LMFDB - Embedded newform 224.2.i.a.193.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [224,2,Mod(65,224)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(224, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("224.65");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 224 = 2^{5} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	224.i (of order $3$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$1.78864900528$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(\zeta_{3})$
Coefficient field:	$\Q(\sqrt{2}, \sqrt{-3})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} + 2x^{2} + 4 $ x^4 + 2*x^2 + 4
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			193.2
Root			$0.707107 - 1.22474i$ of defining polynomial
Character	$\chi$	$=$	224.193
Dual form			224.2.i.a.65.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.207107 - 0.358719i) q^{3} +(0.914214 + 1.58346i) q^{5} +(-1.00000 + 2.44949i) q^{7} +(1.41421 + 2.44949i) q^{9} +O(q^{10})$	\(q+(0.207107 - 0.358719i) q^{3} +(0.914214 + 1.58346i) q^{5} +(-1.00000 + 2.44949i) q^{7} +(1.41421 + 2.44949i) q^{9} +(1.20711 - 2.09077i) q^{11} +2.82843 q^{13} +0.757359 q^{15} +(0.0857864 - 0.148586i) q^{17} +(-3.20711 - 5.55487i) q^{19} +(0.671573 + 0.866025i) q^{21} +(2.62132 + 4.54026i) q^{23} +(0.828427 - 1.43488i) q^{25} +2.41421 q^{27} -2.82843 q^{29} +(-2.79289 + 4.83743i) q^{31} +(-0.500000 - 0.866025i) q^{33} +(-4.79289 + 0.655892i) q^{35} +(-4.32843 - 7.49706i) q^{37} +(0.585786 - 1.01461i) q^{39} -6.82843 q^{41} +9.65685 q^{43} +(-2.58579 + 4.47871i) q^{45} +(-5.20711 - 9.01897i) q^{47} +(-5.00000 - 4.89898i) q^{49} +(-0.0355339 - 0.0615465i) q^{51} +(0.500000 - 0.866025i) q^{53} +4.41421 q^{55} -2.65685 q^{57} +(-5.44975 + 9.43924i) q^{59} +(-4.32843 - 7.49706i) q^{61} +(-7.41421 + 1.01461i) q^{63} +(2.58579 + 4.47871i) q^{65} +(1.37868 - 2.38794i) q^{67} +2.17157 q^{69} +13.6569 q^{71} +(7.32843 - 12.6932i) q^{73} +(-0.343146 - 0.594346i) q^{75} +(3.91421 + 5.04757i) q^{77} +(-3.03553 - 5.25770i) q^{79} +(-3.74264 + 6.48244i) q^{81} -7.31371 q^{83} +0.313708 q^{85} +(-0.585786 + 1.01461i) q^{87} +(4.50000 + 7.79423i) q^{89} +(-2.82843 + 6.92820i) q^{91} +(1.15685 + 2.00373i) q^{93} +(5.86396 - 10.1567i) q^{95} -1.17157 q^{97} +6.82843 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 2 q^{3} - 2 q^{5} - 4 q^{7}+O(q^{10}) $ 4 * q - 2 * q^3 - 2 * q^5 - 4 * q^7	$ 4 q - 2 q^{3} - 2 q^{5} - 4 q^{7} + 2 q^{11} + 20 q^{15} + 6 q^{17} - 10 q^{19} + 14 q^{21} + 2 q^{23} - 8 q^{25} + 4 q^{27} - 14 q^{31} - 2 q^{33} - 22 q^{35} - 6 q^{37} + 8 q^{39} - 16 q^{41} + 16 q^{43} - 16 q^{45} - 18 q^{47} - 20 q^{49} + 14 q^{51} + 2 q^{53} + 12 q^{55} + 12 q^{57} - 2 q^{59} - 6 q^{61} - 24 q^{63} + 16 q^{65} + 14 q^{67} + 20 q^{69} + 32 q^{71} + 18 q^{73} - 24 q^{75} + 10 q^{77} + 2 q^{79} + 2 q^{81} + 16 q^{83} - 44 q^{85} - 8 q^{87} + 18 q^{89} - 18 q^{93} - 2 q^{95} - 16 q^{97} + 16 q^{99}+O(q^{100}) $ 4 * q - 2 * q^3 - 2 * q^5 - 4 * q^7 + 2 * q^11 + 20 * q^15 + 6 * q^17 - 10 * q^19 + 14 * q^21 + 2 * q^23 - 8 * q^25 + 4 * q^27 - 14 * q^31 - 2 * q^33 - 22 * q^35 - 6 * q^37 + 8 * q^39 - 16 * q^41 + 16 * q^43 - 16 * q^45 - 18 * q^47 - 20 * q^49 + 14 * q^51 + 2 * q^53 + 12 * q^55 + 12 * q^57 - 2 * q^59 - 6 * q^61 - 24 * q^63 + 16 * q^65 + 14 * q^67 + 20 * q^69 + 32 * q^71 + 18 * q^73 - 24 * q^75 + 10 * q^77 + 2 * q^79 + 2 * q^81 + 16 * q^83 - 44 * q^85 - 8 * q^87 + 18 * q^89 - 18 * q^93 - 2 * q^95 - 16 * q^97 + 16 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/224\mathbb{Z}\right)^\times$.

$n$	$127$	$129$	$197$
$\chi(n)$	$1$	$e\left(\frac{2}{3}\right)$	$1$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	0.207107	−	0.358719i	0.119573	−	0.207107i	−0.800025	−	0.599966i	$-0.795181\pi$
$3$	0.207107	−	0.358719i	0.119573	−	0.207107i	0.919599	+	0.392859i	$0.128514\pi$
$4$		0			0
$5$	0.914214	+	1.58346i	0.408849	+	0.708147i	0.994761	−	0.102228i	$-0.0325970\pi$
$5$	0.914214	+	1.58346i	0.408849	+	0.708147i	−0.585912	+	0.810374i	$0.699264\pi$
$6$		0			0
$7$	−1.00000	+	2.44949i	−0.377964	+	0.925820i
$7$	−1.00000	+	2.44949i	−0.377964	+	0.925820i
$8$		0			0
$9$	1.41421	+	2.44949i	0.471405	+	0.816497i
$10$		0			0
$11$	1.20711	−	2.09077i	0.363956	−	0.630391i	−0.624652	−	0.780903i	$-0.714759\pi$
$11$	1.20711	−	2.09077i	0.363956	−	0.630391i	0.988608	+	0.150513i	$0.0480924\pi$
$12$		0			0
$13$	2.82843			0.784465			0.392232	−	0.919866i	$-0.371703\pi$
$13$	2.82843			0.784465			0.392232	+	0.919866i	$0.371703\pi$
$14$		0			0
$15$	0.757359			0.195549
$16$		0			0
$17$	0.0857864	−	0.148586i	0.0208063	−	0.0360375i	−0.855435	−	0.517911i	$-0.826710\pi$
$17$	0.0857864	−	0.148586i	0.0208063	−	0.0360375i	0.876241	+	0.481873i	$0.160043\pi$
$18$		0			0
$19$	−3.20711	−	5.55487i	−0.735761	−	1.27438i	−0.954389	−	0.298567i	$-0.903491\pi$
$19$	−3.20711	−	5.55487i	−0.735761	−	1.27438i	0.218628	−	0.975808i	$-0.429842\pi$
$20$		0			0
$21$	0.671573	+	0.866025i	0.146549	+	0.188982i
$22$		0			0
$23$	2.62132	+	4.54026i	0.546583	+	0.946710i	0.998505	+	0.0546524i	$0.0174051\pi$
$23$	2.62132	+	4.54026i	0.546583	+	0.946710i	−0.451922	+	0.892057i	$0.649262\pi$
$24$		0			0
$25$	0.828427	−	1.43488i	0.165685	−	0.286976i
$26$		0			0
$27$	2.41421			0.464616
$28$		0			0
$29$	−2.82843			−0.525226			−0.262613	−	0.964901i	$-0.584584\pi$
$29$	−2.82843			−0.525226			−0.262613	+	0.964901i	$0.584584\pi$
$30$		0			0
$31$	−2.79289	+	4.83743i	−0.501618	+	0.868829i	0.498380	+	0.866959i	$0.333929\pi$
$31$	−2.79289	+	4.83743i	−0.501618	+	0.868829i	−0.999998	+	0.00186981i	$0.999405\pi$
$32$		0			0
$33$	−0.500000	−	0.866025i	−0.0870388	−	0.150756i
$34$		0			0
$35$	−4.79289	+	0.655892i	−0.810147	+	0.110866i
$36$		0			0
$37$	−4.32843	−	7.49706i	−0.711589	−	1.23251i	−0.964260	−	0.264956i	$-0.914642\pi$
$37$	−4.32843	−	7.49706i	−0.711589	−	1.23251i	0.252671	−	0.967552i	$-0.418691\pi$
$38$		0			0
$39$	0.585786	−	1.01461i	0.0938009	−	0.162468i
$40$		0			0
$41$	−6.82843			−1.06642			−0.533211	−	0.845983i	$-0.679015\pi$
$41$	−6.82843			−1.06642			−0.533211	+	0.845983i	$0.679015\pi$
$42$		0			0
$43$	9.65685			1.47266			0.736328	−	0.676625i	$-0.236558\pi$
$43$	9.65685			1.47266			0.736328	+	0.676625i	$0.236558\pi$
$44$		0			0
$45$	−2.58579	+	4.47871i	−0.385466	+	0.667647i
$46$		0			0
$47$	−5.20711	−	9.01897i	−0.759535	−	1.31555i	−0.943088	−	0.332543i	$-0.892093\pi$
$47$	−5.20711	−	9.01897i	−0.759535	−	1.31555i	0.183554	−	0.983010i	$-0.441240\pi$
$48$		0			0
$49$	−5.00000	−	4.89898i	−0.714286	−	0.699854i
$50$		0			0
$51$	−0.0355339	−	0.0615465i	−0.00497574	−	0.00861824i
$52$		0			0
$53$	0.500000	−	0.866025i	0.0686803	−	0.118958i	−0.829640	−	0.558298i	$-0.811454\pi$
$53$	0.500000	−	0.866025i	0.0686803	−	0.118958i	0.898321	+	0.439340i	$0.144788\pi$
$54$		0			0
$55$	4.41421			0.595212
$56$		0			0
$57$	−2.65685			−0.351909
$58$		0			0
$59$	−5.44975	+	9.43924i	−0.709497	+	1.22888i	0.255547	+	0.966797i	$0.417744\pi$
$59$	−5.44975	+	9.43924i	−0.709497	+	1.22888i	−0.965044	+	0.262088i	$0.915589\pi$
$60$		0			0
$61$	−4.32843	−	7.49706i	−0.554198	−	0.959900i	−0.997965	−	0.0637575i	$-0.979692\pi$
$61$	−4.32843	−	7.49706i	−0.554198	−	0.959900i	0.443767	−	0.896142i	$-0.353642\pi$
$62$		0			0
$63$	−7.41421	+	1.01461i	−0.934103	+	0.127829i
$64$		0			0
$65$	2.58579	+	4.47871i	0.320727	+	0.555516i
$66$		0			0
$67$	1.37868	−	2.38794i	0.168433	−	0.291734i	−0.769436	−	0.638723i	$-0.779463\pi$
$67$	1.37868	−	2.38794i	0.168433	−	0.291734i	0.937869	+	0.346990i	$0.112796\pi$
$68$		0			0
$69$	2.17157			0.261427
$70$		0			0
$71$	13.6569			1.62077			0.810385	−	0.585897i	$-0.199258\pi$
$71$	13.6569			1.62077			0.810385	+	0.585897i	$0.199258\pi$
$72$		0			0
$73$	7.32843	−	12.6932i	0.857728	−	1.48563i	−0.0163639	−	0.999866i	$-0.505209\pi$
$73$	7.32843	−	12.6932i	0.857728	−	1.48563i	0.874091	−	0.485762i	$-0.161458\pi$
$74$		0			0
$75$	−0.343146	−	0.594346i	−0.0396231	−	0.0686292i
$76$		0			0
$77$	3.91421	+	5.04757i	0.446066	+	0.575224i
$78$		0			0
$79$	−3.03553	−	5.25770i	−0.341524	−	0.591537i	0.643192	−	0.765705i	$-0.277610\pi$
$79$	−3.03553	−	5.25770i	−0.341524	−	0.591537i	−0.984716	+	0.174168i	$0.944276\pi$
$80$		0			0
$81$	−3.74264	+	6.48244i	−0.415849	+	0.720272i
$82$		0			0
$83$	−7.31371			−0.802784			−0.401392	−	0.915906i	$-0.631473\pi$
$83$	−7.31371			−0.802784			−0.401392	+	0.915906i	$0.631473\pi$
$84$		0			0
$85$	0.313708			0.0340265
$86$		0			0
$87$	−0.585786	+	1.01461i	−0.0628029	+	0.108778i
$88$		0			0
$89$	4.50000	+	7.79423i	0.476999	+	0.826187i	0.999653	−	0.0263586i	$-0.00839118\pi$
$89$	4.50000	+	7.79423i	0.476999	+	0.826187i	−0.522654	+	0.852545i	$0.675058\pi$
$90$		0			0
$91$	−2.82843	+	6.92820i	−0.296500	+	0.726273i
$92$		0			0
$93$	1.15685	+	2.00373i	0.119960	+	0.207777i
$94$		0			0
$95$	5.86396	−	10.1567i	0.601630	−	1.04205i
$96$		0			0
$97$	−1.17157			−0.118955			−0.0594776	−	0.998230i	$-0.518943\pi$
$97$	−1.17157			−0.118955			−0.0594776	+	0.998230i	$0.518943\pi$
$98$		0			0
$99$	6.82843			0.686283
$100$		0			0
$101$	−6.74264	+	11.6786i	−0.670918	+	1.16206i	0.306726	+	0.951798i	$0.400766\pi$
$101$	−6.74264	+	11.6786i	−0.670918	+	1.16206i	−0.977644	+	0.210266i	$0.932567\pi$
$102$		0			0
$103$	−4.20711	−	7.28692i	−0.414539	−	0.718002i	0.580841	−	0.814017i	$-0.302724\pi$
$103$	−4.20711	−	7.28692i	−0.414539	−	0.718002i	−0.995380	+	0.0960150i	$0.969390\pi$
$104$		0			0
$105$	−0.757359	+	1.85514i	−0.0739107	+	0.181044i
$106$		0			0
$107$	6.44975	+	11.1713i	0.623521	+	1.07997i	0.988825	+	0.149081i	$0.0476316\pi$
$107$	6.44975	+	11.1713i	0.623521	+	1.07997i	−0.365304	+	0.930888i	$0.619035\pi$
$108$		0			0
$109$	4.08579	−	7.07679i	0.391347	−	0.677834i	−0.601280	−	0.799038i	$-0.705342\pi$
$109$	4.08579	−	7.07679i	0.391347	−	0.677834i	0.992628	+	0.121205i	$0.0386758\pi$
$110$		0			0
$111$	−3.58579			−0.340348
$112$		0			0
$113$	18.1421			1.70667			0.853334	−	0.521364i	$-0.174577\pi$
$113$	18.1421			1.70667			0.853334	+	0.521364i	$0.174577\pi$
$114$		0			0
$115$	−4.79289	+	8.30153i	−0.446940	+	0.774122i
$116$		0			0
$117$	4.00000	+	6.92820i	0.369800	+	0.640513i
$118$		0			0
$119$	0.278175	+	0.358719i	0.0255002	+	0.0328838i
$120$		0			0
$121$	2.58579	+	4.47871i	0.235071	+	0.407156i
$122$		0			0
$123$	−1.41421	+	2.44949i	−0.127515	+	0.220863i
$124$		0			0
$125$	12.1716			1.08866
$126$		0			0
$127$	−5.65685			−0.501965			−0.250982	−	0.967992i	$-0.580754\pi$
$127$	−5.65685			−0.501965			−0.250982	+	0.967992i	$0.580754\pi$
$128$		0			0
$129$	2.00000	−	3.46410i	0.176090	−	0.304997i
$130$		0			0
$131$	−3.86396	−	6.69258i	−0.337596	−	0.584733i	0.646384	−	0.763012i	$-0.276280\pi$
$131$	−3.86396	−	6.69258i	−0.337596	−	0.584733i	−0.983980	+	0.178279i	$0.942947\pi$
$132$		0			0
$133$	16.8137	−	2.30090i	1.45793	−	0.199514i
$134$		0			0
$135$	2.20711	+	3.82282i	0.189958	+	0.329016i
$136$		0			0
$137$	−5.57107	+	9.64937i	−0.475968	+	0.824402i	−0.999621	−	0.0275304i	$-0.991236\pi$
$137$	−5.57107	+	9.64937i	−0.475968	+	0.824402i	0.523653	+	0.851932i	$0.324569\pi$
$138$		0			0
$139$	15.3137			1.29889			0.649446	−	0.760408i	$-0.275001\pi$
$139$	15.3137			1.29889			0.649446	+	0.760408i	$0.275001\pi$
$140$		0			0
$141$	−4.31371			−0.363280
$142$		0			0
$143$	3.41421	−	5.91359i	0.285511	−	0.494519i
$144$		0			0
$145$	−2.58579	−	4.47871i	−0.214738	−	0.371937i
$146$		0			0
$147$	−2.79289	+	0.778985i	−0.230354	+	0.0642496i
$148$		0			0
$149$	−3.08579	−	5.34474i	−0.252797	−	0.437858i	0.711497	−	0.702689i	$-0.248017\pi$
$149$	−3.08579	−	5.34474i	−0.252797	−	0.437858i	−0.964295	+	0.264831i	$0.914684\pi$
$150$		0			0
$151$	−0.449747	+	0.778985i	−0.0365999	+	0.0633929i	−0.883745	−	0.467969i	$-0.844986\pi$
$151$	−0.449747	+	0.778985i	−0.0365999	+	0.0633929i	0.847145	+	0.531361i	$0.178319\pi$
$152$		0			0
$153$	0.485281			0.0392327
$154$		0			0
$155$	−10.2132			−0.820344
$156$		0			0
$157$	−4.67157	+	8.09140i	−0.372832	+	0.645764i	−0.990000	−	0.141067i	$-0.954947\pi$
$157$	−4.67157	+	8.09140i	−0.372832	+	0.645764i	0.617168	+	0.786831i	$0.288280\pi$
$158$		0			0
$159$	−0.207107	−	0.358719i	−0.0164246	−	0.0284483i
$160$		0			0
$161$	−13.7426	+	1.88064i	−1.08307	+	0.148215i
$162$		0			0
$163$	−3.37868	−	5.85204i	−0.264639	−	0.458368i	0.702830	−	0.711358i	$-0.251919\pi$
$163$	−3.37868	−	5.85204i	−0.264639	−	0.458368i	−0.967469	+	0.252990i	$0.918586\pi$
$164$		0			0
$165$	0.914214	−	1.58346i	0.0711714	−	0.123273i
$166$		0			0
$167$	2.00000			0.154765			0.0773823	−	0.997001i	$-0.475344\pi$
$167$	2.00000			0.154765			0.0773823	+	0.997001i	$0.475344\pi$
$168$		0			0
$169$	−5.00000			−0.384615
$170$		0			0
$171$	9.07107	−	15.7116i	0.693682	−	1.20149i
$172$		0			0
$173$	−5.50000	−	9.52628i	−0.418157	−	0.724270i	0.577597	−	0.816322i	$-0.303991\pi$
$173$	−5.50000	−	9.52628i	−0.418157	−	0.724270i	−0.995754	+	0.0920525i	$0.970657\pi$
$174$		0			0
$175$	2.68629	+	3.46410i	0.203065	+	0.261861i
$176$		0			0
$177$	2.25736	+	3.90986i	0.169674	+	0.293883i
$178$		0			0
$179$	−2.79289	+	4.83743i	−0.208751	+	0.361567i	−0.951321	−	0.308201i	$-0.900273\pi$
$179$	−2.79289	+	4.83743i	−0.208751	+	0.361567i	0.742571	+	0.669768i	$0.233606\pi$
$180$		0			0
$181$	−9.31371			−0.692283			−0.346141	−	0.938182i	$-0.612508\pi$
$181$	−9.31371			−0.692283			−0.346141	+	0.938182i	$0.612508\pi$
$182$		0			0
$183$	−3.58579			−0.265069
$184$		0			0
$185$	7.91421	−	13.7078i	0.581865	−	1.00782i
$186$		0			0
$187$	−0.207107	−	0.358719i	−0.0151451	−	0.0262322i
$188$		0			0
$189$	−2.41421	+	5.91359i	−0.175608	+	0.430150i
$190$		0			0
$191$	4.44975	+	7.70719i	0.321972	+	0.557673i	0.980895	−	0.194538i	$-0.0623208\pi$
$191$	4.44975	+	7.70719i	0.321972	+	0.557673i	−0.658923	+	0.752211i	$0.728987\pi$
$192$		0			0
$193$	4.57107	−	7.91732i	0.329033	−	0.569901i	−0.653288	−	0.757110i	$-0.726611\pi$
$193$	4.57107	−	7.91732i	0.329033	−	0.569901i	0.982320	+	0.187209i	$0.0599440\pi$
$194$		0			0
$195$	2.14214			0.153402
$196$		0			0
$197$	−18.8284			−1.34147			−0.670735	−	0.741697i	$-0.734021\pi$
$197$	−18.8284			−1.34147			−0.670735	+	0.741697i	$0.734021\pi$
$198$		0			0
$199$	−5.62132	+	9.73641i	−0.398485	+	0.690196i	−0.993539	−	0.113489i	$-0.963797\pi$
$199$	−5.62132	+	9.73641i	−0.398485	+	0.690196i	0.595054	+	0.803685i	$0.297131\pi$
$200$		0			0
$201$	−0.571068	−	0.989118i	−0.0402800	−	0.0697670i
$202$		0			0
$203$	2.82843	−	6.92820i	0.198517	−	0.486265i
$204$		0			0
$205$	−6.24264	−	10.8126i	−0.436005	−	0.755183i
$206$		0			0
$207$	−7.41421	+	12.8418i	−0.515323	+	0.892566i
$208$		0			0
$209$	−15.4853			−1.07114
$210$		0			0
$211$	−12.0000			−0.826114			−0.413057	−	0.910705i	$-0.635539\pi$
$211$	−12.0000			−0.826114			−0.413057	+	0.910705i	$0.635539\pi$
$212$		0			0
$213$	2.82843	−	4.89898i	0.193801	−	0.335673i
$214$		0			0
$215$	8.82843	+	15.2913i	0.602094	+	1.04286i
$216$		0			0
$217$	−9.05635	−	11.6786i	−0.614785	−	0.792795i
$218$		0			0
$219$	−3.03553	−	5.25770i	−0.205122	−	0.355282i
$220$		0			0
$221$	0.242641	−	0.420266i	0.0163218	−	0.0282702i
$222$		0			0
$223$	2.34315			0.156909			0.0784543	−	0.996918i	$-0.475002\pi$
$223$	2.34315			0.156909			0.0784543	+	0.996918i	$0.475002\pi$
$224$		0			0
$225$	4.68629			0.312419
$226$		0			0
$227$	8.03553	−	13.9180i	0.533337	−	0.923767i	−0.465905	−	0.884835i	$-0.654271\pi$
$227$	8.03553	−	13.9180i	0.533337	−	0.923767i	0.999242	−	0.0389321i	$-0.0123956\pi$
$228$		0			0
$229$	2.08579	+	3.61269i	0.137833	+	0.238733i	0.926676	−	0.375861i	$-0.122653\pi$
$229$	2.08579	+	3.61269i	0.137833	+	0.238733i	−0.788843	+	0.614594i	$0.789320\pi$
$230$		0			0
$231$	2.62132	−	0.358719i	0.172470	−	0.0236020i
$232$		0			0
$233$	−1.08579	−	1.88064i	−0.0711322	−	0.123205i	0.828266	−	0.560336i	$-0.189328\pi$
$233$	−1.08579	−	1.88064i	−0.0711322	−	0.123205i	−0.899398	+	0.437131i	$0.855995\pi$
$234$		0			0
$235$	9.52082	−	16.4905i	0.621070	−	1.07572i
$236$		0			0
$237$	−2.51472			−0.163349
$238$		0			0
$239$	1.31371			0.0849767			0.0424884	−	0.999097i	$-0.486471\pi$
$239$	1.31371			0.0849767			0.0424884	+	0.999097i	$0.486471\pi$
$240$		0			0
$241$	−5.15685	+	8.93193i	−0.332182	+	0.575356i	−0.982939	−	0.183929i	$-0.941118\pi$
$241$	−5.15685	+	8.93193i	−0.332182	+	0.575356i	0.650757	+	0.759286i	$0.274452\pi$
$242$		0			0
$243$	5.17157	+	8.95743i	0.331757	+	0.574619i
$244$		0			0
$245$	3.18629	−	12.3960i	0.203565	−	0.791954i
$246$		0			0
$247$	−9.07107	−	15.7116i	−0.577178	−	0.999702i
$248$		0			0
$249$	−1.51472	+	2.62357i	−0.0959914	+	0.166262i
$250$		0			0
$251$	−30.9706			−1.95484			−0.977422	−	0.211295i	$-0.932232\pi$
$251$	−30.9706			−1.95484			−0.977422	+	0.211295i	$0.932232\pi$
$252$		0			0
$253$	12.6569			0.795730
$254$		0			0
$255$	0.0649712	−	0.112533i	0.00406865	−	0.00704711i
$256$		0			0
$257$	−2.25736	−	3.90986i	−0.140810	−	0.243890i	0.786992	−	0.616964i	$-0.211637\pi$
$257$	−2.25736	−	3.90986i	−0.140810	−	0.243890i	−0.927802	+	0.373073i	$0.878304\pi$
$258$		0			0
$259$	22.6924	−	3.10538i	1.41004	−	0.192959i
$260$		0			0
$261$	−4.00000	−	6.92820i	−0.247594	−	0.428845i
$262$		0			0
$263$	−5.44975	+	9.43924i	−0.336046	+	0.582048i	−0.983685	−	0.179899i	$-0.942423\pi$
$263$	−5.44975	+	9.43924i	−0.336046	+	0.582048i	0.647639	+	0.761947i	$0.275756\pi$
$264$		0			0
$265$	1.82843			0.112319
$266$		0			0
$267$	3.72792			0.228145
$268$		0			0
$269$	−6.32843	+	10.9612i	−0.385851	+	0.668314i	−0.991887	−	0.127124i	$-0.959425\pi$
$269$	−6.32843	+	10.9612i	−0.385851	+	0.668314i	0.606036	+	0.795437i	$0.292759\pi$
$270$		0			0
$271$	15.1066	+	26.1654i	0.917661	+	1.58943i	0.802958	+	0.596035i	$0.203258\pi$
$271$	15.1066	+	26.1654i	0.917661	+	1.58943i	0.114702	+	0.993400i	$0.463409\pi$
$272$		0			0
$273$	1.89949	+	2.44949i	0.114963	+	0.148250i
$274$		0			0
$275$	−2.00000	−	3.46410i	−0.120605	−	0.208893i
$276$		0			0
$277$	−5.15685	+	8.93193i	−0.309845	+	0.536668i	−0.978328	−	0.207060i	$-0.933611\pi$
$277$	−5.15685	+	8.93193i	−0.309845	+	0.536668i	0.668483	+	0.743727i	$0.266944\pi$
$278$		0			0
$279$	−15.7990			−0.945861
$280$		0			0
$281$	−12.4853			−0.744809			−0.372405	−	0.928070i	$-0.621467\pi$
$281$	−12.4853			−0.744809			−0.372405	+	0.928070i	$0.621467\pi$
$282$		0			0
$283$	−2.79289	+	4.83743i	−0.166020	+	0.287556i	−0.937017	−	0.349283i	$-0.886425\pi$
$283$	−2.79289	+	4.83743i	−0.166020	+	0.287556i	0.770997	+	0.636839i	$0.219758\pi$
$284$		0			0
$285$	−2.42893	−	4.20703i	−0.143878	−	0.249203i
$286$		0			0
$287$	6.82843	−	16.7262i	0.403069	−	0.987314i
$288$		0			0
$289$	8.48528	+	14.6969i	0.499134	+	0.864526i
$290$		0			0
$291$	−0.242641	+	0.420266i	−0.0142238	+	0.0246364i
$292$		0			0
$293$	28.6274			1.67243			0.836216	−	0.548401i	$-0.184763\pi$
$293$	28.6274			1.67243			0.836216	+	0.548401i	$0.184763\pi$
$294$		0			0
$295$	−19.9289			−1.16031
$296$		0			0
$297$	2.91421	−	5.04757i	0.169100	−	0.292889i
$298$		0			0
$299$	7.41421	+	12.8418i	0.428775	+	0.742660i
$300$		0			0
$301$	−9.65685	+	23.6544i	−0.556612	+	1.36341i
$302$		0			0
$303$	2.79289	+	4.83743i	0.160448	+	0.277903i
$304$		0			0
$305$	7.91421	−	13.7078i	0.453167	−	0.784907i
$306$		0			0
$307$	14.3431			0.818607			0.409303	−	0.912398i	$-0.365772\pi$
$307$	14.3431			0.818607			0.409303	+	0.912398i	$0.365772\pi$
$308$		0			0
$309$	−3.48528			−0.198271
$310$		0			0
$311$	9.37868	−	16.2443i	0.531816	−	0.921133i	−0.467494	−	0.883996i	$-0.654843\pi$
$311$	9.37868	−	16.2443i	0.531816	−	0.921133i	0.999310	−	0.0371364i	$-0.0118236\pi$
$312$		0			0
$313$	14.6421	+	25.3609i	0.827622	+	1.43348i	0.899898	+	0.436099i	$0.143640\pi$
$313$	14.6421	+	25.3609i	0.827622	+	1.43348i	−0.0722760	+	0.997385i	$0.523026\pi$
$314$		0			0
$315$	−8.38478	−	10.8126i	−0.472429	−	0.609219i
$316$		0			0
$317$	4.84315	+	8.38857i	0.272018	+	0.471149i	0.969379	−	0.245571i	$-0.0789756\pi$
$317$	4.84315	+	8.38857i	0.272018	+	0.471149i	−0.697360	+	0.716721i	$0.745642\pi$
$318$		0			0
$319$	−3.41421	+	5.91359i	−0.191159	+	0.331098i
$320$		0			0
$321$	5.34315			0.298225
$322$		0			0
$323$	−1.10051			−0.0612337
$324$		0			0
$325$	2.34315	−	4.05845i	0.129974	−	0.225122i
$326$		0			0
$327$	−1.69239	−	2.93130i	−0.0935893	−	0.162101i
$328$		0			0
$329$	27.2990	−	3.73578i	1.50504	−	0.205960i
$330$		0			0
$331$	−14.2071	−	24.6074i	−0.780893	−	1.35255i	−0.931422	−	0.363941i	$-0.881431\pi$
$331$	−14.2071	−	24.6074i	−0.780893	−	1.35255i	0.150529	−	0.988606i	$-0.451902\pi$
$332$		0			0
$333$	12.2426	−	21.2049i	0.670893	−	1.16202i
$334$		0			0
$335$	5.04163			0.275454
$336$		0			0
$337$	9.17157			0.499607			0.249804	−	0.968296i	$-0.419634\pi$
$337$	9.17157			0.499607			0.249804	+	0.968296i	$0.419634\pi$
$338$		0			0
$339$	3.75736	−	6.50794i	0.204072	−	0.353463i
$340$		0			0
$341$	6.74264	+	11.6786i	0.365134	+	0.632431i
$342$		0			0
$343$	17.0000	−	7.34847i	0.917914	−	0.396780i
$344$		0			0
$345$	1.98528	+	3.43861i	0.106884	+	0.185128i
$346$		0			0
$347$	−17.4497	+	30.2238i	−0.936752	+	1.62250i	−0.165271	+	0.986248i	$0.552850\pi$
$347$	−17.4497	+	30.2238i	−0.936752	+	1.62250i	−0.771480	+	0.636253i	$0.780483\pi$
$348$		0			0
$349$	5.17157			0.276828			0.138414	−	0.990374i	$-0.455800\pi$
$349$	5.17157			0.276828			0.138414	+	0.990374i	$0.455800\pi$
$350$		0			0
$351$	6.82843			0.364474
$352$		0			0
$353$	−1.08579	+	1.88064i	−0.0577906	+	0.100096i	−0.893473	−	0.449116i	$-0.851739\pi$
$353$	−1.08579	+	1.88064i	−0.0577906	+	0.100096i	0.835683	+	0.549212i	$0.185072\pi$
$354$		0			0
$355$	12.4853	+	21.6251i	0.662650	+	1.14774i
$356$		0			0
$357$	0.186292	−	0.0254934i	0.00985959	−	0.00134925i
$358$		0			0
$359$	−5.69239	−	9.85951i	−0.300433	−	0.520365i	0.675801	−	0.737084i	$-0.263798\pi$
$359$	−5.69239	−	9.85951i	−0.300433	−	0.520365i	−0.976234	+	0.216719i	$0.930464\pi$
$360$		0			0
$361$	−11.0711	+	19.1757i	−0.582688	+	1.00924i
$362$		0			0
$363$	2.14214			0.112433
$364$		0			0
$365$	26.7990			1.40272
$366$		0			0
$367$	−2.13604	+	3.69973i	−0.111500	+	0.193124i	−0.916375	−	0.400320i	$-0.868899\pi$
$367$	−2.13604	+	3.69973i	−0.111500	+	0.193124i	0.804875	+	0.593444i	$0.202232\pi$
$368$		0			0
$369$	−9.65685	−	16.7262i	−0.502716	−	0.870729i
$370$		0			0
$371$	1.62132	+	2.09077i	0.0841748	+	0.108547i
$372$		0			0
$373$	4.15685	+	7.19988i	0.215234	+	0.372796i	0.953345	−	0.301883i	$-0.0976153\pi$
$373$	4.15685	+	7.19988i	0.215234	+	0.372796i	−0.738111	+	0.674679i	$0.764282\pi$
$374$		0			0
$375$	2.52082	−	4.36618i	0.130174	−	0.225469i
$376$		0			0
$377$	−8.00000			−0.412021
$378$		0			0
$379$	−34.9706			−1.79632			−0.898159	−	0.439672i	$-0.855095\pi$
$379$	−34.9706			−1.79632			−0.898159	+	0.439672i	$0.855095\pi$
$380$		0			0
$381$	−1.17157	+	2.02922i	−0.0600215	+	0.103960i
$382$		0			0
$383$	5.62132	+	9.73641i	0.287236	+	0.497507i	0.973149	−	0.230176i	$-0.0739303\pi$
$383$	5.62132	+	9.73641i	0.287236	+	0.497507i	−0.685913	+	0.727684i	$0.740597\pi$
$384$		0			0
$385$	−4.41421	+	10.8126i	−0.224969	+	0.551060i
$386$		0			0
$387$	13.6569	+	23.6544i	0.694217	+	1.20242i
$388$		0			0
$389$	−9.08579	+	15.7370i	−0.460668	+	0.797900i	−0.998994	−	0.0448365i	$-0.985723\pi$
$389$	−9.08579	+	15.7370i	−0.460668	+	0.797900i	0.538327	+	0.842736i	$0.319057\pi$
$390$		0			0
$391$	0.899495			0.0454894
$392$		0			0
$393$	−3.20101			−0.161470
$394$		0			0
$395$	5.55025	−	9.61332i	0.279264	−	0.483699i
$396$		0			0
$397$	2.08579	+	3.61269i	0.104683	+	0.181316i	0.913608	−	0.406595i	$-0.133284\pi$
$397$	2.08579	+	3.61269i	0.104683	+	0.181316i	−0.808926	+	0.587911i	$0.799951\pi$
$398$		0			0
$399$	2.65685	−	6.50794i	0.133009	−	0.325804i
$400$		0			0
$401$	−3.91421	−	6.77962i	−0.195466	−	0.338558i	0.751587	−	0.659634i	$-0.229289\pi$
$401$	−3.91421	−	6.77962i	−0.195466	−	0.338558i	−0.947053	+	0.321076i	$0.895955\pi$
$402$		0			0
$403$	−7.89949	+	13.6823i	−0.393502	+	0.681565i
$404$		0			0
$405$	−13.6863			−0.680077
$406$		0			0
$407$	−20.8995			−1.03595
$408$		0			0
$409$	−7.22792	+	12.5191i	−0.357398	+	0.619031i	−0.987525	−	0.157461i	$-0.949669\pi$
$409$	−7.22792	+	12.5191i	−0.357398	+	0.619031i	0.630128	+	0.776492i	$0.283003\pi$
$410$		0			0
$411$	2.30761	+	3.99690i	0.113826	+	0.197153i
$412$		0			0
$413$	−17.6716	−	22.7883i	−0.869561	−	1.12134i
$414$		0			0
$415$	−6.68629	−	11.5810i	−0.328217	−	0.568489i
$416$		0			0
$417$	3.17157	−	5.49333i	0.155313	−	0.269009i
$418$		0			0
$419$	9.65685			0.471768			0.235884	−	0.971781i	$-0.424201\pi$
$419$	9.65685			0.471768			0.235884	+	0.971781i	$0.424201\pi$
$420$		0			0
$421$	−16.4853			−0.803443			−0.401722	−	0.915762i	$-0.631588\pi$
$421$	−16.4853			−0.803443			−0.401722	+	0.915762i	$0.631588\pi$
$422$		0			0
$423$	14.7279	−	25.5095i	0.716096	−	1.24031i
$424$		0			0
$425$	−0.142136	−	0.246186i	−0.00689459	−	0.0119418i
$426$		0			0
$427$	22.6924	−	3.10538i	1.09816	−	0.150280i
$428$		0			0
$429$	−1.41421	−	2.44949i	−0.0682789	−	0.118262i
$430$		0			0
$431$	6.37868	−	11.0482i	0.307250	−	0.532173i	−0.670510	−	0.741901i	$-0.733924\pi$
$431$	6.37868	−	11.0482i	0.307250	−	0.532173i	0.977760	+	0.209728i	$0.0672578\pi$
$432$		0			0
$433$	11.5147			0.553362			0.276681	−	0.960962i	$-0.410765\pi$
$433$	11.5147			0.553362			0.276681	+	0.960962i	$0.410765\pi$
$434$		0			0
$435$	−2.14214			−0.102708
$436$		0			0
$437$	16.8137	−	29.1222i	0.804309	−	1.39310i
$438$		0			0
$439$	−11.3492	−	19.6575i	−0.541670	−	0.938200i	−0.998808	−	0.0488041i	$-0.984459\pi$
$439$	−11.3492	−	19.6575i	−0.541670	−	0.938200i	0.457139	−	0.889395i	$-0.348874\pi$
$440$		0			0
$441$	4.92893	−	19.1757i	0.234711	−	0.913126i
$442$		0			0
$443$	5.96447	+	10.3308i	0.283380	+	0.490829i	0.972215	−	0.234089i	$-0.0752108\pi$
$443$	5.96447	+	10.3308i	0.283380	+	0.490829i	−0.688835	+	0.724918i	$0.741877\pi$
$444$		0			0
$445$	−8.22792	+	14.2512i	−0.390041	+	0.675571i
$446$		0			0
$447$	−2.55635			−0.120911
$448$		0			0
$449$	1.17157			0.0552899			0.0276450	−	0.999618i	$-0.491199\pi$
$449$	1.17157			0.0552899			0.0276450	+	0.999618i	$0.491199\pi$
$450$		0			0
$451$	−8.24264	+	14.2767i	−0.388131	+	0.672262i
$452$		0			0
$453$	0.186292	+	0.322666i	0.00875274	+	0.0151602i
$454$		0			0
$455$	−13.5563	+	1.85514i	−0.635531	+	0.0869705i
$456$		0			0
$457$	−9.64214	−	16.7007i	−0.451040	−	0.781224i	0.547411	−	0.836864i	$-0.315614\pi$
$457$	−9.64214	−	16.7007i	−0.451040	−	0.781224i	−0.998451	+	0.0556397i	$0.982280\pi$
$458$		0			0
$459$	0.207107	−	0.358719i	0.00966692	−	0.0167436i
$460$		0			0
$461$	−25.4558			−1.18560			−0.592798	−	0.805351i	$-0.701977\pi$
$461$	−25.4558			−1.18560			−0.592798	+	0.805351i	$0.701977\pi$
$462$		0			0
$463$	−11.3137			−0.525793			−0.262896	−	0.964824i	$-0.584678\pi$
$463$	−11.3137			−0.525793			−0.262896	+	0.964824i	$0.584678\pi$
$464$		0			0
$465$	−2.11522	+	3.66367i	−0.0980911	+	0.169899i
$466$		0			0
$467$	6.27817	+	10.8741i	0.290519	+	0.503194i	0.973933	−	0.226837i	$-0.0728386\pi$
$467$	6.27817	+	10.8741i	0.290519	+	0.503194i	−0.683413	+	0.730032i	$0.739505\pi$
$468$		0			0
$469$	4.47056	+	5.76500i	0.206431	+	0.266203i
$470$		0			0
$471$	1.93503	+	3.35157i	0.0891614	+	0.154432i
$472$		0			0
$473$	11.6569	−	20.1903i	0.535983	−	0.928349i
$474$		0			0
$475$	−10.6274			−0.487619
$476$		0			0
$477$	2.82843			0.129505
$478$		0			0
$479$	14.3492	−	24.8536i	0.655634	−	1.13559i	−0.326101	−	0.945335i	$-0.605735\pi$
$479$	14.3492	−	24.8536i	0.655634	−	1.13559i	0.981735	−	0.190256i	$-0.0609317\pi$
$480$		0			0
$481$	−12.2426	−	21.2049i	−0.558216	−	0.966859i
$482$		0			0
$483$	−2.17157	+	5.31925i	−0.0988100	+	0.242034i
$484$		0			0
$485$	−1.07107	−	1.85514i	−0.0486347	−	0.0842377i
$486$		0			0
$487$	5.86396	−	10.1567i	0.265721	−	0.460243i	−0.702031	−	0.712146i	$-0.747723\pi$
$487$	5.86396	−	10.1567i	0.265721	−	0.460243i	0.967752	+	0.251903i	$0.0810565\pi$
$488$		0			0
$489$	−2.79899			−0.126575
$490$		0			0
$491$	3.65685			0.165032			0.0825158	−	0.996590i	$-0.473705\pi$
$491$	3.65685			0.165032			0.0825158	+	0.996590i	$0.473705\pi$
$492$		0			0
$493$	−0.242641	+	0.420266i	−0.0109280	+	0.0189278i
$494$		0			0
$495$	6.24264	+	10.8126i	0.280586	+	0.485989i
$496$		0			0
$497$	−13.6569	+	33.4523i	−0.612594	+	1.50054i
$498$		0			0
$499$	2.27817	+	3.94591i	0.101985	+	0.176643i	0.912502	−	0.409071i	$-0.134147\pi$
$499$	2.27817	+	3.94591i	0.101985	+	0.176643i	−0.810517	+	0.585715i	$0.800814\pi$
$500$		0			0
$501$	0.414214	−	0.717439i	0.0185057	−	0.0320528i
$502$		0			0
$503$	−10.3431			−0.461178			−0.230589	−	0.973051i	$-0.574065\pi$
$503$	−10.3431			−0.461178			−0.230589	+	0.973051i	$0.574065\pi$
$504$		0			0
$505$	−24.6569			−1.09722
$506$		0			0
$507$	−1.03553	+	1.79360i	−0.0459897	+	0.0796565i
$508$		0			0
$509$	−20.7426	−	35.9273i	−0.919401	−	1.59245i	−0.800326	−	0.599565i	$-0.795340\pi$
$509$	−20.7426	−	35.9273i	−0.919401	−	1.59245i	−0.119075	−	0.992885i	$-0.537993\pi$
$510$		0			0
$511$	23.7635	+	30.6441i	1.05123	+	1.35562i
$512$		0			0
$513$	−7.74264	−	13.4106i	−0.341846	−	0.592095i
$514$		0			0
$515$	7.69239	−	13.3236i	0.338967	−	0.587108i
$516$		0			0
$517$	−25.1421			−1.10575
$518$		0			0
$519$	−4.55635			−0.200002
$520$		0			0
$521$	−3.50000	+	6.06218i	−0.153338	+	0.265589i	−0.932453	−	0.361293i	$-0.882336\pi$
$521$	−3.50000	+	6.06218i	−0.153338	+	0.265589i	0.779115	+	0.626881i	$0.215669\pi$
$522$		0			0
$523$	−8.86396	−	15.3528i	−0.387594	−	0.671332i	0.604531	−	0.796581i	$-0.293360\pi$
$523$	−8.86396	−	15.3528i	−0.387594	−	0.671332i	−0.992125	+	0.125249i	$0.960027\pi$
$524$		0			0
$525$	1.79899	−	0.246186i	0.0785144	−	0.0107444i
$526$		0			0
$527$	0.479185	+	0.829972i	0.0208736	+	0.0361542i
$528$		0			0
$529$	−2.24264	+	3.88437i	−0.0975061	+	0.168886i
$530$		0			0
$531$	−30.8284			−1.33784
$532$		0			0
$533$	−19.3137			−0.836570
$534$		0			0
$535$	−11.7929	+	20.4259i	−0.509851	+	0.883088i
$536$		0			0
$537$	1.15685	+	2.00373i	0.0499219	+	0.0864673i
$538$		0			0
$539$	−16.2782	+	4.54026i	−0.701151	+	0.195563i
$540$		0			0
$541$	12.9142	+	22.3681i	0.555225	+	0.961679i	0.997886	+	0.0649894i	$0.0207013\pi$
$541$	12.9142	+	22.3681i	0.555225	+	0.961679i	−0.442661	+	0.896689i	$0.645965\pi$
$542$		0			0
$543$	−1.92893	+	3.34101i	−0.0827784	+	0.143376i
$544$		0			0
$545$	14.9411			0.640007
$546$		0			0
$547$	10.9706			0.469067			0.234534	−	0.972108i	$-0.424644\pi$
$547$	10.9706			0.469067			0.234534	+	0.972108i	$0.424644\pi$
$548$		0			0
$549$	12.2426	−	21.2049i	0.522503	−	0.905002i
$550$		0			0
$551$	9.07107	+	15.7116i	0.386440	+	0.669335i
$552$		0			0
$553$	15.9142	−	2.17781i	0.676741	−	0.0926099i
$554$		0			0
$555$	−3.27817	−	5.67796i	−0.139151	−	0.241016i
$556$		0			0
$557$	0.0857864	−	0.148586i	0.00363489	−	0.00629581i	−0.864202	−	0.503145i	$-0.832176\pi$
$557$	0.0857864	−	0.148586i	0.00363489	−	0.00629581i	0.867837	+	0.496849i	$0.165510\pi$
$558$		0			0
$559$	27.3137			1.15525
$560$		0			0
$561$	−0.171573			−0.00724381
$562$		0			0
$563$	7.03553	−	12.1859i	0.296512	−	0.513575i	−0.678823	−	0.734302i	$-0.737510\pi$
$563$	7.03553	−	12.1859i	0.296512	−	0.513575i	0.975336	+	0.220727i	$0.0708431\pi$
$564$		0			0
$565$	16.5858	+	28.7274i	0.697769	+	1.20857i
$566$		0			0
$567$	−12.1360	−	15.6500i	−0.509666	−	0.657238i
$568$		0			0
$569$	−18.3284	−	31.7458i	−0.768368	−	1.33085i	−0.938448	−	0.345422i	$-0.887736\pi$
$569$	−18.3284	−	31.7458i	−0.768368	−	1.33085i	0.170080	−	0.985430i	$-0.445597\pi$
$570$		0			0
$571$	9.20711	−	15.9472i	0.385305	−	0.667369i	−0.606506	−	0.795079i	$-0.707429\pi$
$571$	9.20711	−	15.9472i	0.385305	−	0.667369i	0.991812	+	0.127710i	$0.0407628\pi$
$572$		0			0
$573$	3.68629			0.153997
$574$		0			0
$575$	8.68629			0.362243
$576$		0			0
$577$	−19.5000	+	33.7750i	−0.811796	+	1.40607i	0.0998105	+	0.995006i	$0.468176\pi$
$577$	−19.5000	+	33.7750i	−0.811796	+	1.40607i	−0.911606	+	0.411065i	$0.865157\pi$
$578$		0			0
$579$	−1.89340	−	3.27946i	−0.0786869	−	0.136290i
$580$		0			0
$581$	7.31371	−	17.9149i	0.303424	−	0.743233i
$582$		0			0
$583$	−1.20711	−	2.09077i	−0.0499933	−	0.0865909i
$584$		0			0
$585$	−7.31371	+	12.6677i	−0.302385	+	0.523746i
$586$		0			0
$587$	28.9706			1.19574			0.597872	−	0.801592i	$-0.296013\pi$
$587$	28.9706			1.19574			0.597872	+	0.801592i	$0.296013\pi$
$588$		0			0
$589$	35.8284			1.47628
$590$		0			0
$591$	−3.89949	+	6.75412i	−0.160404	+	0.277828i
$592$		0			0
$593$	−2.74264	−	4.75039i	−0.112627	−	0.195075i	0.804202	−	0.594356i	$-0.202593\pi$
$593$	−2.74264	−	4.75039i	−0.112627	−	0.195075i	−0.916829	+	0.399281i	$0.869260\pi$
$594$		0			0
$595$	−0.313708	+	0.768426i	−0.0128608	+	0.0315024i
$596$		0			0
$597$	2.32843	+	4.03295i	0.0952962	+	0.165058i
$598$		0			0
$599$	−17.9350	+	31.0644i	−0.732805	+	1.26926i	0.222874	+	0.974847i	$0.428456\pi$
$599$	−17.9350	+	31.0644i	−0.732805	+	1.26926i	−0.955680	+	0.294409i	$0.904877\pi$
$600$		0			0
$601$	26.1421			1.06636			0.533180	−	0.846002i	$-0.320997\pi$
$601$	26.1421			1.06636			0.533180	+	0.846002i	$0.320997\pi$
$602$		0			0
$603$	7.79899			0.317599
$604$		0			0
$605$	−4.72792	+	8.18900i	−0.192217	+	0.332930i
$606$		0			0
$607$	−17.6924	−	30.6441i	−0.718112	−	1.24381i	−0.961747	−	0.273939i	$-0.911673\pi$
$607$	−17.6924	−	30.6441i	−0.718112	−	1.24381i	0.243635	−	0.969867i	$-0.421660\pi$
$608$		0			0
$609$	−1.89949	−	2.44949i	−0.0769714	−	0.0992583i
$610$		0			0
$611$	−14.7279	−	25.5095i	−0.595828	−	1.03200i
$612$		0			0
$613$	−2.25736	+	3.90986i	−0.0911739	+	0.157918i	−0.908005	−	0.418959i	$-0.862395\pi$
$613$	−2.25736	+	3.90986i	−0.0911739	+	0.157918i	0.816831	+	0.576876i	$0.195729\pi$
$614$		0			0
$615$	−5.17157			−0.208538
$616$		0			0
$617$	19.1127			0.769448			0.384724	−	0.923032i	$-0.374297\pi$
$617$	19.1127			0.769448			0.384724	+	0.923032i	$0.374297\pi$
$618$		0			0
$619$	−8.96447	+	15.5269i	−0.360312	+	0.624079i	−0.988012	−	0.154376i	$-0.950663\pi$
$619$	−8.96447	+	15.5269i	−0.360312	+	0.624079i	0.627700	+	0.778455i	$0.283997\pi$
$620$		0			0
$621$	6.32843	+	10.9612i	0.253951	+	0.439856i
$622$		0			0
$623$	−23.5919	+	3.22848i	−0.945189	+	0.129346i
$624$		0			0
$625$	6.98528	+	12.0989i	0.279411	+	0.483954i
$626$		0			0
$627$	−3.20711	+	5.55487i	−0.128080	+	0.221840i
$628$		0			0
$629$	−1.48528			−0.0592220
$630$		0			0
$631$	29.6569			1.18062			0.590310	−	0.807176i	$-0.299005\pi$
$631$	29.6569			1.18062			0.590310	+	0.807176i	$0.299005\pi$
$632$		0			0
$633$	−2.48528	+	4.30463i	−0.0987811	+	0.171094i
$634$		0			0
$635$	−5.17157	−	8.95743i	−0.205228	−	0.355465i
$636$		0			0
$637$	−14.1421	−	13.8564i	−0.560332	−	0.549011i
$638$		0			0
$639$	19.3137	+	33.4523i	0.764038	+	1.32335i
$640$		0			0
$641$	8.50000	−	14.7224i	0.335730	−	0.581501i	−0.647895	−	0.761730i	$-0.724350\pi$
$641$	8.50000	−	14.7224i	0.335730	−	0.581501i	0.983625	+	0.180229i	$0.0576838\pi$
$642$		0			0
$643$	11.0294			0.434959			0.217479	−	0.976065i	$-0.430217\pi$
$643$	11.0294			0.434959			0.217479	+	0.976065i	$0.430217\pi$
$644$		0			0
$645$	7.31371			0.287977
$646$		0			0
$647$	−13.9350	+	24.1362i	−0.547843	+	0.948891i	0.450580	+	0.892736i	$0.351217\pi$
$647$	−13.9350	+	24.1362i	−0.547843	+	0.948891i	−0.998422	+	0.0561548i	$0.982116\pi$
$648$		0			0
$649$	13.1569	+	22.7883i	0.516452	+	0.894521i
$650$		0			0
$651$	−6.06497	+	0.829972i	−0.237705	+	0.0325292i
$652$		0			0
$653$	19.4706	+	33.7240i	0.761942	+	1.31972i	0.941848	+	0.336038i	$0.109087\pi$
$653$	19.4706	+	33.7240i	0.761942	+	1.31972i	−0.179906	+	0.983684i	$0.557579\pi$
$654$		0			0
$655$	7.06497	−	12.2369i	0.276051	−	0.478135i
$656$		0			0
$657$	41.4558			1.61735
$658$		0			0
$659$	34.6274			1.34889			0.674446	−	0.738324i	$-0.264382\pi$
$659$	34.6274			1.34889			0.674446	+	0.738324i	$0.264382\pi$
$660$		0			0
$661$	15.3284	−	26.5496i	0.596207	−	1.03266i	−0.397169	−	0.917746i	$-0.630007\pi$
$661$	15.3284	−	26.5496i	0.596207	−	1.03266i	0.993375	−	0.114915i	$-0.0366595\pi$
$662$		0			0
$663$	−0.100505	−	0.174080i	−0.00390329	−	0.00676070i
$664$		0			0
$665$	19.0147	+	24.5204i	0.737359	+	0.950860i
$666$		0			0
$667$	−7.41421	−	12.8418i	−0.287079	−	0.497236i
$668$		0			0
$669$	0.485281	−	0.840532i	0.0187621	−	0.0324968i
$670$		0			0
$671$	−20.8995			−0.806816
$672$		0			0
$673$	−2.14214			−0.0825733			−0.0412866	−	0.999147i	$-0.513146\pi$
$673$	−2.14214			−0.0825733			−0.0412866	+	0.999147i	$0.513146\pi$
$674$		0			0
$675$	2.00000	−	3.46410i	0.0769800	−	0.133333i
$676$		0			0
$677$	9.39949	+	16.2804i	0.361252	+	0.625707i	0.988167	−	0.153381i	$-0.0490161\pi$
$677$	9.39949	+	16.2804i	0.361252	+	0.625707i	−0.626915	+	0.779087i	$0.715683\pi$
$678$		0			0
$679$	1.17157	−	2.86976i	0.0449608	−	0.110131i
$680$		0			0
$681$	−3.32843	−	5.76500i	−0.127546	−	0.220915i
$682$		0			0
$683$	8.72183	−	15.1066i	0.333731	−	0.578040i	−0.649509	−	0.760354i	$-0.725025\pi$
$683$	8.72183	−	15.1066i	0.333731	−	0.578040i	0.983240	+	0.182314i	$0.0583588\pi$
$684$		0			0
$685$	−20.3726			−0.778396
$686$		0			0
$687$	1.72792			0.0659243
$688$		0			0
$689$	1.41421	−	2.44949i	0.0538772	−	0.0933181i
$690$		0			0
$691$	−13.5208	−	23.4187i	−0.514356	−	0.890891i	−0.999861	−	0.0166570i	$-0.994698\pi$
$691$	−13.5208	−	23.4187i	−0.514356	−	0.890891i	0.485505	−	0.874234i	$-0.338636\pi$
$692$		0			0
$693$	−6.82843	+	16.7262i	−0.259390	+	0.635374i
$694$		0			0
$695$	14.0000	+	24.2487i	0.531050	+	0.919806i
$696$		0			0
$697$	−0.585786	+	1.01461i	−0.0221882	+	0.0384312i
$698$		0			0
$699$	−0.899495			−0.0340220
$700$		0			0
$701$	14.0000			0.528773			0.264386	−	0.964417i	$-0.414831\pi$
$701$	14.0000			0.528773			0.264386	+	0.964417i	$0.414831\pi$
$702$		0			0
$703$	−27.7635	+	48.0877i	−1.04712	+	1.81366i
$704$		0			0
$705$	−3.94365	−	6.83060i	−0.148526	−	0.257255i
$706$		0			0
$707$	−21.8640	−	28.1946i	−0.822279	−	1.06037i
$708$		0			0
$709$	18.2990	+	31.6948i	0.687233	+	1.19032i	0.972729	+	0.231943i	$0.0745082\pi$
$709$	18.2990	+	31.6948i	0.687233	+	1.19032i	−0.285496	+	0.958380i	$0.592158\pi$
$710$		0			0
$711$	8.58579	−	14.8710i	0.321992	−	0.557707i
$712$		0			0
$713$	−29.2843			−1.09670
$714$		0			0
$715$	12.4853			0.466923
$716$		0			0
$717$	0.272078	−	0.471253i	0.0101609	−	0.0175993i
$718$		0			0
$719$	−15.5208	−	26.8828i	−0.578829	−	1.00256i	−0.995614	−	0.0935558i	$-0.970177\pi$
$719$	−15.5208	−	26.8828i	−0.578829	−	1.00256i	0.416785	−	0.909005i	$-0.363157\pi$
$720$		0			0
$721$	22.0563	−	3.01834i	0.821421	−	0.112409i
$722$		0			0
$723$	2.13604	+	3.69973i	0.0794401	+	0.137594i
$724$		0			0
$725$	−2.34315	+	4.05845i	−0.0870222	+	0.150727i
$726$		0			0
$727$	34.3431			1.27372			0.636858	−	0.770981i	$-0.280234\pi$
$727$	34.3431			1.27372			0.636858	+	0.770981i	$0.280234\pi$
$728$		0			0
$729$	−18.1716			−0.673021
$730$		0			0
$731$	0.828427	−	1.43488i	0.0306405	−	0.0530709i
$732$		0			0
$733$	−11.8431	−	20.5129i	−0.437437	−	0.757662i	0.560054	−	0.828456i	$-0.310780\pi$
$733$	−11.8431	−	20.5129i	−0.437437	−	0.757662i	−0.997491	+	0.0707935i	$0.977447\pi$
$734$		0			0
$735$	−3.78680	−	3.71029i	−0.139678	−	0.136856i
$736$		0			0
$737$	−3.32843	−	5.76500i	−0.122604	−	0.212357i
$738$		0			0
$739$	3.34924	−	5.80106i	0.123204	−	0.213395i	−0.797826	−	0.602888i	$-0.794016\pi$
$739$	3.34924	−	5.80106i	0.123204	−	0.213395i	0.921029	+	0.389493i	$0.127350\pi$
$740$		0			0
$741$	−7.51472			−0.276060
$742$		0			0
$743$	26.3431			0.966436			0.483218	−	0.875500i	$-0.339468\pi$
$743$	26.3431			0.966436			0.483218	+	0.875500i	$0.339468\pi$
$744$		0			0
$745$	5.64214	−	9.77247i	0.206712	−	0.358035i
$746$		0			0
$747$	−10.3431	−	17.9149i	−0.378436	−	0.655470i
$748$		0			0
$749$	−33.8137	+	4.62730i	−1.23553	+	0.169078i
$750$		0			0
$751$	−10.8640	−	18.8169i	−0.396432	−	0.686640i	0.596851	−	0.802352i	$-0.296418\pi$
$751$	−10.8640	−	18.8169i	−0.396432	−	0.686640i	−0.993283	+	0.115712i	$0.963085\pi$
$752$		0			0
$753$	−6.41421	+	11.1097i	−0.233747	+	0.404862i
$754$		0			0
$755$	−1.64466			−0.0598553
$756$		0			0
$757$	−6.14214			−0.223240			−0.111620	−	0.993751i	$-0.535604\pi$
$757$	−6.14214			−0.223240			−0.111620	+	0.993751i	$0.535604\pi$
$758$		0			0
$759$	2.62132	−	4.54026i	0.0951479	−	0.164801i
$760$		0			0
$761$	21.0563	+	36.4707i	0.763292	+	1.32206i	0.941145	+	0.338004i	$0.109752\pi$
$761$	21.0563	+	36.4707i	0.763292	+	1.32206i	−0.177853	+	0.984057i	$0.556915\pi$
$762$		0			0
$763$	13.2487	+	17.0849i	0.479636	+	0.618514i
$764$		0			0
$765$	0.443651	+	0.768426i	0.0160402	+	0.0277825i
$766$		0			0
$767$	−15.4142	+	26.6982i	−0.556575	+	0.964016i
$768$		0			0
$769$	13.8579			0.499727			0.249864	−	0.968281i	$-0.419614\pi$
$769$	13.8579			0.499727			0.249864	+	0.968281i	$0.419614\pi$
$770$		0			0
$771$	−1.87006			−0.0673485
$772$		0			0
$773$	4.57107	−	7.91732i	0.164410	−	0.284766i	−0.772036	−	0.635579i	$-0.780761\pi$
$773$	4.57107	−	7.91732i	0.164410	−	0.284766i	0.936446	+	0.350813i	$0.114095\pi$
$774$		0			0
$775$	4.62742	+	8.01492i	0.166222	+	0.287904i
$776$		0			0
$777$	3.58579	−	8.78335i	0.128639	−	0.315101i
$778$		0			0
$779$	21.8995	+	37.9310i	0.784631	+	1.35902i
$780$		0			0
$781$	16.4853	−	28.5533i	0.589890	−	1.02172i
$782$		0			0
$783$	−6.82843			−0.244028
$784$		0			0
$785$	−17.0833			−0.609728
$786$		0			0
$787$	−23.1066	+	40.0218i	−0.823661	+	1.42662i	0.0792766	+	0.996853i	$0.474739\pi$
$787$	−23.1066	+	40.0218i	−0.823661	+	1.42662i	−0.902938	+	0.429771i	$0.858594\pi$
$788$		0			0
$789$	2.25736	+	3.90986i	0.0803641	+	0.139195i
$790$		0			0
$791$	−18.1421	+	44.4390i	−0.645060	+	1.58007i
$792$		0			0
$793$	−12.2426	−	21.2049i	−0.434749	−	0.753007i
$794$		0			0
$795$	0.378680	−	0.655892i	0.0134304	−	0.0232621i
$796$		0			0
$797$	47.1127			1.66882			0.834409	−	0.551146i	$-0.185809\pi$
$797$	47.1127			1.66882			0.834409	+	0.551146i	$0.185809\pi$
$798$		0			0
$799$	−1.78680			−0.0632123
$800$		0			0
$801$	−12.7279	+	22.0454i	−0.449719	+	0.778936i
$802$		0			0
$803$	−17.6924	−	30.6441i	−0.624351	−	1.08141i
$804$		0			0
$805$	−15.5416	−	20.0417i	−0.547771	−	0.706376i
$806$		0			0
$807$	2.62132	+	4.54026i	0.0922748	+	0.159825i
$808$		0			0
$809$	8.98528	−	15.5630i	0.315906	−	0.547165i	−0.663724	−	0.747978i	$-0.731025\pi$
$809$	8.98528	−	15.5630i	0.315906	−	0.547165i	0.979630	+	0.200813i	$0.0643584\pi$
$810$		0			0
$811$	−17.6569			−0.620016			−0.310008	−	0.950734i	$-0.600332\pi$
$811$	−17.6569			−0.620016			−0.310008	+	0.950734i	$0.600332\pi$
$812$		0			0
$813$	12.5147			0.438910
$814$		0			0
$815$	6.17767	−	10.7000i	0.216394	−	0.374806i
$816$		0			0
$817$	−30.9706	−	53.6426i	−1.08352	−	1.87672i
$818$		0			0
$819$	−20.9706	+	2.86976i	−0.732771	+	0.100277i
$820$		0			0
$821$	−7.57107	−	13.1135i	−0.264232	−	0.457663i	0.703130	−	0.711061i	$-0.251785\pi$
$821$	−7.57107	−	13.1135i	−0.264232	−	0.457663i	−0.967362	+	0.253398i	$0.918452\pi$
$822$		0			0
$823$	24.0061	−	41.5798i	0.836800	−	1.44938i	−0.0557566	−	0.998444i	$-0.517757\pi$
$823$	24.0061	−	41.5798i	0.836800	−	1.44938i	0.892556	−	0.450936i	$-0.148910\pi$
$824$		0			0
$825$	−1.65685			−0.0576843
$826$		0			0
$827$	41.6569			1.44855			0.724275	−	0.689511i	$-0.242174\pi$
$827$	41.6569			1.44855			0.724275	+	0.689511i	$0.242174\pi$
$828$		0			0
$829$	−0.600505	+	1.04011i	−0.0208564	+	0.0361243i	−0.876265	−	0.481829i	$-0.839973\pi$
$829$	−0.600505	+	1.04011i	−0.0208564	+	0.0361243i	0.855409	+	0.517953i	$0.173306\pi$
$830$		0			0
$831$	2.13604	+	3.69973i	0.0740984	+	0.128342i
$832$		0			0
$833$	−1.15685	+	0.322666i	−0.0400826	+	0.0111797i
$834$		0			0
$835$	1.82843	+	3.16693i	0.0632753	+	0.109596i
$836$		0			0
$837$	−6.74264	+	11.6786i	−0.233060	+	0.403671i
$838$		0			0
$839$	−3.31371			−0.114402			−0.0572010	−	0.998363i	$-0.518218\pi$
$839$	−3.31371			−0.114402			−0.0572010	+	0.998363i	$0.518218\pi$
$840$		0			0
$841$	−21.0000			−0.724138
$842$		0			0
$843$	−2.58579	+	4.47871i	−0.0890592	+	0.154255i
$844$		0			0
$845$	−4.57107	−	7.91732i	−0.157250	−	0.272364i
$846$		0			0
$847$	−13.5563	+	1.85514i	−0.465802	+	0.0637435i
$848$		0			0
$849$	1.15685	+	2.00373i	0.0397031	+	0.0687678i
$850$		0			0
$851$	22.6924	−	39.3044i	0.777885	−	1.34734i
$852$		0			0
$853$	−40.4853			−1.38619			−0.693095	−	0.720846i	$-0.743753\pi$
$853$	−40.4853			−1.38619			−0.693095	+	0.720846i	$0.743753\pi$
$854$		0			0
$855$	33.1716			1.13444
$856$		0			0
$857$	−12.6716	+	21.9478i	−0.432853	+	0.749723i	−0.997118	−	0.0758709i	$-0.975826\pi$
$857$	−12.6716	+	21.9478i	−0.432853	+	0.749723i	0.564265	+	0.825594i	$0.309160\pi$
$858$		0			0
$859$	−2.72183	−	4.71434i	−0.0928675	−	0.160851i	0.815849	−	0.578265i	$-0.196270\pi$
$859$	−2.72183	−	4.71434i	−0.0928675	−	0.160851i	−0.908717	+	0.417414i	$0.862937\pi$
$860$		0			0
$861$	−4.58579	−	5.91359i	−0.156283	−	0.201535i
$862$		0			0
$863$	−16.6924	−	28.9121i	−0.568216	−	0.984178i	−0.996743	−	0.0806492i	$-0.974301\pi$
$863$	−16.6924	−	28.9121i	−0.568216	−	0.984178i	0.428527	−	0.903529i	$-0.359033\pi$
$864$		0			0
$865$	10.0563	−	17.4181i	0.341926	−	0.592233i
$866$		0			0
$867$	7.02944			0.238732
$868$		0			0
$869$	−14.6569			−0.497200
$870$		0			0
$871$	3.89949	−	6.75412i	0.132129	−	0.228855i
$872$		0			0
$873$	−1.65685	−	2.86976i	−0.0560760	−	0.0971265i
$874$		0			0
$875$	−12.1716	+	29.8141i	−0.411474	+	1.00790i
$876$		0			0
$877$	−25.7132	−	44.5366i	−0.868273	−	1.50389i	−0.863760	−	0.503903i	$-0.831897\pi$
$877$	−25.7132	−	44.5366i	−0.868273	−	1.50389i	−0.00451320	−	0.999990i	$-0.501437\pi$
$878$		0			0
$879$	5.92893	−	10.2692i	0.199978	−	0.346372i
$880$		0			0
$881$	−26.0000			−0.875962			−0.437981	−	0.898984i	$-0.644306\pi$
$881$	−26.0000			−0.875962			−0.437981	+	0.898984i	$0.644306\pi$
$882$		0			0
$883$	−41.2548			−1.38834			−0.694168	−	0.719813i	$-0.744227\pi$
$883$	−41.2548			−1.38834			−0.694168	+	0.719813i	$0.744227\pi$
$884$		0			0
$885$	−4.12742	+	7.14890i	−0.138742	+	0.240308i
$886$		0			0
$887$	−15.5503	−	26.9338i	−0.522126	−	0.904349i	−0.999669	−	0.0257406i	$-0.991806\pi$
$887$	−15.5503	−	26.9338i	−0.522126	−	0.904349i	0.477542	−	0.878609i	$-0.341528\pi$
$888$		0			0
$889$	5.65685	−	13.8564i	0.189725	−	0.464729i
$890$		0			0
$891$	9.03553	+	15.6500i	0.302702	+	0.524295i
$892$		0			0
$893$	−33.3995	+	57.8496i	−1.11767	+	1.93586i
$894$		0			0
$895$	−10.2132			−0.341390
$896$		0			0
$897$	6.14214			0.205080
$898$		0			0
$899$	7.89949	−	13.6823i	0.263463	−	0.456331i
$900$		0			0
$901$	−0.0857864	−	0.148586i	−0.00285796	−	0.00495013i
$902$		0			0
$903$	6.48528	+	8.36308i	0.215817	+	0.278306i
$904$		0			0
$905$	−8.51472	−	14.7479i	−0.283039	−	0.490238i
$906$		0			0
$907$	−12.7635	+	22.1070i	−0.423804	+	0.734049i	−0.996308	−	0.0858524i	$-0.972639\pi$
$907$	−12.7635	+	22.1070i	−0.423804	+	0.734049i	0.572504	+	0.819902i	$0.305972\pi$
$908$		0			0
$909$	−38.1421			−1.26509
$910$		0			0
$911$	8.00000			0.265052			0.132526	−	0.991180i	$-0.457691\pi$
$911$	8.00000			0.265052			0.132526	+	0.991180i	$0.457691\pi$
$912$		0			0
$913$	−8.82843	+	15.2913i	−0.292178	+	0.506068i
$914$		0			0
$915$	−3.27817	−	5.67796i	−0.108373	−	0.187708i
$916$		0			0
$917$	20.2574	−	2.77216i	0.668957	−	0.0915447i
$918$		0			0
$919$	3.27817	+	5.67796i	0.108137	+	0.187299i	0.915016	−	0.403419i	$-0.132178\pi$
$919$	3.27817	+	5.67796i	0.108137	+	0.187299i	−0.806879	+	0.590717i	$0.798845\pi$
$920$		0			0
$921$	2.97056	−	5.14517i	0.0978834	−	0.169539i
$922$		0			0
$923$	38.6274			1.27144
$924$		0			0
$925$	−14.3431			−0.471600
$926$		0			0
$927$	11.8995	−	20.6105i	0.390831	−	0.676939i
$928$		0			0
$929$	9.67157	+	16.7517i	0.317314	+	0.549604i	0.979927	−	0.199358i	$-0.0638857\pi$
$929$	9.67157	+	16.7517i	0.317314	+	0.549604i	−0.662613	+	0.748962i	$0.730552\pi$
$930$		0			0
$931$	−11.1777	+	43.4859i	−0.366333	+	1.42519i
$932$		0			0
$933$	−3.88478	−	6.72863i	−0.127182	−	0.220285i
$934$		0			0
$935$	0.378680	−	0.655892i	0.0123841	−	0.0214500i
$936$		0			0
$937$	16.6274			0.543194			0.271597	−	0.962411i	$-0.412448\pi$
$937$	16.6274			0.543194			0.271597	+	0.962411i	$0.412448\pi$
$938$		0			0
$939$	12.1299			0.395846
$940$		0			0
$941$	19.1274	−	33.1297i	0.623536	−	1.08000i	−0.365286	−	0.930895i	$-0.619029\pi$
$941$	19.1274	−	33.1297i	0.623536	−	1.08000i	0.988822	−	0.149101i	$-0.0476378\pi$
$942$		0			0
$943$	−17.8995	−	31.0028i	−0.582888	−	1.00959i
$944$		0			0
$945$	−11.5711	+	1.58346i	−0.376407	+	0.0515101i
$946$		0			0
$947$	9.10660	+	15.7731i	0.295925	+	0.512557i	0.975200	−	0.221327i	$-0.0710389\pi$
$947$	9.10660	+	15.7731i	0.295925	+	0.512557i	−0.679275	+	0.733884i	$0.737706\pi$
$948$		0			0
$949$	20.7279	−	35.9018i	0.672857	−	1.16542i
$950$		0			0
$951$	4.01219			0.130104
$952$		0			0
$953$	−27.1127			−0.878266			−0.439133	−	0.898422i	$-0.644714\pi$
$953$	−27.1127			−0.878266			−0.439133	+	0.898422i	$0.644714\pi$
$954$		0			0
$955$	−8.13604	+	14.0920i	−0.263276	+	0.456007i
$956$		0			0
$957$	1.41421	+	2.44949i	0.0457150	+	0.0791808i
$958$		0			0
$959$	−18.0650	−	23.2956i	−0.583348	−	0.752256i
$960$		0			0
$961$	−0.100505	−	0.174080i	−0.00324210	−	0.00561548i
$962$		0			0
$963$	−18.2426	+	31.5972i	−0.587861	+	1.01820i
$964$		0			0
$965$	16.7157			0.538098
$966$		0			0
$967$	−18.3431			−0.589876			−0.294938	−	0.955516i	$-0.595299\pi$
$967$	−18.3431			−0.589876			−0.294938	+	0.955516i	$0.595299\pi$
$968$		0			0
$969$	−0.227922	+	0.394773i	−0.00732191	+	0.0126819i
$970$		0			0
$971$	17.7929	+	30.8182i	0.571001	+	0.989003i	0.996463	+	0.0840268i	$0.0267781\pi$
$971$	17.7929	+	30.8182i	0.571001	+	0.989003i	−0.425462	+	0.904976i	$0.639889\pi$
$972$		0			0
$973$	−15.3137	+	37.5108i	−0.490935	+	1.20254i
$974$		0			0
$975$	−0.970563	−	1.68106i	−0.0310829	−	0.0538371i
$976$		0			0
$977$	17.2574	−	29.8906i	0.552112	−	0.956286i	−0.446010	−	0.895028i	$-0.647155\pi$
$977$	17.2574	−	29.8906i	0.552112	−	0.956286i	0.998122	−	0.0612578i	$-0.0195112\pi$
$978$		0			0
$979$	21.7279			0.694427
$980$		0			0
$981$	23.1127			0.737932
$982$		0			0
$983$	−13.4203	+	23.2447i	−0.428041	+	0.741389i	−0.996699	−	0.0811848i	$-0.974130\pi$
$983$	−13.4203	+	23.2447i	−0.428041	+	0.741389i	0.568658	+	0.822574i	$0.307463\pi$
$984$		0			0
$985$	−17.2132	−	29.8141i	−0.548458	−	0.949958i
$986$		0			0
$987$	4.31371	−	10.5664i	0.137307	−	0.336332i
$988$		0			0
$989$	25.3137	+	43.8446i	0.804929	+	1.39418i
$990$		0			0
$991$	22.3492	−	38.7100i	0.709947	−	1.22966i	−0.254929	−	0.966960i	$-0.582052\pi$
$991$	22.3492	−	38.7100i	0.709947	−	1.22966i	0.964876	−	0.262705i	$-0.0846145\pi$
$992$		0			0
$993$	−11.7696			−0.373495
$994$		0			0
$995$	−20.5563			−0.651680
$996$		0			0
$997$	22.6421	−	39.2173i	0.717084	−	1.24203i	−0.245067	−	0.969506i	$-0.578810\pi$
$997$	22.6421	−	39.2173i	0.717084	−	1.24203i	0.962150	−	0.272519i	$-0.0878568\pi$
$998$		0			0
$999$	−10.4497	−	18.0995i	−0.330615	−	0.572643i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	224.2.i.a.193.2	yes	4
3.2	odd	2		2016.2.s.q.865.1		4
4.3	odd	2		224.2.i.d.193.1	yes	4
7.2	even	3	inner	224.2.i.a.65.2	✓	4
7.3	odd	6		1568.2.a.j.1.2		2
7.4	even	3		1568.2.a.w.1.1		2
7.5	odd	6		1568.2.i.x.961.1		4
7.6	odd	2		1568.2.i.x.1537.1		4
8.3	odd	2		448.2.i.g.193.2		4
8.5	even	2		448.2.i.j.193.1		4
12.11	even	2		2016.2.s.s.865.1		4
21.2	odd	6		2016.2.s.q.289.1		4
28.3	even	6		1568.2.a.u.1.1		2
28.11	odd	6		1568.2.a.l.1.2		2
28.19	even	6		1568.2.i.o.961.2		4
28.23	odd	6		224.2.i.d.65.1	yes	4
28.27	even	2		1568.2.i.o.1537.2		4
56.3	even	6		3136.2.a.be.1.2		2
56.11	odd	6		3136.2.a.bw.1.1		2
56.37	even	6		448.2.i.j.65.1		4
56.45	odd	6		3136.2.a.bx.1.1		2
56.51	odd	6		448.2.i.g.65.2		4
56.53	even	6		3136.2.a.bd.1.2		2
84.23	even	6		2016.2.s.s.289.1		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
224.2.i.a.65.2	✓	4	7.2	even	3	inner
224.2.i.a.193.2	yes	4	1.1	even	1	trivial
224.2.i.d.65.1	yes	4	28.23	odd	6
224.2.i.d.193.1	yes	4	4.3	odd	2
448.2.i.g.65.2		4	56.51	odd	6
448.2.i.g.193.2		4	8.3	odd	2
448.2.i.j.65.1		4	56.37	even	6
448.2.i.j.193.1		4	8.5	even	2
1568.2.a.j.1.2		2	7.3	odd	6
1568.2.a.l.1.2		2	28.11	odd	6
1568.2.a.u.1.1		2	28.3	even	6
1568.2.a.w.1.1		2	7.4	even	3
1568.2.i.o.961.2		4	28.19	even	6
1568.2.i.o.1537.2		4	28.27	even	2
1568.2.i.x.961.1		4	7.5	odd	6
1568.2.i.x.1537.1		4	7.6	odd	2
2016.2.s.q.289.1		4	21.2	odd	6
2016.2.s.q.865.1		4	3.2	odd	2
2016.2.s.s.289.1		4	84.23	even	6
2016.2.s.s.865.1		4	12.11	even	2
3136.2.a.bd.1.2		2	56.53	even	6
3136.2.a.be.1.2		2	56.3	even	6
3136.2.a.bw.1.1		2	56.11	odd	6
3136.2.a.bx.1.1		2	56.45	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:	\( N \)	\(=\)	\( 224 = 2^{5} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	224.i (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.207107 - 0.358719i) q^{3} +(0.914214 + 1.58346i) q^{5} +(-1.00000 + 2.44949i) q^{7} +(1.41421 + 2.44949i) q^{9} +O(q^{10})\)	\(q+(0.207107 - 0.358719i) q^{3} +(0.914214 + 1.58346i) q^{5} +(-1.00000 + 2.44949i) q^{7} +(1.41421 + 2.44949i) q^{9} +(1.20711 - 2.09077i) q^{11} +2.82843 q^{13} +0.757359 q^{15} +(0.0857864 - 0.148586i) q^{17} +(-3.20711 - 5.55487i) q^{19} +(0.671573 + 0.866025i) q^{21} +(2.62132 + 4.54026i) q^{23} +(0.828427 - 1.43488i) q^{25} +2.41421 q^{27} -2.82843 q^{29} +(-2.79289 + 4.83743i) q^{31} +(-0.500000 - 0.866025i) q^{33} +(-4.79289 + 0.655892i) q^{35} +(-4.32843 - 7.49706i) q^{37} +(0.585786 - 1.01461i) q^{39} -6.82843 q^{41} +9.65685 q^{43} +(-2.58579 + 4.47871i) q^{45} +(-5.20711 - 9.01897i) q^{47} +(-5.00000 - 4.89898i) q^{49} +(-0.0355339 - 0.0615465i) q^{51} +(0.500000 - 0.866025i) q^{53} +4.41421 q^{55} -2.65685 q^{57} +(-5.44975 + 9.43924i) q^{59} +(-4.32843 - 7.49706i) q^{61} +(-7.41421 + 1.01461i) q^{63} +(2.58579 + 4.47871i) q^{65} +(1.37868 - 2.38794i) q^{67} +2.17157 q^{69} +13.6569 q^{71} +(7.32843 - 12.6932i) q^{73} +(-0.343146 - 0.594346i) q^{75} +(3.91421 + 5.04757i) q^{77} +(-3.03553 - 5.25770i) q^{79} +(-3.74264 + 6.48244i) q^{81} -7.31371 q^{83} +0.313708 q^{85} +(-0.585786 + 1.01461i) q^{87} +(4.50000 + 7.79423i) q^{89} +(-2.82843 + 6.92820i) q^{91} +(1.15685 + 2.00373i) q^{93} +(5.86396 - 10.1567i) q^{95} -1.17157 q^{97} +6.82843 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 2 q^{3} - 2 q^{5} - 4 q^{7}+O(q^{10}) \) 4 * q - 2 * q^3 - 2 * q^5 - 4 * q^7	\( 4 q - 2 q^{3} - 2 q^{5} - 4 q^{7} + 2 q^{11} + 20 q^{15} + 6 q^{17} - 10 q^{19} + 14 q^{21} + 2 q^{23} - 8 q^{25} + 4 q^{27} - 14 q^{31} - 2 q^{33} - 22 q^{35} - 6 q^{37} + 8 q^{39} - 16 q^{41} + 16 q^{43} - 16 q^{45} - 18 q^{47} - 20 q^{49} + 14 q^{51} + 2 q^{53} + 12 q^{55} + 12 q^{57} - 2 q^{59} - 6 q^{61} - 24 q^{63} + 16 q^{65} + 14 q^{67} + 20 q^{69} + 32 q^{71} + 18 q^{73} - 24 q^{75} + 10 q^{77} + 2 q^{79} + 2 q^{81} + 16 q^{83} - 44 q^{85} - 8 q^{87} + 18 q^{89} - 18 q^{93} - 2 q^{95} - 16 q^{97} + 16 q^{99}+O(q^{100}) \) 4 * q - 2 * q^3 - 2 * q^5 - 4 * q^7 + 2 * q^11 + 20 * q^15 + 6 * q^17 - 10 * q^19 + 14 * q^21 + 2 * q^23 - 8 * q^25 + 4 * q^27 - 14 * q^31 - 2 * q^33 - 22 * q^35 - 6 * q^37 + 8 * q^39 - 16 * q^41 + 16 * q^43 - 16 * q^45 - 18 * q^47 - 20 * q^49 + 14 * q^51 + 2 * q^53 + 12 * q^55 + 12 * q^57 - 2 * q^59 - 6 * q^61 - 24 * q^63 + 16 * q^65 + 14 * q^67 + 20 * q^69 + 32 * q^71 + 18 * q^73 - 24 * q^75 + 10 * q^77 + 2 * q^79 + 2 * q^81 + 16 * q^83 - 44 * q^85 - 8 * q^87 + 18 * q^89 - 18 * q^93 - 2 * q^95 - 16 * q^97 + 16 * q^99

Introduction

L-functions

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Database

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