+	0.732701i	$0.261741\pi$
$912$		0			0
$913$	0.0839190	+	0.145352i	0.00277731	+	0.00481045i
$914$		0			0
$915$	22.8168	−	39.5198i	0.754299	−	1.30648i
$916$		0			0
$917$	15.6524	−	3.44467i	0.516889	−	0.113753i
$918$		0			0
$919$	−5.81324	+	10.0688i	−0.191761	+	0.332140i	−0.945834	−	0.324651i	$-0.894753\pi$
$919$	−5.81324	+	10.0688i	−0.191761	+	0.332140i	0.754073	+	0.656791i	$0.228087\pi$
$920$		0			0
$921$	15.7479	+	27.2762i	0.518911	+	0.898780i
$922$		0			0
$923$	−50.9562			−1.67724
$924$		0			0
$925$	−34.9019			−1.14757
$926$		0			0
$927$	−1.04003	−	1.80139i	−0.0341592	−	0.0591654i
$928$		0			0
$929$	−12.3834	+	21.4487i	−0.406287	+	0.703709i	−0.994470	−	0.105018i	$-0.966510\pi$
$929$	−12.3834	+	21.4487i	−0.406287	+	0.703709i	0.588184	+	0.808727i	$0.299843\pi$
$930$		0			0
$931$	8.47417	+	5.97282i	0.277730	+	0.195751i
$932$		0			0
$933$	−20.6799	+	35.8187i	−0.677030	+	1.17265i
$934$		0			0
$935$	−2.95611	−	5.12014i	−0.0966753	−	0.167447i
$936$		0			0
$937$	1.15046			0.0375839			0.0187920	−	0.999823i	$-0.494018\pi$
$937$	1.15046			0.0375839			0.0187920	+	0.999823i	$0.494018\pi$
$938$		0			0
$939$	−31.3381			−1.02268
$940$		0			0
$941$	−5.05510	−	8.75570i	−0.164792	−	0.285428i	0.771790	−	0.635878i	$-0.219362\pi$
$941$	−5.05510	−	8.75570i	−0.164792	−	0.285428i	−0.936581	+	0.350450i	$0.886029\pi$
$942$		0			0
$943$	−2.14937	+	3.72282i	−0.0699931	+	0.121232i
$944$		0			0
$945$	−41.3228	+	9.09402i	−1.34423	+	0.295828i
$946$		0			0
$947$	−12.2277	+	21.1789i	−0.397346	+	0.688223i	−0.993398	−	0.114723i	$-0.963402\pi$
$947$	−12.2277	+	21.1789i	−0.397346	+	0.688223i	0.596052	+	0.802946i	$0.296735\pi$
$948$		0			0
$949$	13.4833	+	23.3537i	0.437685	+	0.758093i
$950$		0			0
$951$	−8.53101			−0.276637
$952$		0			0
$953$	−16.1696			−0.523784			−0.261892	−	0.965097i	$-0.584346\pi$
$953$	−16.1696			−0.523784			−0.261892	+	0.965097i	$0.584346\pi$
$954$		0			0
$955$	−17.8843	−	30.9765i	−0.578722	−	1.00238i
$956$		0			0
$957$	2.94490	−	5.10071i	0.0951950	−	0.164883i
$958$		0			0
$959$	5.93500	−	18.7224i	0.191651	−	0.604578i
$960$		0			0
$961$	−9.56368	+	16.5648i	−0.308506	+	0.534347i
$962$		0			0
$963$	−1.56500	−	2.71066i	−0.0504313	−	0.0873497i
$964$		0			0
$965$	−90.3823			−2.90951
$966$		0			0
$967$	1.55941			0.0501472			0.0250736	−	0.999686i	$-0.492018\pi$
$967$	1.55941			0.0501472			0.0250736	+	0.999686i	$0.492018\pi$
$968$		0			0
$969$	2.34591	+	4.06323i	0.0753614	+	0.130530i
$970$		0			0
$971$	−4.52364	+	7.83518i	−0.145171	+	0.251443i	−0.929437	−	0.368982i	$-0.879706\pi$
$971$	−4.52364	+	7.83518i	−0.145171	+	0.251443i	0.784266	+	0.620425i	$0.213040\pi$
$972$		0			0
$973$	−19.3154	−	21.1447i	−0.619224	−	0.677866i
$974$		0			0
$975$	−43.7337	+	75.7490i	−1.40060	+	2.42591i
$976$		0			0
$977$	3.37824	+	5.85128i	0.108079	+	0.187199i	0.914992	−	0.403472i	$-0.132197\pi$
$977$	3.37824	+	5.85128i	0.108079	+	0.187199i	−0.806913	+	0.590671i	$0.798863\pi$
$978$		0			0
$979$	−2.56885			−0.0821008
$980$		0			0
$981$	−9.77188			−0.311992
$982$		0			0
$983$	13.2152	+	22.8895i	0.421501	+	0.730060i	0.996086	−	0.0883838i	$-0.0281702\pi$
$983$	13.2152	+	22.8895i	0.421501	+	0.730060i	−0.574586	+	0.818444i	$0.694837\pi$
$984$		0			0
$985$	−43.8628	+	75.9727i	−1.39759	+	2.42069i
$986$		0			0
$987$	5.65277	+	6.18810i	0.179930	+	0.196969i
$988$		0			0
$989$	−2.67301	+	4.62979i	−0.0849969	+	0.147219i
$990$		0			0
$991$	−0.317093	−	0.549221i	−0.0100728	−	0.0174466i	0.860945	−	0.508698i	$-0.169873\pi$
$991$	−0.317093	−	0.549221i	−0.0100728	−	0.0174466i	−0.871018	+	0.491251i	$0.836540\pi$
$992$		0			0
$993$	36.4080			1.15537
$994$		0			0
$995$	19.9545			0.632599
$996$		0			0
$997$	−5.06368	−	8.77054i	−0.160368	−	0.277766i	0.774633	−	0.632412i	$-0.217935\pi$
$997$	−5.06368	−	8.77054i	−0.160368	−	0.277766i	−0.935001	+	0.354646i	$0.884601\pi$
$998$		0			0
$999$	10.1076	−	17.5068i	0.319789	−	0.553891i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1232.2.q.k.177.3		6
4.3	odd	2		77.2.e.b.23.2	✓	6
7.2	even	3		8624.2.a.cl.1.1		3
7.4	even	3	inner	1232.2.q.k.529.3		6
7.5	odd	6		8624.2.a.ck.1.3		3
12.11	even	2		693.2.i.g.100.2		6
28.3	even	6		539.2.e.l.67.2		6
28.11	odd	6		77.2.e.b.67.2	yes	6
28.19	even	6		539.2.a.i.1.2		3
28.23	odd	6		539.2.a.h.1.2		3
28.27	even	2		539.2.e.l.177.2		6
44.3	odd	10		847.2.n.e.9.2		24
44.7	even	10		847.2.n.d.632.2		24
44.15	odd	10		847.2.n.e.632.2		24
44.19	even	10		847.2.n.d.9.2		24
44.27	odd	10		847.2.n.e.366.2		24
44.31	odd	10		847.2.n.e.807.2		24
44.35	even	10		847.2.n.d.807.2		24
44.39	even	10		847.2.n.d.366.2		24
44.43	even	2		847.2.e.d.485.2		6
84.11	even	6		693.2.i.g.298.2		6
84.23	even	6		4851.2.a.bo.1.2		3
84.47	odd	6		4851.2.a.bn.1.2		3
308.39	even	30		847.2.n.d.487.2		24
308.95	even	30		847.2.n.d.753.2		24
308.123	even	30		847.2.n.d.81.2		24
308.131	odd	6		5929.2.a.w.1.2		3
308.151	even	30		847.2.n.d.130.2		24
308.179	odd	30		847.2.n.e.130.2		24
308.207	odd	30		847.2.n.e.81.2		24
308.219	even	6		5929.2.a.v.1.2		3
308.235	odd	30		847.2.n.e.753.2		24
308.263	even	6		847.2.e.d.606.2		6
308.291	odd	30		847.2.n.e.487.2		24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
77.2.e.b.23.2	✓	6	4.3	odd	2
77.2.e.b.67.2	yes	6	28.11	odd	6
539.2.a.h.1.2		3	28.23	odd	6
539.2.a.i.1.2		3	28.19	even	6
539.2.e.l.67.2		6	28.3	even	6
539.2.e.l.177.2		6	28.27	even	2
693.2.i.g.100.2		6	12.11	even	2
693.2.i.g.298.2		6	84.11	even	6
847.2.e.d.485.2		6	44.43	even	2
847.2.e.d.606.2		6	308.263	even	6
847.2.n.d.9.2		24	44.19	even	10
847.2.n.d.81.2		24	308.123	even	30
847.2.n.d.130.2		24	308.151	even	30
847.2.n.d.366.2		24	44.39	even	10
847.2.n.d.487.2		24	308.39	even	30
847.2.n.d.632.2		24	44.7	even	10
847.2.n.d.753.2		24	308.95	even	30
847.2.n.d.807.2		24	44.35	even	10
847.2.n.e.9.2		24	44.3	odd	10
847.2.n.e.81.2		24	308.207	odd	30
847.2.n.e.130.2		24	308.179	odd	30
847.2.n.e.366.2		24	44.27	odd	10
847.2.n.e.487.2		24	308.291	odd	30
847.2.n.e.632.2		24	44.15	odd	10
847.2.n.e.753.2		24	308.235	odd	30
847.2.n.e.807.2		24	44.31	odd	10
1232.2.q.k.177.3		6	1.1	even	1	trivial
1232.2.q.k.529.3		6	7.4	even	3	inner
4851.2.a.bn.1.2		3	84.47	odd	6
4851.2.a.bo.1.2		3	84.23	even	6
5929.2.a.v.1.2		3	308.219	even	6
5929.2.a.w.1.2		3	308.131	odd	6
8624.2.a.ck.1.3		3	7.5	odd	6
8624.2.a.cl.1.1		3	7.2	even	3

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(0.956115 + 1.65604i) q^{3} +(1.78442 - 3.09071i) q^{5} +(-1.78442 - 1.95341i) q^{7} +(-0.328310 + 0.568650i) q^{9} +O(q^{10})\)	\(q+(0.956115 + 1.65604i) q^{3} +(1.78442 - 3.09071i) q^{5} +(-1.78442 - 1.95341i) q^{7} +(-0.328310 + 0.568650i) q^{9} +(-0.500000 - 0.866025i) q^{11} -5.91223 q^{13} +6.82446 q^{15} +(0.828310 + 1.43468i) q^{17} +(0.740539 - 1.28265i) q^{19} +(1.52882 - 4.82277i) q^{21} +(1.67169 - 2.89545i) q^{23} +(-3.86834 - 6.70017i) q^{25} +4.48108 q^{27} +3.08007 q^{29} +(-3.54003 - 6.13152i) q^{31} +(0.956115 - 1.65604i) q^{33} +(-9.22162 + 2.02943i) q^{35} +(2.25561 - 3.90683i) q^{37} +(-5.65277 - 9.79088i) q^{39} -1.28575 q^{41} -1.59899 q^{43} +(1.17169 + 2.02943i) q^{45} +(-0.828310 + 1.43468i) q^{47} +(-0.631656 + 6.97144i) q^{49} +(-1.58392 + 2.74343i) q^{51} +(-4.61274 - 7.98949i) q^{53} -3.56885 q^{55} +2.83216 q^{57} +(4.42598 + 7.66602i) q^{59} +(3.34338 - 5.79090i) q^{61} +(1.69665 - 0.373387i) q^{63} +(-10.5499 + 18.2730i) q^{65} +(-4.91223 - 8.50823i) q^{67} +6.39331 q^{69} +8.61878 q^{71} +(-2.28057 - 3.95007i) q^{73} +(7.39716 - 12.8123i) q^{75} +(-0.799494 + 2.52206i) q^{77} +(-3.19665 + 5.53677i) q^{79} +(5.26936 + 9.12679i) q^{81} -0.167838 q^{83} +5.91223 q^{85} +(2.94490 + 5.10071i) q^{87} +(1.28442 - 2.22469i) q^{89} +(10.5499 + 11.5490i) q^{91} +(6.76936 - 11.7249i) q^{93} +(-2.64287 - 4.57759i) q^{95} +9.73669 q^{97} +0.656620 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q - q^{3} + 2 q^{5} - 2 q^{7}+O(q^{10}) \) 6 * q - q^3 + 2 * q^5 - 2 * q^7	\( 6 q - q^{3} + 2 q^{5} - 2 q^{7} - 3 q^{11} - 22 q^{13} + 14 q^{15} + 3 q^{17} - 11 q^{19} + 10 q^{21} + 12 q^{23} - 3 q^{25} - 4 q^{27} - 18 q^{29} - 3 q^{31} - q^{33} - 9 q^{35} + 4 q^{37} - 5 q^{39} - 10 q^{41} - 4 q^{43} + 9 q^{45} - 3 q^{47} - 24 q^{49} + 2 q^{51} - 17 q^{53} - 4 q^{55} + 40 q^{57} + 8 q^{59} + 24 q^{61} - 12 q^{63} - 15 q^{65} - 16 q^{67} - 6 q^{69} - 14 q^{71} + 20 q^{73} + 25 q^{75} - 2 q^{77} + 3 q^{79} + 17 q^{81} + 22 q^{83} + 22 q^{85} + 30 q^{87} - q^{89} + 15 q^{91} + 26 q^{93} - 17 q^{95} + 18 q^{97}+O(q^{100}) \) 6 * q - q^3 + 2 * q^5 - 2 * q^7 - 3 * q^11 - 22 * q^13 + 14 * q^15 + 3 * q^17 - 11 * q^19 + 10 * q^21 + 12 * q^23 - 3 * q^25 - 4 * q^27 - 18 * q^29 - 3 * q^31 - q^33 - 9 * q^35 + 4 * q^37 - 5 * q^39 - 10 * q^41 - 4 * q^43 + 9 * q^45 - 3 * q^47 - 24 * q^49 + 2 * q^51 - 17 * q^53 - 4 * q^55 + 40 * q^57 + 8 * q^59 + 24 * q^61 - 12 * q^63 - 15 * q^65 - 16 * q^67 - 6 * q^69 - 14 * q^71 + 20 * q^73 + 25 * q^75 - 2 * q^77 + 3 * q^79 + 17 * q^81 + 22 * q^83 + 22 * q^85 + 30 * q^87 - q^89 + 15 * q^91 + 26 * q^93 - 17 * q^95 + 18 * q^97

Introduction

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