LMFDB - Embedded newform 448.2.q.c.31.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [448,2,Mod(31,448)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(448, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("448.31");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 448 = 2^{6} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	448.q (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:	$3.57729801055$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$6$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 4x^{9} - 16x^{8} + 8x^{7} + 8x^{6} + 32x^{5} + 240x^{4} + 120x^{3} + 32x^{2} + 16x + 4 $ x^12 - 4x^9 - 16x^8 + 8x^7 + 8x^6 + 32x^5 + 240x^4 + 120x^3 + 32x^2 + 16*x + 4
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{6} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			31.6
Root			$0.0946732 - 0.353325i$ of defining polynomial
Character	$\chi$	$=$	448.31
Dual form			448.2.q.c.159.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(2.48220 + 1.43310i) q^{3} +(0.241348 + 0.418027i) q^{5} +(0.447998 - 2.60755i) q^{7} +(2.60755 + 4.51640i) q^{9} +O(q^{10})$	\(q+(2.48220 + 1.43310i) q^{3} +(0.241348 + 0.418027i) q^{5} +(0.447998 - 2.60755i) q^{7} +(2.60755 + 4.51640i) q^{9} +(-2.03420 + 3.52334i) q^{11} +3.21509 q^{13} +1.38350i q^{15} +(-0.724044 - 0.418027i) q^{17} +(4.66225 - 2.69175i) q^{19} +(4.84889 - 5.83043i) q^{21} +(-7.44660 + 4.29930i) q^{23} +(2.38350 - 4.12835i) q^{25} +6.34889i q^{27} -4.36010i q^{29} +(-3.76625 + 6.52334i) q^{31} +(-10.0986 + 5.83043i) q^{33} +(1.19815 - 0.442051i) q^{35} +(-1.50000 + 0.866025i) q^{37} +(7.98050 + 4.60755i) q^{39} -4.36010i q^{41} -6.92820 q^{43} +(-1.25865 + 2.18005i) q^{45} +(-5.26655 - 9.12194i) q^{47} +(-6.59859 - 2.33635i) q^{49} +(-1.19815 - 2.07525i) q^{51} +(10.0986 + 5.83043i) q^{53} -1.96380 q^{55} +15.4302 q^{57} +(-3.08650 - 1.78199i) q^{59} +(-1.71509 - 2.97063i) q^{61} +(12.9449 - 4.77596i) q^{63} +(0.775956 + 1.34400i) q^{65} +(3.31825 - 5.74739i) q^{67} -24.6453 q^{69} -6.00000i q^{71} +(5.54668 + 3.20238i) q^{73} +(11.8327 - 6.83159i) q^{75} +(8.27596 + 6.88273i) q^{77} +(1.58620 - 0.915795i) q^{79} +(-1.27596 + 2.21002i) q^{81} +11.0346i q^{83} -0.403560i q^{85} +(6.24845 - 10.8226i) q^{87} +(-4.50000 + 2.59808i) q^{89} +(1.44036 - 8.38350i) q^{91} +(-18.6972 + 10.7948i) q^{93} +(2.25045 + 1.29930i) q^{95} -14.1690i q^{97} -21.2171 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + 6 q^{5} + 4 q^{9}+O(q^{10}) $ 12 * q + 6 * q^5 + 4 * q^9	$ 12 q + 6 q^{5} + 4 q^{9} - 16 q^{13} - 18 q^{17} + 34 q^{21} - 8 q^{25} - 30 q^{33} - 18 q^{37} - 12 q^{45} + 12 q^{49} + 30 q^{53} + 76 q^{57} + 34 q^{61} - 132 q^{69} - 6 q^{73} + 90 q^{77} - 6 q^{81} - 54 q^{89} - 42 q^{93}+O(q^{100}) $ 12 * q + 6 * q^5 + 4 * q^9 - 16 * q^13 - 18 * q^17 + 34 * q^21 - 8 * q^25 - 30 * q^33 - 18 * q^37 - 12 * q^45 + 12 * q^49 + 30 * q^53 + 76 * q^57 + 34 * q^61 - 132 * q^69 - 6 * q^73 + 90 * q^77 - 6 * q^81 - 54 * q^89 - 42 * q^93

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/448\mathbb{Z}\right)^\times$.

$n$	$127$	$129$	$197$
$\chi(n)$	$-1$	$e\left(\frac{1}{6}\right)$	$-1$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	2.48220	+	1.43310i	1.43310	+	0.827400i	0.997356	−	0.0726709i	$-0.0231523\pi$
$3$	2.48220	+	1.43310i	1.43310	+	0.827400i	0.435743	+	0.900071i	$0.356486\pi$
$4$		0			0
$5$	0.241348	+	0.418027i	0.107934	+	0.186947i	0.914933	−	0.403605i	$-0.132243\pi$
$5$	0.241348	+	0.418027i	0.107934	+	0.186947i	−0.806999	+	0.590553i	$0.798910\pi$
$6$		0			0
$7$	0.447998	−	2.60755i	0.169327	−	0.985560i
$7$	0.447998	−	2.60755i	0.169327	−	0.985560i
$8$		0			0
$9$	2.60755	+	4.51640i	0.869182	+	1.50547i
$10$		0			0
$11$	−2.03420	+	3.52334i	−0.613335	+	1.06233i	0.377339	+	0.926075i	$0.376839\pi$
$11$	−2.03420	+	3.52334i	−0.613335	+	1.06233i	−0.990674	+	0.136252i	$0.956494\pi$
$12$		0			0
$13$	3.21509			0.891706			0.445853	−	0.895106i	$-0.352900\pi$
$13$	3.21509			0.891706			0.445853	+	0.895106i	$0.352900\pi$
$14$		0			0
$15$			1.38350i			0.357219i
$16$		0			0
$17$	−0.724044	−	0.418027i	−0.175606	−	0.101386i	0.409620	−	0.912256i	$-0.365661\pi$
$17$	−0.724044	−	0.418027i	−0.175606	−	0.101386i	−0.585227	+	0.810870i	$0.698995\pi$
$18$		0			0
$19$	4.66225	−	2.69175i	1.06959	−	0.617530i	0.141523	−	0.989935i	$-0.454800\pi$
$19$	4.66225	−	2.69175i	1.06959	−	0.617530i	0.928070	+	0.372405i	$0.121467\pi$
$20$		0			0
$21$	4.84889	−	5.83043i	1.05812	−	1.27230i
$22$		0			0
$23$	−7.44660	+	4.29930i	−1.55272	+	0.896465i	−0.554805	+	0.831980i	$0.687207\pi$
$23$	−7.44660	+	4.29930i	−1.55272	+	0.896465i	−0.997919	+	0.0644851i	$0.979459\pi$
$24$		0			0
$25$	2.38350	−	4.12835i	0.476700	−	0.825669i
$26$		0			0
$27$			6.34889i			1.22185i
$28$		0			0
$29$		−	4.36010i		−	0.809650i	−0.914394	−	0.404825i	$-0.867332\pi$
$29$		−	4.36010i		−	0.809650i	0.914394	−	0.404825i	$-0.132668\pi$
$30$		0			0
$31$	−3.76625	+	6.52334i	−0.676439	+	1.17163i	0.299607	+	0.954063i	$0.403144\pi$
$31$	−3.76625	+	6.52334i	−0.676439	+	1.17163i	−0.976046	+	0.217564i	$0.930189\pi$
$32$		0			0
$33$	−10.0986	+	5.83043i	−1.75794	+	1.01495i
$34$		0			0
$35$	1.19815	−	0.442051i	0.202524	−	0.0747202i
$36$		0			0
$37$	−1.50000	+	0.866025i	−0.246598	+	0.142374i	−0.618206	−	0.786016i	$-0.712140\pi$
$37$	−1.50000	+	0.866025i	−0.246598	+	0.142374i	0.371607	+	0.928390i	$0.378807\pi$
$38$		0			0
$39$	7.98050	+	4.60755i	1.27790	+	0.737798i
$40$		0			0
$41$		−	4.36010i		−	0.680933i	−0.940257	−	0.340466i	$-0.889415\pi$
$41$		−	4.36010i		−	0.680933i	0.940257	−	0.340466i	$-0.110585\pi$
$42$		0			0
$43$	−6.92820			−1.05654			−0.528271	−	0.849076i	$-0.677159\pi$
$43$	−6.92820			−1.05654			−0.528271	+	0.849076i	$0.677159\pi$
$44$		0			0
$45$	−1.25865	+	2.18005i	−0.187629	+	0.324983i
$46$		0			0
$47$	−5.26655	−	9.12194i	−0.768206	−	1.33057i	−0.938535	−	0.345184i	$-0.887817\pi$
$47$	−5.26655	−	9.12194i	−0.768206	−	1.33057i	0.170329	−	0.985387i	$-0.445517\pi$
$48$		0			0
$49$	−6.59859	−	2.33635i	−0.942656	−	0.333765i
$50$		0			0
$51$	−1.19815	−	2.07525i	−0.167774	−	0.290594i
$52$		0			0
$53$	10.0986	+	5.83043i	1.38715	+	0.800871i	0.992993	−	0.118173i	$-0.0377038\pi$
$53$	10.0986	+	5.83043i	1.38715	+	0.800871i	0.394156	+	0.919044i	$0.371037\pi$
$54$		0			0
$55$	−1.96380			−0.264799
$56$		0			0
$57$	15.4302			2.04378
$58$		0			0
$59$	−3.08650	−	1.78199i	−0.401828	−	0.231996i	0.285444	−	0.958395i	$-0.407859\pi$
$59$	−3.08650	−	1.78199i	−0.401828	−	0.231996i	−0.687273	+	0.726400i	$0.741192\pi$
$60$		0			0
$61$	−1.71509	−	2.97063i	−0.219595	−	0.380350i	0.735089	−	0.677970i	$-0.237140\pi$
$61$	−1.71509	−	2.97063i	−0.219595	−	0.380350i	−0.954684	+	0.297621i	$0.903807\pi$
$62$		0			0
$63$	12.9449	−	4.77596i	1.63090	−	0.601714i
$64$		0			0
$65$	0.775956	+	1.34400i	0.0962455	+	0.166702i
$66$		0			0
$67$	3.31825	−	5.74739i	0.405389	−	0.702155i	−0.588977	−	0.808150i	$-0.700469\pi$
$67$	3.31825	−	5.74739i	0.405389	−	0.702155i	0.994367	+	0.105995i	$0.0338026\pi$
$68$		0			0
$69$	−24.6453			−2.96694
$70$		0			0
$71$		−	6.00000i		−	0.712069i	−0.934473	−	0.356034i	$-0.884129\pi$
$71$		−	6.00000i		−	0.712069i	0.934473	−	0.356034i	$-0.115871\pi$
$72$		0			0
$73$	5.54668	+	3.20238i	0.649190	+	0.374810i	0.788146	−	0.615489i	$-0.211041\pi$
$73$	5.54668	+	3.20238i	0.649190	+	0.374810i	−0.138956	+	0.990299i	$0.544375\pi$
$74$		0			0
$75$	11.8327	−	6.83159i	1.36632	−	0.788844i
$76$		0			0
$77$	8.27596	+	6.88273i	0.943133	+	0.784360i
$78$		0			0
$79$	1.58620	−	0.915795i	0.178462	−	0.103035i	−0.408108	−	0.912934i	$-0.633811\pi$
$79$	1.58620	−	0.915795i	0.178462	−	0.103035i	0.586570	+	0.809899i	$0.300478\pi$
$80$		0			0
$81$	−1.27596	+	2.21002i	−0.141773	+	0.245558i
$82$		0			0
$83$			11.0346i			1.21121i	0.795767	+	0.605603i	$0.207068\pi$
$83$			11.0346i			1.21121i	−0.795767	+	0.605603i	$0.792932\pi$
$84$		0			0
$85$		−	0.403560i		−	0.0437722i
$86$		0			0
$87$	6.24845	−	10.8226i	0.669905	−	1.16031i
$88$		0			0
$89$	−4.50000	+	2.59808i	−0.476999	+	0.275396i	−0.719165	−	0.694839i	$-0.755475\pi$
$89$	−4.50000	+	2.59808i	−0.476999	+	0.275396i	0.242166	+	0.970235i	$0.422142\pi$
$90$		0			0
$91$	1.44036	−	8.38350i	0.150990	−	0.878830i
$92$		0			0
$93$	−18.6972	+	10.7948i	−1.93881	+	1.11937i
$94$		0			0
$95$	2.25045	+	1.29930i	0.230891	+	0.133305i
$96$		0			0
$97$		−	14.1690i		−	1.43865i	−0.694676	−	0.719323i	$-0.744452\pi$
$97$		−	14.1690i		−	1.43865i	0.694676	−	0.719323i	$-0.255548\pi$
$98$		0			0
$99$	−21.2171			−2.13240
$100$		0			0
$101$	−3.24135	+	5.61418i	−0.322526	+	0.558632i	−0.981009	−	0.193964i	$-0.937865\pi$
$101$	−3.24135	+	5.61418i	−0.322526	+	0.558632i	0.658482	+	0.752596i	$0.271199\pi$
$102$		0			0
$103$	3.31825	+	5.74739i	0.326957	+	0.566307i	0.981907	−	0.189366i	$-0.0606433\pi$
$103$	3.31825	+	5.74739i	0.326957	+	0.566307i	−0.654949	+	0.755673i	$0.727310\pi$
$104$		0			0
$105$	3.60755	+	0.619807i	0.352060	+	0.0604870i
$106$		0			0
$107$	−2.87026	−	4.97143i	−0.277478	−	0.480606i	0.693279	−	0.720669i	$-0.256165\pi$
$107$	−2.87026	−	4.97143i	−0.277478	−	0.480606i	−0.970757	+	0.240063i	$0.922832\pi$
$108$		0			0
$109$	−3.32264	−	1.91833i	−0.318251	−	0.183742i	0.332362	−	0.943152i	$-0.392155\pi$
$109$	−3.32264	−	1.91833i	−0.318251	−	0.183742i	−0.650613	+	0.759410i	$0.725488\pi$
$110$		0			0
$111$	−4.96440			−0.471200
$112$		0			0
$113$	−9.64528			−0.907351			−0.453676	−	0.891167i	$-0.649888\pi$
$113$	−9.64528			−0.907351			−0.453676	+	0.891167i	$0.649888\pi$
$114$		0			0
$115$	−3.59444	−	2.07525i	−0.335184	−	0.193518i
$116$		0			0
$117$	8.38350	+	14.5207i	0.775055	+	1.34243i
$118$		0			0
$119$	−1.41440	+	1.70070i	−0.129657	+	0.155903i
$120$		0			0
$121$	−2.77596	−	4.80810i	−0.252360	−	0.437100i
$122$		0			0
$123$	6.24845	−	10.8226i	0.563404	−	0.975844i
$124$		0			0
$125$	4.71449			0.421677
$126$		0			0
$127$		−	5.10382i		−	0.452891i	−0.974024	−	0.226446i	$-0.927289\pi$
$127$		−	5.10382i		−	0.452891i	0.974024	−	0.226446i	$-0.0727105\pi$
$128$		0			0
$129$	−17.1972	−	9.92880i	−1.51413	−	0.874182i
$130$		0			0
$131$	−3.92256	+	2.26469i	−0.342715	+	0.197867i	−0.661472	−	0.749970i	$-0.730068\pi$
$131$	−3.92256	+	2.26469i	−0.342715	+	0.197867i	0.318757	+	0.947837i	$0.396735\pi$
$132$		0			0
$133$	−4.93018	−	13.3629i	−0.427501	−	1.15871i
$134$		0			0
$135$	−2.65401	+	1.53229i	−0.228421	+	0.131879i
$136$		0			0
$137$	0.724044	−	1.25408i	0.0618592	−	0.107143i	−0.833437	−	0.552614i	$-0.813630\pi$
$137$	0.724044	−	1.25408i	0.0618592	−	0.107143i	0.895296	+	0.445471i	$0.146964\pi$
$138$		0			0
$139$		−	0.430185i		−	0.0364878i	−0.999834	−	0.0182439i	$-0.994192\pi$
$139$		−	0.430185i		−	0.0364878i	0.999834	−	0.0182439i	$-0.00580754\pi$
$140$		0			0
$141$		−	30.1900i		−	2.54245i
$142$		0			0
$143$	−6.54015	+	11.3279i	−0.546915	+	0.947284i
$144$		0			0
$145$	1.82264	−	1.05230i	0.151362	−	0.0873888i
$146$		0			0
$147$	−13.0308	−	15.2557i	−1.07476	−	1.25827i
$148$		0			0
$149$	19.4731	−	11.2428i	1.59530	−	0.921048i	0.602927	−	0.797797i	$-0.294001\pi$
$149$	19.4731	−	11.2428i	1.59530	−	0.921048i	0.992375	−	0.123252i	$-0.0393322\pi$
$150$		0			0
$151$	2.55765	+	1.47666i	0.208138	+	0.120169i	0.600446	−	0.799665i	$-0.294990\pi$
$151$	2.55765	+	1.47666i	0.208138	+	0.120169i	−0.392308	+	0.919834i	$0.628323\pi$
$152$		0			0
$153$		−	4.36010i		−	0.352493i
$154$		0			0
$155$	−3.63591			−0.292043
$156$		0			0
$157$	−7.71509	+	13.3629i	−0.615731	+	1.06648i	0.374524	+	0.927217i	$0.377806\pi$
$157$	−7.71509	+	13.3629i	−0.615731	+	1.06648i	−0.990256	+	0.139261i	$0.955527\pi$
$158$		0			0
$159$	16.7112	+	28.9446i	1.32528	+	2.29545i
$160$		0			0
$161$	7.87455	+	21.3434i	0.620602	+	1.68210i
$162$		0			0
$163$	5.05031	+	8.74739i	0.395570	+	0.685148i	0.993174	−	0.116644i	$-0.0372136\pi$
$163$	5.05031	+	8.74739i	0.395570	+	0.685148i	−0.597603	+	0.801792i	$0.703880\pi$
$164$		0			0
$165$	−4.87455	−	2.81432i	−0.379483	−	0.219095i
$166$		0			0
$167$	−14.7524			−1.14158			−0.570788	−	0.821098i	$-0.693362\pi$
$167$	−14.7524			−1.14158			−0.570788	+	0.821098i	$0.693362\pi$
$168$		0			0
$169$	−2.66318			−0.204860
$170$		0			0
$171$	24.3141	+	14.0377i	1.85934	+	1.07349i
$172$		0			0
$173$	8.06399	+	13.9672i	0.613094	+	1.06191i	0.990716	+	0.135949i	$0.0434085\pi$
$173$	8.06399	+	13.9672i	0.613094	+	1.06191i	−0.377622	+	0.925960i	$0.623258\pi$
$174$		0			0
$175$	−9.69705	−	8.06459i	−0.733028	−	0.609625i
$176$		0			0
$177$	−5.10755	−	8.84653i	−0.383907	−	0.664946i
$178$		0			0
$179$	−8.49890	+	14.7205i	−0.635238	+	1.10026i	0.351227	+	0.936290i	$0.385765\pi$
$179$	−8.49890	+	14.7205i	−0.635238	+	1.10026i	−0.986465	+	0.163974i	$0.947569\pi$
$180$		0			0
$181$	−13.8708			−1.03101			−0.515505	−	0.856886i	$-0.672396\pi$
$181$	−13.8708			−1.03101			−0.515505	+	0.856886i	$0.672396\pi$
$182$		0			0
$183$		−	9.83159i		−	0.726772i
$184$		0			0
$185$	−0.724044	−	0.418027i	−0.0532328	−	0.0307340i
$186$		0			0
$187$	2.94570	−	1.70070i	0.215411	−	0.124368i
$188$		0			0
$189$	16.5550	+	2.84429i	1.20420	+	0.206892i
$190$		0			0
$191$	13.9867	−	8.07525i	1.01205	−	0.584305i	0.100256	−	0.994962i	$-0.468034\pi$
$191$	13.9867	−	8.07525i	1.01205	−	0.584305i	0.911790	+	0.410657i	$0.134701\pi$
$192$		0			0
$193$	−4.10755	+	7.11448i	−0.295668	+	0.512111i	−0.975140	−	0.221590i	$-0.928875\pi$
$193$	−4.10755	+	7.11448i	−0.295668	+	0.512111i	0.679472	+	0.733701i	$0.262209\pi$
$194$		0			0
$195$			4.44809i			0.318534i
$196$		0			0
$197$			11.9135i			0.848803i	0.905474	+	0.424402i	$0.139515\pi$
$197$			11.9135i			0.848803i	−0.905474	+	0.424402i	$0.860485\pi$
$198$		0			0
$199$	−0.0703998	+	0.121936i	−0.00499051	+	0.00864382i	−0.868510	−	0.495672i	$-0.834922\pi$
$199$	−0.0703998	+	0.121936i	−0.00499051	+	0.00864382i	0.863519	+	0.504316i	$0.168255\pi$
$200$		0			0
$201$	16.4731	−	9.51078i	1.16193	−	0.670838i
$202$		0			0
$203$	−11.3692	−	1.95332i	−0.797958	−	0.137096i
$204$		0			0
$205$	1.82264	−	1.05230i	0.127299	−	0.0734959i
$206$		0			0
$207$	−38.8347	−	22.4212i	−2.69920	−	1.55838i
$208$		0			0
$209$			21.9023i			1.51501i
$210$		0			0
$211$	19.3941			1.33514			0.667572	−	0.744545i	$-0.267333\pi$
$211$	19.3941			1.33514			0.667572	+	0.744545i	$0.267333\pi$
$212$		0			0
$213$	8.59859	−	14.8932i	0.589166	−	1.02047i
$214$		0			0
$215$	−1.67211	−	2.89618i	−0.114037	−	0.197518i
$216$		0			0
$217$	15.3226	+	12.7431i	1.04017	+	0.865060i
$218$		0			0
$219$	9.17865	+	15.8979i	0.620236	+	1.07428i
$220$		0			0
$221$	−2.32787	−	1.34400i	−0.156589	−	0.0904069i
$222$		0			0
$223$	15.1849			1.01686			0.508428	−	0.861105i	$-0.330227\pi$
$223$	15.1849			1.01686			0.508428	+	0.861105i	$0.330227\pi$
$224$		0			0
$225$	24.8604			1.65736
$226$		0			0
$227$	18.3468	+	10.5926i	1.21772	+	0.703053i	0.964430	−	0.264337i	$-0.0851531\pi$
$227$	18.3468	+	10.5926i	1.21772	+	0.703053i	0.253293	+	0.967390i	$0.418486\pi$
$228$		0			0
$229$	6.10755	+	10.5786i	0.403598	+	0.699052i	0.994157	−	0.107942i	$-0.0344261\pi$
$229$	6.10755	+	10.5786i	0.403598	+	0.699052i	−0.590559	+	0.806994i	$0.701093\pi$
$230$		0			0
$231$	10.6790	+	28.9446i	0.702623	+	1.90441i
$232$		0			0
$233$	−3.32264	−	5.75498i	−0.217673	−	0.377021i	0.736423	−	0.676521i	$-0.236513\pi$
$233$	−3.32264	−	5.75498i	−0.217673	−	0.377021i	−0.954096	+	0.299500i	$0.903180\pi$
$234$		0			0
$235$	2.54214	−	4.40312i	0.165831	−	0.287228i
$236$		0			0
$237$	5.24970			0.341005
$238$		0			0
$239$		−	12.5415i		−	0.811239i	−0.914042	−	0.405620i	$-0.867056\pi$
$239$		−	12.5415i		−	0.811239i	0.914042	−	0.405620i	$-0.132944\pi$
$240$		0			0
$241$	17.1453	+	9.89883i	1.10442	+	0.637640i	0.937380	−	0.348310i	$-0.113244\pi$
$241$	17.1453	+	9.89883i	1.10442	+	0.637640i	0.167045	+	0.985949i	$0.446578\pi$
$242$		0			0
$243$	10.1606	−	5.86620i	0.651800	−	0.376317i
$244$		0			0
$245$	−0.615899	−	3.32226i	−0.0393483	−	0.212252i
$246$		0			0
$247$	14.9896	−	8.65423i	0.953763	−	0.550655i
$248$		0			0
$249$	−15.8137	+	27.3901i	−1.00215	+	1.73578i
$250$		0			0
$251$			22.6107i			1.42717i	0.700567	+	0.713586i	$0.252930\pi$
$251$			22.6107i			1.42717i	−0.700567	+	0.713586i	$0.747070\pi$
$252$		0			0
$253$		−	34.9826i		−	2.19933i
$254$		0			0
$255$	0.578341	−	1.00172i	0.0362171	−	0.0627299i
$256$		0			0
$257$	6.82787	−	3.94207i	0.425911	−	0.245900i	−0.271692	−	0.962384i	$-0.587583\pi$
$257$	6.82787	−	3.94207i	0.425911	−	0.245900i	0.697603	+	0.716485i	$0.254250\pi$
$258$		0			0
$259$	1.58620	+	4.29930i	0.0985619	+	0.267145i
$260$		0			0
$261$	19.6920	−	11.3692i	1.21890	−	0.703733i
$262$		0			0
$263$	8.14186	+	4.70070i	0.502048	+	0.289858i	0.729559	−	0.683918i	$-0.239725\pi$
$263$	8.14186	+	4.70070i	0.502048	+	0.289858i	−0.227511	+	0.973776i	$0.573059\pi$
$264$		0			0
$265$			5.62865i			0.345765i
$266$		0			0
$267$	−14.8932			−0.911449
$268$		0			0
$269$	−1.98270	+	3.43413i	−0.120887	+	0.209383i	−0.920118	−	0.391642i	$-0.871907\pi$
$269$	−1.98270	+	3.43413i	−0.120887	+	0.209383i	0.799231	+	0.601024i	$0.205241\pi$
$270$		0			0
$271$	8.57435	+	14.8512i	0.520855	+	0.902147i	0.999706	+	0.0242507i	$0.00771999\pi$
$271$	8.57435	+	14.8512i	0.520855	+	0.902147i	−0.478851	+	0.877896i	$0.658947\pi$
$272$		0			0
$273$	15.5896	−	18.7454i	0.943528	−	1.13452i
$274$		0			0
$275$	9.69705	+	16.7958i	0.584754	+	1.01282i
$276$		0			0
$277$	5.65051	+	3.26232i	0.339506	+	0.196014i	0.660054	−	0.751219i	$-0.270534\pi$
$277$	5.65051	+	3.26232i	0.339506	+	0.196014i	−0.320548	+	0.947232i	$0.603867\pi$
$278$		0			0
$279$	−39.2827			−2.35179
$280$		0			0
$281$	−12.7491			−0.760548			−0.380274	−	0.924874i	$-0.624170\pi$
$281$	−12.7491			−0.760548			−0.380274	+	0.924874i	$0.624170\pi$
$282$		0			0
$283$	−22.0636	−	12.7384i	−1.31155	−	0.757221i	−0.329194	−	0.944262i	$-0.606777\pi$
$283$	−22.0636	−	12.7384i	−1.31155	−	0.757221i	−0.982352	+	0.187041i	$0.940110\pi$
$284$		0			0
$285$	3.72404	+	6.45023i	0.220593	+	0.382079i
$286$		0			0
$287$	−11.3692	−	1.95332i	−0.671100	−	0.115301i
$288$		0			0
$289$	−8.15051	−	14.1171i	−0.479442	−	0.830417i
$290$		0			0
$291$	20.3056	−	35.1703i	1.19034	−	2.06172i
$292$		0			0
$293$	−7.93078			−0.463321			−0.231661	−	0.972797i	$-0.574416\pi$
$293$	−7.93078			−0.463321			−0.231661	+	0.972797i	$0.574416\pi$
$294$		0			0
$295$		−	1.72032i		−	0.100161i
$296$		0			0
$297$	−22.3693	−	12.9149i	−1.29800	−	0.749400i
$298$		0			0
$299$	−23.9415	+	13.8226i	−1.38457	+	0.799384i
$300$		0			0
$301$	−3.10382	+	18.0656i	−0.178901	+	1.04128i
$302$		0			0
$303$	−16.0914	+	9.29035i	−0.924424	+	0.533716i
$304$		0			0
$305$	0.827868	−	1.43391i	0.0474036	−	0.0821054i
$306$		0			0
$307$		−	1.23300i		−	0.0703708i	−0.999381	−	0.0351854i	$-0.988798\pi$
$307$		−	1.23300i		−	0.0703708i	0.999381	−	0.0351854i	$-0.0112022\pi$
$308$		0			0
$309$			19.0216i			1.08210i
$310$		0			0
$311$	−3.08650	+	5.34598i	−0.175020	+	0.303143i	−0.940168	−	0.340711i	$-0.889332\pi$
$311$	−3.08650	+	5.34598i	−0.175020	+	0.303143i	0.765149	+	0.643854i	$0.222666\pi$
$312$		0			0
$313$	−16.0986	+	9.29453i	−0.909946	+	0.525358i	−0.880414	−	0.474206i	$-0.842735\pi$
$313$	−16.0986	+	9.29453i	−0.909946	+	0.525358i	−0.0295325	+	0.999564i	$0.509402\pi$
$314$		0			0
$315$	5.12071	+	4.25865i	0.288519	+	0.239948i
$316$		0			0
$317$	6.45332	−	3.72582i	0.362454	−	0.209263i	−0.307702	−	0.951483i	$-0.599560\pi$
$317$	6.45332	−	3.72582i	0.362454	−	0.209263i	0.670157	+	0.742219i	$0.266227\pi$
$318$		0			0
$319$	15.3621	+	8.86932i	0.860113	+	0.496587i
$320$		0			0
$321$		−	16.4534i		−	0.918342i
$322$		0			0
$323$	−4.50090			−0.250437
$324$		0			0
$325$	7.66318	−	13.2730i	0.425077	−	0.736255i
$326$		0			0
$327$	−5.49830	−	9.52334i	−0.304057	−	0.526642i
$328$		0			0
$329$	−26.1453	+	9.64617i	−1.44144	+	0.531810i
$330$		0			0
$331$	0.921958	+	1.59688i	0.0506754	+	0.0877724i	0.890250	−	0.455471i	$-0.150529\pi$
$331$	0.921958	+	1.59688i	0.0506754	+	0.0877724i	−0.839575	+	0.543244i	$0.817196\pi$
$332$		0			0
$333$	−7.82264	−	4.51640i	−0.428678	−	0.247497i
$334$		0			0
$335$	3.20342			0.175021
$336$		0			0
$337$	−11.9821			−0.652706			−0.326353	−	0.945248i	$-0.605820\pi$
$337$	−11.9821			−0.652706			−0.326353	+	0.945248i	$0.605820\pi$
$338$		0			0
$339$	−23.9415	−	13.8226i	−1.30032	−	0.750743i
$340$		0			0
$341$	−15.3226	−	26.5396i	−0.829767	−	1.43720i
$342$		0			0
$343$	−9.04831	+	16.1595i	−0.488563	+	0.872529i
$344$		0			0
$345$	−5.94809	−	10.3024i	−0.320234	−	0.554662i
$346$		0			0
$347$	−7.73830	+	13.4031i	−0.415413	+	0.719517i	−0.995472	−	0.0950577i	$-0.969696\pi$
$347$	−7.73830	+	13.4031i	−0.415413	+	0.719517i	0.580058	+	0.814575i	$0.303030\pi$
$348$		0			0
$349$	−4.87827			−0.261128			−0.130564	−	0.991440i	$-0.541679\pi$
$349$	−4.87827			−0.261128			−0.130564	+	0.991440i	$0.541679\pi$
$350$		0			0
$351$			20.4123i			1.08953i
$352$		0			0
$353$	16.0717	+	9.27902i	0.855412	+	0.493873i	0.862473	−	0.506102i	$-0.168914\pi$
$353$	16.0717	+	9.27902i	0.855412	+	0.493873i	−0.00706092	+	0.999975i	$0.502248\pi$
$354$		0			0
$355$	2.50816	−	1.44809i	0.133119	−	0.0768565i
$356$		0			0
$357$	−5.94809	+	2.19452i	−0.314806	+	0.116146i
$358$		0			0
$359$	20.9958	−	12.1219i	1.10812	−	0.639771i	0.169776	−	0.985483i	$-0.445696\pi$
$359$	20.9958	−	12.1219i	1.10812	−	0.639771i	0.938341	+	0.345711i	$0.112362\pi$
$360$		0			0
$361$	4.99105	−	8.64475i	0.262687	−	0.454987i
$362$		0			0
$363$		−	15.9129i		−	0.835210i
$364$		0			0
$365$			3.09155i			0.161819i
$366$		0			0
$367$	−3.00565	+	5.20593i	−0.156893	+	0.271747i	−0.933747	−	0.357934i	$-0.883481\pi$
$367$	−3.00565	+	5.20593i	−0.156893	+	0.271747i	0.776853	+	0.629681i	$0.216815\pi$
$368$		0			0
$369$	19.6920	−	11.3692i	1.02512	−	0.591855i
$370$		0			0
$371$	19.7273	−	23.7205i	1.02419	−	1.23151i
$372$		0			0
$373$	−31.6400	+	18.2674i	−1.63826	+	0.945850i	−0.656827	+	0.754041i	$0.728102\pi$
$373$	−31.6400	+	18.2674i	−1.63826	+	0.945850i	−0.981432	+	0.191808i	$0.938565\pi$
$374$		0			0
$375$	11.7023	+	6.75634i	0.604305	+	0.348896i
$376$		0			0
$377$		−	14.0181i		−	0.721970i
$378$		0			0
$379$	4.24021			0.217805			0.108903	−	0.994052i	$-0.465266\pi$
$379$	4.24021			0.217805			0.108903	+	0.994052i	$0.465266\pi$
$380$		0			0
$381$	7.31429	−	12.6687i	0.374722	−	0.649038i
$382$		0			0
$383$	1.74251	+	3.01811i	0.0890380	+	0.154218i	0.907105	−	0.420905i	$-0.138287\pi$
$383$	1.74251	+	3.01811i	0.0890380	+	0.154218i	−0.818067	+	0.575123i	$0.804954\pi$
$384$		0			0
$385$	−0.879780	+	5.12071i	−0.0448378	+	0.260975i
$386$		0			0
$387$	−18.0656	−	31.2906i	−0.918327	−	1.59059i
$388$		0			0
$389$	19.4731	+	11.2428i	0.987328	+	0.570034i	0.904474	−	0.426528i	$-0.140263\pi$
$389$	19.4731	+	11.2428i	0.987328	+	0.570034i	0.0828533	+	0.996562i	$0.473597\pi$
$390$		0			0
$391$	7.18889			0.363558
$392$		0			0
$393$	−12.9821			−0.654860
$394$		0			0
$395$	0.765654	+	0.442051i	0.0385242	+	0.0222420i
$396$		0			0
$397$	−1.55563	−	2.69444i	−0.0780750	−	0.135230i	0.824344	−	0.566089i	$-0.191544\pi$
$397$	−1.55563	−	2.69444i	−0.0780750	−	0.135230i	−0.902419	+	0.430859i	$0.858211\pi$
$398$		0			0
$399$	6.91270	−	40.2349i	0.346068	−	2.01427i
$400$		0			0
$401$	16.3693	+	28.3525i	0.817445	+	1.41586i	0.907559	+	0.419925i	$0.137944\pi$
$401$	16.3693	+	28.3525i	0.817445	+	1.41586i	−0.0901141	+	0.995931i	$0.528723\pi$
$402$		0			0
$403$	−12.1089	+	20.9731i	−0.603185	+	1.04475i
$404$		0			0
$405$	−1.23180			−0.0612085
$406$		0			0
$407$		−	7.04668i		−	0.349291i
$408$		0			0
$409$	1.63068	+	0.941473i	0.0806319	+	0.0465528i	0.539774	−	0.841810i	$-0.318510\pi$
$409$	1.63068	+	0.941473i	0.0806319	+	0.0465528i	−0.459142	+	0.888363i	$0.651843\pi$
$410$		0			0
$411$	3.59444	−	2.07525i	0.177301	−	0.102365i
$412$		0			0
$413$	−6.02938	+	7.24987i	−0.296686	+	0.356743i
$414$		0			0
$415$	−4.61276	+	2.66318i	−0.226432	+	0.130730i
$416$		0			0
$417$	0.616498	−	1.06781i	0.0301900	−	0.0522907i
$418$		0			0
$419$		−	12.1626i		−	0.594181i	−0.954849	−	0.297090i	$-0.903984\pi$
$419$		−	12.1626i		−	0.594181i	0.954849	−	0.297090i	$-0.0960163\pi$
$420$		0			0
$421$			4.82360i			0.235088i	0.993068	+	0.117544i	$0.0375021\pi$
$421$			4.82360i			0.235088i	−0.993068	+	0.117544i	$0.962498\pi$
$422$		0			0
$423$	27.4656	−	47.5717i	1.33542	−	2.31302i
$424$		0			0
$425$	−3.45152	+	1.99274i	−0.167423	+	0.0966619i
$426$		0			0
$427$	−8.51441	+	3.14135i	−0.412041	+	0.152020i
$428$		0			0
$429$	−32.4679	+	18.7454i	−1.56757	+	0.905035i
$430$		0			0
$431$	−11.9940	−	6.92475i	−0.577731	−	0.333553i	0.182500	−	0.983206i	$-0.441581\pi$
$431$	−11.9940	−	6.92475i	−0.577731	−	0.333553i	−0.760231	+	0.649653i	$0.774914\pi$
$432$		0			0
$433$		−	3.89660i		−	0.187258i	−0.995607	−	0.0936292i	$-0.970153\pi$
$433$		−	3.89660i		−	0.187258i	0.995607	−	0.0936292i	$-0.0298468\pi$
$434$		0			0
$435$	6.03221			0.289222
$436$		0			0
$437$	−23.1453	+	40.0888i	−1.10719	+	1.91771i
$438$		0			0
$439$	−17.2191	−	29.8244i	−0.821823	−	1.42344i	−0.904323	−	0.426848i	$-0.859624\pi$
$439$	−17.2191	−	29.8244i	−0.821823	−	1.42344i	0.0825007	−	0.996591i	$-0.473709\pi$
$440$		0			0
$441$	−6.65423	−	35.8941i	−0.316868	−	1.70924i
$442$		0			0
$443$	−14.8228	−	25.6738i	−0.704253	−	1.21980i	−0.966961	−	0.254926i	$-0.917949\pi$
$443$	−14.8228	−	25.6738i	−0.704253	−	1.21980i	0.262708	−	0.964875i	$-0.415384\pi$
$444$		0			0
$445$	−2.17213	−	1.25408i	−0.102969	−	0.0594491i
$446$		0			0
$447$	64.4483			3.04830
$448$		0			0
$449$	20.8425			0.983617			0.491808	−	0.870703i	$-0.336336\pi$
$449$	20.8425			0.983617			0.491808	+	0.870703i	$0.336336\pi$
$450$		0			0
$451$	15.3621	+	8.86932i	0.723374	+	0.417640i
$452$		0			0
$453$	4.23240	+	7.33073i	0.198855	+	0.344428i
$454$		0			0
$455$	3.85216	−	1.42123i	0.180592	−	0.0666285i
$456$		0			0
$457$	10.8835	+	18.8508i	0.509109	+	0.881802i	0.999944	+	0.0105500i	$0.00335824\pi$
$457$	10.8835	+	18.8508i	0.509109	+	0.881802i	−0.490836	+	0.871252i	$0.663308\pi$
$458$		0			0
$459$	2.65401	−	4.59688i	0.123879	−	0.214564i
$460$		0			0
$461$	5.41348			0.252131			0.126065	−	0.992022i	$-0.459765\pi$
$461$	5.41348			0.252131			0.126065	+	0.992022i	$0.459765\pi$
$462$		0			0
$463$		−	15.6274i		−	0.726266i	−0.931737	−	0.363133i	$-0.881707\pi$
$463$		−	15.6274i		−	0.726266i	0.931737	−	0.363133i	$-0.118293\pi$
$464$		0			0
$465$	−9.02506	−	5.21062i	−0.418527	−	0.241637i
$466$		0			0
$467$	−9.99379	+	5.76992i	−0.462458	+	0.267000i	−0.713077	−	0.701086i	$-0.752699\pi$
$467$	−9.99379	+	5.76992i	−0.462458	+	0.267000i	0.250619	+	0.968086i	$0.419366\pi$
$468$		0			0
$469$	−13.5000	−	11.2273i	−0.623372	−	0.518430i
$470$		0			0
$471$	−38.3008	+	22.1130i	−1.76481	+	1.01891i
$472$		0			0
$473$	14.0934	−	24.4104i	0.648014	−	1.12239i
$474$		0			0
$475$		−	25.6632i		−	1.17751i
$476$		0			0
$477$			60.8124i			2.78441i
$478$		0			0
$479$	−13.4788	+	23.3460i	−0.615862	+	1.06671i	0.374370	+	0.927279i	$0.377859\pi$
$479$	−13.4788	+	23.3460i	−0.615862	+	1.06671i	−0.990233	+	0.139426i	$0.955474\pi$
$480$		0			0
$481$	−4.82264	+	2.78435i	−0.219893	+	0.126956i
$482$		0			0
$483$	−11.0410	+	64.2637i	−0.502385	+	2.92410i
$484$		0			0
$485$	5.92303	−	3.41966i	0.268951	−	0.155279i
$486$		0			0
$487$	31.0001	+	17.8979i	1.40475	+	0.811031i	0.994875	−	0.101112i	$-0.0322401\pi$
$487$	31.0001	+	17.8979i	1.40475	+	0.811031i	0.409872	+	0.912143i	$0.365573\pi$
$488$		0			0
$489$			28.9504i			1.30918i
$490$		0			0
$491$	31.0260			1.40018			0.700092	−	0.714052i	$-0.253142\pi$
$491$	31.0260			1.40018			0.700092	+	0.714052i	$0.253142\pi$
$492$		0			0
$493$	−1.82264	+	3.15690i	−0.0820875	+	0.142180i
$494$		0			0
$495$	−5.12071	−	8.86932i	−0.230159	−	0.398646i
$496$		0			0
$497$	−15.6453	−	2.68799i	−0.701787	−	0.120573i
$498$		0			0
$499$	−1.29451	−	2.24216i	−0.0579502	−	0.100373i	0.835595	−	0.549346i	$-0.185123\pi$
$499$	−1.29451	−	2.24216i	−0.0579502	−	0.100373i	−0.893545	+	0.448973i	$0.851790\pi$
$500$		0			0
$501$	−36.6184	−	21.1417i	−1.63599	−	0.944540i
$502$		0			0
$503$	10.6739			0.475926			0.237963	−	0.971274i	$-0.423520\pi$
$503$	10.6739			0.475926			0.237963	+	0.971274i	$0.423520\pi$
$504$		0			0
$505$	−3.12917			−0.139246
$506$		0			0
$507$	−6.61055	−	3.81660i	−0.293585	−	0.169501i
$508$		0			0
$509$	−15.2413	−	26.3988i	−0.675561	−	1.17011i	−0.976305	−	0.216401i	$-0.930568\pi$
$509$	−15.2413	−	26.3988i	−0.675561	−	1.17011i	0.300744	−	0.953705i	$-0.402765\pi$
$510$		0			0
$511$	10.8353	−	13.0286i	0.479323	−	0.576350i
$512$		0			0
$513$	17.0896	+	29.6001i	0.754526	+	1.30688i
$514$		0			0
$515$	−1.60171	+	2.77424i	−0.0705797	+	0.122248i
$516$		0			0
$517$	42.8529			1.88467
$518$		0			0
$519$			46.2260i			2.02909i
$520$		0			0
$521$	−12.0519	−	6.95817i	−0.528004	−	0.304843i	0.212199	−	0.977226i	$-0.431937\pi$
$521$	−12.0519	−	6.95817i	−0.528004	−	0.304843i	−0.740203	+	0.672383i	$0.765271\pi$
$522$		0			0
$523$	24.0564	−	13.8889i	1.05191	−	0.607321i	0.128727	−	0.991680i	$-0.458911\pi$
$523$	24.0564	−	13.8889i	1.05191	−	0.607321i	0.923184	+	0.384359i	$0.125578\pi$
$524$		0			0
$525$	−12.5127	−	33.9148i	−0.546098	−	1.48016i
$526$		0			0
$527$	5.45387	−	3.14879i	0.237574	−	0.137163i
$528$		0			0
$529$	25.4679	−	44.1117i	1.10730	−	1.91790i
$530$		0			0
$531$		−	18.5865i		−	0.806586i
$532$		0			0
$533$		−	14.0181i		−	0.607192i
$534$		0			0
$535$	1.38546	−	2.39969i	0.0598987	−	0.103748i
$536$		0			0
$537$	−42.1920	+	24.3595i	−1.82072	+	1.05119i
$538$		0			0
$539$	21.6546	−	18.4965i	0.932732	−	0.796700i
$540$		0			0
$541$	24.4627	−	14.1235i	1.05173	−	0.607218i	0.128599	−	0.991697i	$-0.458952\pi$
$541$	24.4627	−	14.1235i	1.05173	−	0.607218i	0.923134	+	0.384478i	$0.125619\pi$
$542$		0			0
$543$	−34.4302	−	19.8783i	−1.47754	−	0.853058i
$544$		0			0
$545$		−	1.85194i		−	0.0793283i
$546$		0			0
$547$	−26.5150			−1.13370			−0.566850	−	0.823821i	$-0.691838\pi$
$547$	−26.5150			−1.13370			−0.566850	+	0.823821i	$0.691838\pi$
$548$		0			0
$549$	8.94437	−	15.4921i	0.381736	−	0.661187i
$550$		0			0
$551$	−11.7363	−	20.3279i	−0.499983	−	0.865996i
$552$		0			0
$553$	−1.67736	−	4.54637i	−0.0713287	−	0.193331i
$554$		0			0
$555$	−1.19815	−	2.07525i	−0.0508586	−	0.0880896i
$556$		0			0
$557$	−4.12545	−	2.38183i	−0.174801	−	0.100921i	0.410047	−	0.912065i	$-0.365512\pi$
$557$	−4.12545	−	2.38183i	−0.174801	−	0.100921i	−0.584848	+	0.811143i	$0.698846\pi$
$558$		0			0
$559$	−22.2748			−0.942124
$560$		0			0
$561$	9.74910			0.411607
$562$		0			0
$563$	−21.5038	−	12.4152i	−0.906275	−	0.523238i	−0.0270443	−	0.999634i	$-0.508610\pi$
$563$	−21.5038	−	12.4152i	−0.906275	−	0.523238i	−0.879231	+	0.476396i	$0.841943\pi$
$564$		0			0
$565$	−2.32787	−	4.03199i	−0.0979342	−	0.169627i
$566$		0			0
$567$	5.19110	+	4.31720i	0.218006	+	0.181305i
$568$		0			0
$569$	−11.5467	−	19.9994i	−0.484062	−	0.838420i	0.515770	−	0.856727i	$-0.327506\pi$
$569$	−11.5467	−	19.9994i	−0.484062	−	0.838420i	−0.999832	+	0.0183067i	$0.994172\pi$
$570$		0			0
$571$	−17.5317	+	30.3658i	−0.733679	+	1.27077i	0.221621	+	0.975133i	$0.428865\pi$
$571$	−17.5317	+	30.3658i	−0.733679	+	1.27077i	−0.955300	+	0.295637i	$0.904468\pi$
$572$		0			0
$573$	46.2906			1.93382
$574$		0			0
$575$			40.9895i			1.70938i
$576$		0			0
$577$	1.50000	+	0.866025i	0.0624458	+	0.0360531i	0.530898	−	0.847436i	$-0.321855\pi$
$577$	1.50000	+	0.866025i	0.0624458	+	0.0360531i	−0.468452	+	0.883489i	$0.655188\pi$
$578$		0			0
$579$	−20.3915	+	11.7730i	−0.847442	+	0.489271i
$580$		0			0
$581$	28.7733	+	4.94349i	1.19372	+	0.205090i
$582$		0			0
$583$	−41.0852	+	23.7205i	−1.70157	+	0.982404i
$584$		0			0
$585$	−4.04668	+	7.00906i	−0.167310	+	0.289789i
$586$		0			0
$587$		−	1.76820i		−	0.0729815i	−0.999334	−	0.0364908i	$-0.988382\pi$
$587$		−	1.76820i		−	0.0729815i	0.999334	−	0.0364908i	$-0.0116179\pi$
$588$		0			0
$589$			40.5513i			1.67089i
$590$		0			0
$591$	−17.0733	+	29.5717i	−0.702300	+	1.21642i
$592$		0			0
$593$	−12.8641	+	7.42709i	−0.528265	+	0.304994i	−0.740310	−	0.672266i	$-0.765321\pi$
$593$	−12.8641	+	7.42709i	−0.528265	+	0.304994i	0.212045	+	0.977260i	$0.431988\pi$
$594$		0			0
$595$	−1.05230	−	0.180794i	−0.0431401	−	0.00741184i
$596$		0			0
$597$	−0.349493	+	0.201780i	−0.0143038	+	0.00825830i
$598$		0			0
$599$	23.2149	+	13.4031i	0.948535	+	0.547637i	0.892625	−	0.450799i	$-0.148861\pi$
$599$	23.2149	+	13.4031i	0.948535	+	0.547637i	0.0559092	+	0.998436i	$0.482194\pi$
$600$		0			0
$601$			21.0972i			0.860573i	0.902692	+	0.430287i	$0.141588\pi$
$601$			21.0972i			0.860573i	−0.902692	+	0.430287i	$0.858412\pi$
$602$		0			0
$603$	34.6100			1.40943
$604$		0			0
$605$	1.33994	−	2.32085i	0.0544764	−	0.0943559i
$606$		0			0
$607$	−14.0676	−	24.3658i	−0.570987	−	0.988978i	−0.996465	−	0.0840091i	$-0.973228\pi$
$607$	−14.0676	−	24.3658i	−0.570987	−	0.988978i	0.425478	−	0.904969i	$-0.360106\pi$
$608$		0			0
$609$	−25.4212	−	21.1417i	−1.03012	−	0.856703i
$610$		0			0
$611$	−16.9325	−	29.3279i	−0.685014	−	1.18648i
$612$		0			0
$613$	23.3122	+	13.4593i	0.941570	+	0.543616i	0.890452	−	0.455077i	$-0.150388\pi$
$613$	23.3122	+	13.4593i	0.941570	+	0.543616i	0.0511179	+	0.998693i	$0.483722\pi$
$614$		0			0
$615$	6.03221			0.243242
$616$		0			0
$617$	−25.5519			−1.02868			−0.514341	−	0.857586i	$-0.671963\pi$
$617$	−25.5519			−1.02868			−0.514341	+	0.857586i	$0.671963\pi$
$618$		0			0
$619$	0.114838	+	0.0663020i	0.00461575	+	0.00266490i	0.502306	−	0.864690i	$-0.332485\pi$
$619$	0.114838	+	0.0663020i	0.00461575	+	0.00266490i	−0.497690	+	0.867355i	$0.665818\pi$
$620$		0			0
$621$	−27.2958	−	47.2777i	−1.09534	−	1.89719i
$622$		0			0
$623$	4.75861	+	12.8979i	0.190650	+	0.516743i
$624$		0			0
$625$	−10.7797	−	18.6710i	−0.431187	−	0.746838i
$626$		0			0
$627$	−31.3881	+	54.3658i	−1.25352	+	2.17116i
$628$		0			0
$629$	1.44809			0.0577390
$630$		0			0
$631$		−	4.43018i		−	0.176363i	−0.996104	−	0.0881814i	$-0.971894\pi$
$631$		−	4.43018i		−	0.176363i	0.996104	−	0.0881814i	$-0.0281055\pi$
$632$		0			0
$633$	48.1400	+	27.7937i	1.91340	+	1.10470i
$634$		0			0
$635$	2.13354	−	1.23180i	0.0846668	−	0.0488824i
$636$		0			0
$637$	−21.2151	−	7.51159i	−0.840573	−	0.297620i
$638$		0			0
$639$	27.0984	−	15.6453i	1.07200	−	0.618918i
$640$		0			0
$641$	6.05191	−	10.4822i	0.239036	−	0.414023i	−0.721402	−	0.692517i	$-0.756502\pi$
$641$	6.05191	−	10.4822i	0.239036	−	0.414023i	0.960438	+	0.278494i	$0.0898352\pi$
$642$		0			0
$643$			11.6274i			0.458539i	0.973363	+	0.229269i	$0.0736337\pi$
$643$			11.6274i			0.458539i	−0.973363	+	0.229269i	$0.926366\pi$
$644$		0			0
$645$		−	9.58519i		−	0.377416i
$646$		0			0
$647$	−7.44660	+	12.8979i	−0.292756	+	0.507068i	−0.974460	−	0.224559i	$-0.927906\pi$
$647$	−7.44660	+	12.8979i	−0.292756	+	0.507068i	0.681704	+	0.731628i	$0.261239\pi$
$648$		0			0
$649$	12.5571	−	7.24987i	0.492911	−	0.284582i
$650$		0			0
$651$	19.7717	+	53.5899i	0.774914	+	2.10035i
$652$		0			0
$653$	28.0986	−	16.2227i	1.09958	−	0.634845i	0.163472	−	0.986548i	$-0.447731\pi$
$653$	28.0986	−	16.2227i	1.09958	−	0.634845i	0.936111	+	0.351704i	$0.114397\pi$
$654$		0			0
$655$	−1.89340	−	1.09316i	−0.0739814	−	0.0427132i
$656$		0			0
$657$			33.4014i			1.30311i
$658$		0			0
$659$	35.9695			1.40117			0.700587	−	0.713567i	$-0.252922\pi$
$659$	35.9695			1.40117			0.700587	+	0.713567i	$0.252922\pi$
$660$		0			0
$661$	12.2670	−	21.2471i	0.477131	−	0.826415i	−0.522525	−	0.852624i	$-0.675010\pi$
$661$	12.2670	−	21.2471i	0.477131	−	0.826415i	0.999657	+	0.0262083i	$0.00834332\pi$
$662$		0			0
$663$	−3.85216	−	6.67213i	−0.149605	−	0.259124i
$664$		0			0
$665$	4.39618	−	5.28607i	0.170476	−	0.204985i
$666$		0			0
$667$	18.7454	+	32.4679i	0.725823	+	1.25716i
$668$		0			0
$669$	37.6920	+	21.7615i	1.45726	+	0.841347i
$670$		0			0
$671$	13.9554			0.538741
$672$		0			0
$673$	−36.8425			−1.42017			−0.710086	−	0.704115i	$-0.751344\pi$
$673$	−36.8425			−1.42017			−0.710086	+	0.704115i	$0.751344\pi$
$674$		0			0
$675$	26.2104	+	15.1326i	1.00884	+	0.582454i
$676$		0			0
$677$	−20.8399	−	36.0958i	−0.800944	−	1.38728i	−0.918995	−	0.394268i	$-0.870998\pi$
$677$	−20.8399	−	36.0958i	−0.800944	−	1.38728i	0.118051	−	0.993007i	$-0.462335\pi$
$678$		0			0
$679$	−36.9464	−	6.34770i	−1.41787	−	0.243602i
$680$		0			0
$681$	30.3604	+	52.5857i	1.16341	+	2.01509i
$682$		0			0
$683$	21.8319	−	37.8139i	0.835373	−	1.44691i	−0.0583533	−	0.998296i	$-0.518585\pi$
$683$	21.8319	−	37.8139i	0.835373	−	1.44691i	0.893726	−	0.448613i	$-0.148082\pi$
$684$		0			0
$685$	0.698986			0.0267069
$686$		0			0
$687$			35.0109i			1.33575i
$688$		0			0
$689$	32.4679	+	18.7454i	1.23693	+	0.714141i
$690$		0			0
$691$	14.2629	−	8.23471i	0.542588	−	0.313263i	−0.203539	−	0.979067i	$-0.565244\pi$
$691$	14.2629	−	8.23471i	0.542588	−	0.313263i	0.746127	+	0.665804i	$0.231911\pi$
$692$		0			0
$693$	−9.50523	+	55.3246i	−0.361074	+	2.10161i
$694$		0			0
$695$	0.179829	−	0.103824i	0.00682130	−	0.00393828i
$696$		0			0
$697$	−1.82264	+	3.15690i	−0.0690374	+	0.119576i
$698$		0			0
$699$		−	19.0467i		−	0.720412i
$700$		0			0
$701$			7.85521i			0.296687i	0.988936	+	0.148344i	$0.0473941\pi$
$701$			7.85521i			0.296687i	−0.988936	+	0.148344i	$0.952606\pi$
$702$		0			0
$703$	−4.66225	+	8.07525i	−0.175840	+	0.304564i
$704$		0			0
$705$	12.6202	−	7.28629i	0.475305	−	0.274417i
$706$		0			0
$707$	13.1871	+	10.9671i	0.495952	+	0.412461i
$708$		0			0
$709$	−17.1453	+	9.89883i	−0.643904	+	0.371758i	−0.786117	−	0.618078i	$-0.787912\pi$
$709$	−17.1453	+	9.89883i	−0.643904	+	0.371758i	0.142213	+	0.989836i	$0.454578\pi$
$710$		0			0
$711$	8.27220	+	4.77596i	0.310232	+	0.179112i
$712$		0			0
$713$		−	64.7690i		−	2.42562i
$714$		0			0
$715$	−6.31381			−0.236123
$716$		0			0
$717$	17.9731	−	31.1304i	0.671219	−	1.16259i
$718$		0			0
$719$	−18.6750	−	32.3460i	−0.696458	−	1.20630i	−0.969687	−	0.244352i	$-0.921425\pi$
$719$	−18.6750	−	32.3460i	−0.696458	−	1.20630i	0.273228	−	0.961949i	$-0.411909\pi$
$720$		0			0
$721$	16.4731	−	6.07768i	0.613492	−	0.226345i
$722$		0			0
$723$	28.3720	+	49.1418i	1.05517	+	1.82760i
$724$		0			0
$725$	−18.0000	−	10.3923i	−0.668503	−	0.385961i
$726$		0			0
$727$	−14.2579			−0.528796			−0.264398	−	0.964414i	$-0.585173\pi$
$727$	−14.2579			−0.528796			−0.264398	+	0.964414i	$0.585173\pi$
$728$		0			0
$729$	41.2831			1.52900
$730$		0			0
$731$	5.01632	+	2.89618i	0.185535	+	0.107119i
$732$		0			0
$733$	10.3137	+	17.8638i	0.380945	+	0.659816i	0.991198	−	0.132391i	$-0.0422655\pi$
$733$	10.3137	+	17.8638i	0.380945	+	0.659816i	−0.610253	+	0.792207i	$0.708932\pi$
$734$		0			0
$735$	3.23235	−	9.12917i	0.119227	−	0.336735i
$736$		0			0
$737$	13.5000	+	23.3827i	0.497279	+	0.861312i
$738$		0			0
$739$	20.6233	−	35.7205i	0.758639	−	1.31400i	−0.184906	−	0.982756i	$-0.559198\pi$
$739$	20.6233	−	35.7205i	0.758639	−	1.31400i	0.943545	−	0.331245i	$-0.107469\pi$
$740$		0			0
$741$	49.6095			1.82245
$742$		0			0
$743$		−	40.3944i		−	1.48193i	−0.671546	−	0.740963i	$-0.734369\pi$
$743$		−	40.3944i		−	1.48193i	0.671546	−	0.740963i	$-0.265631\pi$
$744$		0			0
$745$	9.39961	+	5.42687i	0.344375	+	0.198825i
$746$		0			0
$747$	−49.8367	+	28.7733i	−1.82343	+	1.05276i
$748$		0			0
$749$	−14.2491	+	5.25713i	−0.520651	+	0.192091i
$750$		0			0
$751$	4.37056	−	2.52334i	0.159484	−	0.0920780i	−0.418134	−	0.908385i	$-0.637316\pi$
$751$	4.37056	−	2.52334i	0.159484	−	0.0920780i	0.577618	+	0.816307i	$0.303982\pi$
$752$		0			0
$753$	−32.4033	+	56.1242i	−1.18084	+	2.04528i
$754$		0			0
$755$			1.42555i			0.0518812i
$756$		0			0
$757$		−	21.4987i		−	0.781384i	−0.920522	−	0.390692i	$-0.872236\pi$
$757$		−	21.4987i		−	0.781384i	0.920522	−	0.390692i	$-0.127764\pi$
$758$		0			0
$759$	50.1335	−	86.8337i	1.81973	−	3.15186i
$760$		0			0
$761$	46.2118	−	26.6804i	1.67518	−	0.967163i	0.710510	−	0.703687i	$-0.248464\pi$
$761$	46.2118	−	26.6804i	1.67518	−	0.967163i	0.964666	−	0.263476i	$-0.0848691\pi$
$762$		0			0
$763$	−6.49066	+	7.80453i	−0.234978	+	0.282543i
$764$		0			0
$765$	1.82264	−	1.05230i	0.0658976	−	0.0380460i
$766$		0			0
$767$	−9.92339	−	5.72927i	−0.358313	−	0.206872i
$768$		0			0
$769$			27.8017i			1.00255i	0.865287	+	0.501277i	$0.167136\pi$
$769$			27.8017i			1.00255i	−0.865287	+	0.501277i	$0.832864\pi$
$770$		0			0
$771$	22.5975			0.813830
$772$		0			0
$773$	−2.86248	+	4.95795i	−0.102956	+	0.178325i	−0.912901	−	0.408180i	$-0.866163\pi$
$773$	−2.86248	+	4.95795i	−0.102956	+	0.178325i	0.809945	+	0.586506i	$0.199497\pi$
$774$		0			0
$775$	17.9537	+	31.0968i	0.644918	+	1.11703i
$776$		0			0
$777$	−2.22404	+	12.9449i	−0.0797871	+	0.464396i
$778$		0			0
$779$	−11.7363	−	20.3279i	−0.420497	−	0.728321i
$780$		0			0
$781$	21.1400	+	12.2052i	0.756450	+	0.436737i
$782$		0			0
$783$	27.6818			0.989267
$784$		0			0
$785$	−7.44809			−0.265834
$786$		0			0
$787$	−48.3704	−	27.9267i	−1.72422	−	0.995478i	−0.909604	−	0.415476i	$-0.863615\pi$
$787$	−48.3704	−	27.9267i	−1.72422	−	0.995478i	−0.814615	−	0.580002i	$-0.803052\pi$
$788$		0			0
$789$	13.4731	+	23.3362i	0.479657	+	0.830790i
$790$		0			0
$791$	−4.32107	+	25.1505i	−0.153640	+	0.894249i
$792$		0			0
$793$	−5.51418	−	9.55084i	−0.195814	−	0.339160i
$794$		0			0
$795$	−8.06641	+	13.9714i	−0.286086	+	0.495516i
$796$		0			0
$797$	−50.2022			−1.77825			−0.889127	−	0.457660i	$-0.848688\pi$
$797$	−50.2022			−1.77825			−0.889127	+	0.457660i	$0.848688\pi$
$798$		0			0
$799$			8.80624i			0.311542i
$800$		0			0
$801$	−23.4679	−	13.5492i	−0.829198	−	0.478738i
$802$		0			0
$803$	−22.5661	+	13.0286i	−0.796342	+	0.459768i
$804$		0			0
$805$	−7.02162	+	8.44297i	−0.247480	+	0.297576i
$806$		0			0
$807$	−9.84290	+	5.68280i	−0.346486	+	0.200044i
$808$		0			0
$809$	10.0986	−	17.4913i	0.355048	−	0.614961i	−0.632078	−	0.774904i	$-0.717798\pi$
$809$	10.0986	−	17.4913i	0.355048	−	0.614961i	0.987126	+	0.159944i	$0.0511313\pi$
$810$		0			0
$811$			17.4197i			0.611689i	0.952081	+	0.305845i	$0.0989388\pi$
$811$			17.4197i			0.611689i	−0.952081	+	0.305845i	$0.901061\pi$
$812$		0			0
$813$			49.1516i			1.72382i
$814$		0			0
$815$	−2.43776	+	4.22233i	−0.0853911	+	0.147902i
$816$		0			0
$817$	−32.3010	+	18.6490i	−1.13007	+	0.652446i
$818$		0			0
$819$	41.6191	−	15.3551i	1.45429	−	0.536552i
$820$		0			0
$821$	−16.0717	+	9.27902i	−0.560908	+	0.323840i	−0.753510	−	0.657437i	$-0.771641\pi$
$821$	−16.0717	+	9.27902i	−0.560908	+	0.323840i	0.192602	+	0.981277i	$0.438307\pi$
$822$		0			0
$823$	−5.60269	−	3.23471i	−0.195297	−	0.112755i	0.399163	−	0.916880i	$-0.369301\pi$
$823$	−5.60269	−	3.23471i	−0.195297	−	0.112755i	−0.594460	+	0.804125i	$0.702634\pi$
$824$		0			0
$825$			55.5873i			1.93530i
$826$		0			0
$827$	12.0644			0.419521			0.209760	−	0.977753i	$-0.432732\pi$
$827$	12.0644			0.419521			0.209760	+	0.977753i	$0.432732\pi$
$828$		0			0
$829$	18.1075	−	31.3632i	0.628901	−	1.08929i	−0.358872	−	0.933387i	$-0.616838\pi$
$829$	18.1075	−	31.3632i	0.628901	−	1.08929i	0.987773	−	0.155902i	$-0.0498283\pi$
$830$		0			0
$831$	9.35046	+	16.1955i	0.324364	+	0.561815i
$832$		0			0
$833$	3.80101	+	4.45001i	0.131697	+	0.154184i
$834$		0			0
$835$	−3.56046	−	6.16690i	−0.123215	−	0.213414i
$836$		0			0
$837$	−41.4160	−	23.9115i	−1.43155	−	0.826504i
$838$		0			0
$839$	−29.5048			−1.01862			−0.509310	−	0.860583i	$-0.670099\pi$
$839$	−29.5048			−1.01862			−0.509310	+	0.860583i	$0.670099\pi$
$840$		0			0
$841$	9.98954			0.344467
$842$		0			0
$843$	−31.6458	−	18.2707i	−1.08994	−	0.629277i
$844$		0			0
$845$	−0.642753	−	1.11328i	−0.0221114	−	0.0382980i
$846$		0			0
$847$	−13.7810	+	5.08441i	−0.473519	+	0.174703i
$848$		0			0
$849$	−36.5109	−	63.2387i	−1.25305	−	2.17035i
$850$		0			0
$851$	7.44660	−	12.8979i	0.255266	−	0.442134i
$852$		0			0
$853$	43.1793			1.47843			0.739215	−	0.673469i	$-0.235197\pi$
$853$	43.1793			1.47843			0.739215	+	0.673469i	$0.235197\pi$
$854$		0			0
$855$			13.5519i			0.463466i
$856$		0			0
$857$	−28.8477	−	16.6552i	−0.985419	−	0.568932i	−0.0815169	−	0.996672i	$-0.525976\pi$
$857$	−28.8477	−	16.6552i	−0.985419	−	0.568932i	−0.903902	+	0.427740i	$0.859310\pi$
$858$		0			0
$859$	−31.9405	+	18.4409i	−1.08980	+	0.629194i	−0.933522	−	0.358520i	$-0.883281\pi$
$859$	−31.9405	+	18.4409i	−1.08980	+	0.629194i	−0.156274	+	0.987714i	$0.549948\pi$
$860$		0			0
$861$	−25.4212	−	21.1417i	−0.866353	−	0.720506i
$862$		0			0
$863$	13.3380	−	7.70070i	0.454031	−	0.262135i	−0.255500	−	0.966809i	$-0.582240\pi$
$863$	13.3380	−	7.70070i	0.454031	−	0.262135i	0.709531	+	0.704674i	$0.248907\pi$
$864$		0			0
$865$	−3.89245	+	6.74193i	−0.132347	+	0.229232i
$866$		0			0
$867$		−	46.7219i		−	1.58676i
$868$		0			0
$869$			7.45165i			0.252780i
$870$		0			0
$871$	10.6685	−	18.4784i	0.361488	−	0.626116i
$872$		0			0
$873$	63.9930	−	36.9464i	2.16583	−	1.25044i
$874$		0			0
$875$	2.11209	−	12.2933i	0.0714015	−	0.415588i
$876$		0			0
$877$	24.1289	−	13.9308i	0.814774	−	0.470410i	−0.0338367	−	0.999427i	$-0.510773\pi$
$877$	24.1289	−	13.9308i	0.814774	−	0.470410i	0.848611	+	0.529017i	$0.177439\pi$
$878$		0			0
$879$	−19.6858	−	11.3656i	−0.663985	−	0.383352i
$880$		0			0
$881$		−	34.8027i		−	1.17253i	−0.810118	−	0.586267i	$-0.800597\pi$
$881$		−	34.8027i		−	1.17253i	0.810118	−	0.586267i	$-0.199403\pi$
$882$		0			0
$883$	37.4597			1.26062			0.630310	−	0.776344i	$-0.282928\pi$
$883$	37.4597			1.26062			0.630310	+	0.776344i	$0.282928\pi$
$884$		0			0
$885$	2.46539	−	4.27018i	0.0828732	−	0.143541i
$886$		0			0
$887$	19.1439	+	33.1582i	0.642788	+	1.11334i	0.984808	+	0.173649i	$0.0555559\pi$
$887$	19.1439	+	33.1582i	0.642788	+	1.11334i	−0.342019	+	0.939693i	$0.611111\pi$
$888$		0			0
$889$	−13.3085	−	2.28651i	−0.446351	−	0.0766869i
$890$		0			0
$891$	−5.19110	−	8.99126i	−0.173909	−	0.301218i
$892$		0			0
$893$	−49.1080	−	28.3525i	−1.64334	−	0.948780i
$894$		0			0
$895$	−8.20477			−0.274255
$896$		0			0
$897$	−79.2368			−2.64564
$898$		0			0
$899$	28.4424	+	16.4212i	0.948608	+	0.547679i
$900$		0			0
$901$	−4.87455	−	8.44297i	−0.162395	−	0.281276i
$902$		0			0
$903$	−33.5941	+	40.3944i	−1.11794	+	1.34424i
$904$		0			0
$905$	−3.34770	−	5.79838i	−0.111281	−	0.192745i
$906$		0			0
$907$	−4.30520	+	7.45683i	−0.142952	+	0.247600i	−0.928607	−	0.371065i	$-0.878993\pi$
$907$	−4.30520	+	7.45683i	−0.142952	+	0.247600i	0.785655	+	0.618665i	$0.212326\pi$
$908$		0			0
$909$	−33.8079			−1.12134
$910$		0			0
$911$			3.69899i			0.122553i	0.998121	+	0.0612764i	$0.0195171\pi$
$911$			3.69899i			0.122553i	−0.998121	+	0.0612764i	$0.980483\pi$
$912$		0			0
$913$	−38.8787	−	22.4466i	−1.28670	−	0.742875i
$914$		0			0
$915$	4.10987	−	2.37283i	0.135868	−	0.0784435i
$916$		0			0
$917$	4.14798	+	11.2428i	0.136978	+	0.371271i
$918$		0			0
$919$	22.3243	−	12.8889i	0.736411	−	0.425167i	−0.0843521	−	0.996436i	$-0.526882\pi$
$919$	22.3243	−	12.8889i	0.736411	−	0.425167i	0.820763	+	0.571269i	$0.193549\pi$
$920$		0			0
$921$	1.76700	−	3.06054i	0.0582248	−	0.100848i
$922$		0			0
$923$		−	19.2906i		−	0.634956i
$924$		0			0
$925$			8.25669i			0.271478i
$926$		0			0
$927$	−17.3050	+	29.9731i	−0.568371	+	0.984447i
$928$		0			0
$929$	40.7439	−	23.5235i	1.33676	−	0.771781i	0.350437	−	0.936586i	$-0.386033\pi$
$929$	40.7439	−	23.5235i	1.33676	−	0.771781i	0.986326	+	0.164806i	$0.0526997\pi$
$930$		0			0
$931$	−37.0532	+	6.86911i	−1.21437	+	0.225126i
$932$		0			0
$933$	−15.3226	+	8.84653i	−0.501641	+	0.289622i
$934$		0			0
$935$	1.42188	+	0.820922i	0.0465004	+	0.0268470i
$936$		0			0
$937$		−	0.239772i		−	0.00783301i	−0.999992	−	0.00391650i	$-0.998753\pi$
$937$		−	0.239772i		−	0.00783301i	0.999992	−	0.00391650i	$-0.00124666\pi$
$938$		0			0
$939$	−53.2799			−1.73872
$940$		0			0
$941$	−15.7197	+	27.2274i	−0.512448	+	0.887587i	0.487447	+	0.873152i	$0.337928\pi$
$941$	−15.7197	+	27.2274i	−0.512448	+	0.887587i	−0.999896	+	0.0144342i	$0.995405\pi$
$942$		0			0
$943$	18.7454	+	32.4679i	0.610433	+	1.05730i
$944$		0			0
$945$	2.80653	+	7.60692i	0.0912965	+	0.247453i
$946$		0			0
$947$	−25.4314	−	44.0484i	−0.826408	−	1.43138i	−0.900838	−	0.434154i	$-0.857047\pi$
$947$	−25.4314	−	44.0484i	−0.826408	−	1.43138i	0.0744305	−	0.997226i	$-0.476286\pi$
$948$		0			0
$949$	17.8331	+	10.2959i	0.578887	+	0.334220i
$950$		0			0
$951$	21.3579			0.692577
$952$		0			0
$953$	−30.9568			−1.00279			−0.501394	−	0.865219i	$-0.667179\pi$
$953$	−30.9568			−1.00279			−0.501394	+	0.865219i	$0.667179\pi$
$954$		0			0
$955$	6.75135	+	3.89789i	0.218468	+	0.126133i
$956$		0			0
$957$	25.4212	+	44.0309i	0.821752	+	1.42332i
$958$		0			0
$959$	−2.94570	−	2.44980i	−0.0951217	−	0.0791083i
$960$		0			0
$961$	−12.8693	−	22.2903i	−0.415139	−	0.719043i
$962$		0			0
$963$	14.9687	−	25.9265i	0.482358	−	0.835469i
$964$		0			0
$965$	−3.96539			−0.127650
$966$		0			0
$967$		−	26.1867i		−	0.842108i	−0.907035	−	0.421054i	$-0.861660\pi$
$967$		−	26.1867i		−	0.842108i	0.907035	−	0.421054i	$-0.138340\pi$
$968$		0			0
$969$	−11.1721	−	6.45023i	−0.358901	−	0.207211i
$970$		0			0
$971$	−2.98473	+	1.72324i	−0.0957846	+	0.0553013i	−0.547127	−	0.837049i	$-0.684279\pi$
$971$	−2.98473	+	1.72324i	−0.0957846	+	0.0553013i	0.451343	+	0.892351i	$0.350945\pi$
$972$		0			0
$973$	−1.12173	−	0.192722i	−0.0359609	−	0.00617839i
$974$		0			0
$975$	38.0431	−	21.9642i	1.21835	−	0.703417i
$976$		0			0
$977$	−4.87455	+	8.44297i	−0.155951	+	0.270115i	−0.933405	−	0.358825i	$-0.883177\pi$
$977$	−4.87455	+	8.44297i	−0.155951	+	0.270115i	0.777454	+	0.628940i	$0.216511\pi$
$978$		0			0
$979$		−	21.1400i		−	0.675639i
$980$		0			0
$981$		−	20.0085i		−	0.638822i
$982$		0			0
$983$	−21.8319	+	37.8139i	−0.696328	+	1.20608i	0.273403	+	0.961900i	$0.411851\pi$
$983$	−21.8319	+	37.8139i	−0.696328	+	1.20608i	−0.969731	+	0.244176i	$0.921482\pi$
$984$		0			0
$985$	−4.98017	+	2.87530i	−0.158681	+	0.0916148i
$986$		0			0
$987$	−78.7217	−	13.5251i	−2.50574	−	0.430507i
$988$		0			0
$989$	51.5916	−	29.7864i	1.64052	−	0.947153i
$990$		0			0
$991$	−37.7174	−	21.7762i	−1.19813	−	0.691743i	−0.237995	−	0.971266i	$-0.576490\pi$
$991$	−37.7174	−	21.7762i	−1.19813	−	0.691743i	−0.960139	+	0.279524i	$0.909823\pi$
$992$		0			0
$993$			5.28503i			0.167715i
$994$		0			0
$995$	−0.0679634			−0.00215459
$996$		0			0
$997$	−29.3604	+	50.8537i	−0.929852	+	1.61055i	−0.146287	+	0.989242i	$0.546732\pi$
$997$	−29.3604	+	50.8537i	−0.929852	+	1.61055i	−0.783566	+	0.621309i	$0.786601\pi$
$998$		0			0
$999$	−5.49830	−	9.52334i	−0.173959	−	0.301305i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	448.2.q.c.31.6	yes	12
4.3	odd	2	inner	448.2.q.c.31.1	yes	12
7.3	odd	6		3136.2.e.e.1567.12		12
7.4	even	3		3136.2.e.d.1567.2		12
7.5	odd	6		448.2.q.b.159.6	yes	12
8.3	odd	2		448.2.q.b.31.6	yes	12
8.5	even	2		448.2.q.b.31.1	✓	12
28.3	even	6		3136.2.e.e.1567.1		12
28.11	odd	6		3136.2.e.d.1567.11		12
28.19	even	6		448.2.q.b.159.1	yes	12
56.3	even	6		3136.2.e.d.1567.12		12
56.5	odd	6	inner	448.2.q.c.159.1	yes	12
56.11	odd	6		3136.2.e.e.1567.2		12
56.19	even	6	inner	448.2.q.c.159.6	yes	12
56.45	odd	6		3136.2.e.d.1567.1		12
56.53	even	6		3136.2.e.e.1567.11		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
448.2.q.b.31.1	✓	12	8.5	even	2
448.2.q.b.31.6	yes	12	8.3	odd	2
448.2.q.b.159.1	yes	12	28.19	even	6
448.2.q.b.159.6	yes	12	7.5	odd	6
448.2.q.c.31.1	yes	12	4.3	odd	2	inner
448.2.q.c.31.6	yes	12	1.1	even	1	trivial
448.2.q.c.159.1	yes	12	56.5	odd	6	inner
448.2.q.c.159.6	yes	12	56.19	even	6	inner
3136.2.e.d.1567.1		12	56.45	odd	6
3136.2.e.d.1567.2		12	7.4	even	3
3136.2.e.d.1567.11		12	28.11	odd	6
3136.2.e.d.1567.12		12	56.3	even	6
3136.2.e.e.1567.1		12	28.3	even	6
3136.2.e.e.1567.2		12	56.11	odd	6
3136.2.e.e.1567.11		12	56.53	even	6
3136.2.e.e.1567.12		12	7.3	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:	\( N \)	\(=\)	\( 448 = 2^{6} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	448.q (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(2.48220 + 1.43310i) q^{3} +(0.241348 + 0.418027i) q^{5} +(0.447998 - 2.60755i) q^{7} +(2.60755 + 4.51640i) q^{9} +O(q^{10})\)	\(q+(2.48220 + 1.43310i) q^{3} +(0.241348 + 0.418027i) q^{5} +(0.447998 - 2.60755i) q^{7} +(2.60755 + 4.51640i) q^{9} +(-2.03420 + 3.52334i) q^{11} +3.21509 q^{13} +1.38350i q^{15} +(-0.724044 - 0.418027i) q^{17} +(4.66225 - 2.69175i) q^{19} +(4.84889 - 5.83043i) q^{21} +(-7.44660 + 4.29930i) q^{23} +(2.38350 - 4.12835i) q^{25} +6.34889i q^{27} -4.36010i q^{29} +(-3.76625 + 6.52334i) q^{31} +(-10.0986 + 5.83043i) q^{33} +(1.19815 - 0.442051i) q^{35} +(-1.50000 + 0.866025i) q^{37} +(7.98050 + 4.60755i) q^{39} -4.36010i q^{41} -6.92820 q^{43} +(-1.25865 + 2.18005i) q^{45} +(-5.26655 - 9.12194i) q^{47} +(-6.59859 - 2.33635i) q^{49} +(-1.19815 - 2.07525i) q^{51} +(10.0986 + 5.83043i) q^{53} -1.96380 q^{55} +15.4302 q^{57} +(-3.08650 - 1.78199i) q^{59} +(-1.71509 - 2.97063i) q^{61} +(12.9449 - 4.77596i) q^{63} +(0.775956 + 1.34400i) q^{65} +(3.31825 - 5.74739i) q^{67} -24.6453 q^{69} -6.00000i q^{71} +(5.54668 + 3.20238i) q^{73} +(11.8327 - 6.83159i) q^{75} +(8.27596 + 6.88273i) q^{77} +(1.58620 - 0.915795i) q^{79} +(-1.27596 + 2.21002i) q^{81} +11.0346i q^{83} -0.403560i q^{85} +(6.24845 - 10.8226i) q^{87} +(-4.50000 + 2.59808i) q^{89} +(1.44036 - 8.38350i) q^{91} +(-18.6972 + 10.7948i) q^{93} +(2.25045 + 1.29930i) q^{95} -14.1690i q^{97} -21.2171 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 6 q^{5} + 4 q^{9}+O(q^{10}) \) 12 * q + 6 * q^5 + 4 * q^9	\( 12 q + 6 q^{5} + 4 q^{9} - 16 q^{13} - 18 q^{17} + 34 q^{21} - 8 q^{25} - 30 q^{33} - 18 q^{37} - 12 q^{45} + 12 q^{49} + 30 q^{53} + 76 q^{57} + 34 q^{61} - 132 q^{69} - 6 q^{73} + 90 q^{77} - 6 q^{81} - 54 q^{89} - 42 q^{93}+O(q^{100}) \) 12 * q + 6 * q^5 + 4 * q^9 - 16 * q^13 - 18 * q^17 + 34 * q^21 - 8 * q^25 - 30 * q^33 - 18 * q^37 - 12 * q^45 + 12 * q^49 + 30 * q^53 + 76 * q^57 + 34 * q^61 - 132 * q^69 - 6 * q^73 + 90 * q^77 - 6 * q^81 - 54 * q^89 - 42 * q^93

Introduction

L-functions

Modular forms

Varieties

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Representations

Groups

Database

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