LMFDB - Embedded newform 208.2.w.c.17.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [208,2,Mod(17,208)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(208, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 0, 1]))

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

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

chi := DirichletCharacter("208.17");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 208 = 2^{4} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	208.w (of order $6$, degree $2$, not minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$1.66088836204$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(\zeta_{6})$
Coefficient field:	8.0.195105024.2
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 4x^{7} + 5x^{6} + 4x^{5} - 20x^{4} + 12x^{3} + 45x^{2} - 108x + 81 $ x^8 - 4x^7 + 5x^6 + 4x^5 - 20x^4 + 12x^3 + 45x^2 - 108*x + 81
Coefficient ring:	$\Z[a_1, \ldots, a_{9}]$
Coefficient ring index:	$ 2^{4} $
Twist minimal:	no (minimal twist has level 104)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			17.2
Root			$1.72124 - 0.193255i$ of defining polynomial
Character	$\chi$	$=$	208.17
Dual form			208.2.w.c.49.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.693255 + 1.20075i) q^{3} -3.44247i q^{5} +(2.74922 - 1.58726i) q^{7} +(0.538796 + 0.933222i) q^{9} +O(q^{10})$	\(q+(-0.693255 + 1.20075i) q^{3} -3.44247i q^{5} +(2.74922 - 1.58726i) q^{7} +(0.538796 + 0.933222i) q^{9} +(-2.74922 - 1.58726i) q^{11} +(3.59476 - 0.278764i) q^{13} +(4.13356 + 2.38651i) q^{15} +(0.886509 + 1.53548i) q^{17} +(5.54387 - 3.20075i) q^{19} +4.40150i q^{21} +(-0.693255 + 1.20075i) q^{23} -6.85061 q^{25} -5.65362 q^{27} +(-2.55596 + 4.42706i) q^{29} +1.35218i q^{31} +(3.81181 - 2.20075i) q^{33} +(-5.46410 - 9.46410i) q^{35} +(-9.79308 - 5.65404i) q^{37} +(-2.15736 + 4.50967i) q^{39} +(-1.96410 - 1.13397i) q^{41} +(2.13573 + 3.69919i) q^{43} +(3.21259 - 1.85479i) q^{45} +1.57603i q^{47} +(1.53880 - 2.66527i) q^{49} -2.45831 q^{51} +3.73869 q^{53} +(-5.46410 + 9.46410i) q^{55} +8.87574i q^{57} +(-11.7118 + 6.76178i) q^{59} +(5.40657 + 9.36446i) q^{61} +(2.96254 + 1.71042i) q^{63} +(-0.959638 - 12.3749i) q^{65} +(-0.882772 - 0.509669i) q^{67} +(-0.961204 - 1.66485i) q^{69} +(11.5439 - 6.66485i) q^{71} +5.33055i q^{73} +(4.74922 - 8.22589i) q^{75} -10.0776 q^{77} +11.1521 q^{79} +(2.30301 - 3.98893i) q^{81} +14.3490i q^{83} +(5.28584 - 3.05178i) q^{85} +(-3.54387 - 6.13815i) q^{87} +(4.00567 + 2.31268i) q^{89} +(9.44030 - 6.47220i) q^{91} +(-1.62363 - 0.937403i) q^{93} +(-11.0185 - 19.0846i) q^{95} +(-10.2385 + 5.91117i) q^{97} -3.42084i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 2 q^{3} + 6 q^{7} - 6 q^{9}+O(q^{10}) $ 8 * q - 2 * q^3 + 6 * q^7 - 6 * q^9	$ 8 q - 2 q^{3} + 6 q^{7} - 6 q^{9} - 6 q^{11} + 6 q^{13} + 6 q^{19} - 2 q^{23} - 20 q^{25} + 28 q^{27} - 8 q^{29} + 6 q^{33} - 16 q^{35} - 24 q^{37} + 14 q^{39} + 12 q^{41} - 6 q^{43} + 30 q^{45} + 2 q^{49} - 68 q^{51} + 20 q^{53} - 16 q^{55} - 18 q^{59} - 4 q^{61} - 36 q^{63} + 14 q^{65} + 42 q^{67} - 18 q^{69} + 54 q^{71} + 22 q^{75} - 60 q^{77} - 16 q^{79} - 20 q^{81} + 6 q^{85} + 10 q^{87} - 18 q^{89} + 46 q^{91} + 36 q^{93} - 16 q^{95} + 30 q^{97}+O(q^{100}) $ 8 * q - 2 * q^3 + 6 * q^7 - 6 * q^9 - 6 * q^11 + 6 * q^13 + 6 * q^19 - 2 * q^23 - 20 * q^25 + 28 * q^27 - 8 * q^29 + 6 * q^33 - 16 * q^35 - 24 * q^37 + 14 * q^39 + 12 * q^41 - 6 * q^43 + 30 * q^45 + 2 * q^49 - 68 * q^51 + 20 * q^53 - 16 * q^55 - 18 * q^59 - 4 * q^61 - 36 * q^63 + 14 * q^65 + 42 * q^67 - 18 * q^69 + 54 * q^71 + 22 * q^75 - 60 * q^77 - 16 * q^79 - 20 * q^81 + 6 * q^85 + 10 * q^87 - 18 * q^89 + 46 * q^91 + 36 * q^93 - 16 * q^95 + 30 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/208\mathbb{Z}\right)^\times$.

$n$	$53$	$79$	$145$
$\chi(n)$	$1$	$1$	$e\left(\frac{1}{6}\right)$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	−0.693255	+	1.20075i	−0.400251	+	0.693255i	−0.993756	−	0.111576i	$-0.964410\pi$
$3$	−0.693255	+	1.20075i	−0.400251	+	0.693255i	0.593505	+	0.804830i	$0.297744\pi$
$4$		0			0
$5$		−	3.44247i		−	1.53952i	−0.638333	−	0.769760i	$-0.720376\pi$
$5$		−	3.44247i		−	1.53952i	0.638333	−	0.769760i	$-0.279624\pi$
$6$		0			0
$7$	2.74922	−	1.58726i	1.03911	−	0.599928i	0.119526	−	0.992831i	$-0.461862\pi$
$7$	2.74922	−	1.58726i	1.03911	−	0.599928i	0.919580	+	0.392903i	$0.128529\pi$
$8$		0			0
$9$	0.538796	+	0.933222i	0.179599	+	0.311074i
$10$		0			0
$11$	−2.74922	−	1.58726i	−0.828920	−	0.478577i	0.0245627	−	0.999698i	$-0.492181\pi$
$11$	−2.74922	−	1.58726i	−0.828920	−	0.478577i	−0.853483	+	0.521121i	$0.825514\pi$
$12$		0			0
$13$	3.59476	−	0.278764i	0.997007	−	0.0773153i
$13$	3.59476	−	0.278764i	0.997007	−	0.0773153i
$14$		0			0
$15$	4.13356	+	2.38651i	1.06728	+	0.616194i
$16$		0			0
$17$	0.886509	+	1.53548i	0.215010	+	0.372408i	0.953276	−	0.302102i	$-0.0976882\pi$
$17$	0.886509	+	1.53548i	0.215010	+	0.372408i	−0.738266	+	0.674510i	$0.764355\pi$
$18$		0			0
$19$	5.54387	−	3.20075i	1.27185	−	0.734303i	0.296514	−	0.955029i	$-0.404176\pi$
$19$	5.54387	−	3.20075i	1.27185	−	0.734303i	0.975336	+	0.220726i	$0.0708425\pi$
$20$		0			0
$21$			4.40150i			0.960487i
$22$		0			0
$23$	−0.693255	+	1.20075i	−0.144554	+	0.250374i	−0.929206	−	0.369561i	$-0.879508\pi$
$23$	−0.693255	+	1.20075i	−0.144554	+	0.250374i	0.784653	+	0.619936i	$0.212841\pi$
$24$		0			0
$25$	−6.85061			−1.37012
$26$		0			0
$27$	−5.65362			−1.08804
$28$		0			0
$29$	−2.55596	+	4.42706i	−0.474630	+	0.822084i	−0.999578	−	0.0290507i	$-0.990752\pi$
$29$	−2.55596	+	4.42706i	−0.474630	+	0.822084i	0.524948	+	0.851135i	$0.324085\pi$
$30$		0			0
$31$			1.35218i			0.242858i	0.992600	+	0.121429i	$0.0387477\pi$
$31$			1.35218i			0.242858i	−0.992600	+	0.121429i	$0.961252\pi$
$32$		0			0
$33$	3.81181	−	2.20075i	0.663552	−	0.383102i
$34$		0			0
$35$	−5.46410	−	9.46410i	−0.923602	−	1.59973i
$36$		0			0
$37$	−9.79308	−	5.65404i	−1.60997	−	0.929518i	−0.989374	−	0.145390i	$-0.953556\pi$
$37$	−9.79308	−	5.65404i	−1.60997	−	0.929518i	−0.620598	−	0.784129i	$-0.713110\pi$
$38$		0			0
$39$	−2.15736	+	4.50967i	−0.345453	+	0.722125i
$40$		0			0
$41$	−1.96410	−	1.13397i	−0.306741	−	0.177097i	0.338726	−	0.940885i	$-0.390004\pi$
$41$	−1.96410	−	1.13397i	−0.306741	−	0.177097i	−0.645467	+	0.763788i	$0.723337\pi$
$42$		0			0
$43$	2.13573	+	3.69919i	0.325695	+	0.564121i	0.981653	−	0.190677i	$-0.0610683\pi$
$43$	2.13573	+	3.69919i	0.325695	+	0.564121i	−0.655958	+	0.754798i	$0.727735\pi$
$44$		0			0
$45$	3.21259	−	1.85479i	0.478905	−	0.276496i
$46$		0			0
$47$			1.57603i			0.229887i	0.993372	+	0.114944i	$0.0366687\pi$
$47$			1.57603i			0.229887i	−0.993372	+	0.114944i	$0.963331\pi$
$48$		0			0
$49$	1.53880	−	2.66527i	0.219828	−	0.380753i
$50$		0			0
$51$	−2.45831			−0.344232
$52$		0			0
$53$	3.73869			0.513548			0.256774	−	0.966471i	$-0.417340\pi$
$53$	3.73869			0.513548			0.256774	+	0.966471i	$0.417340\pi$
$54$		0			0
$55$	−5.46410	+	9.46410i	−0.736779	+	1.27614i
$56$		0			0
$57$			8.87574i			1.17562i
$58$		0			0
$59$	−11.7118	+	6.76178i	−1.52474	+	0.880309i	−0.525170	+	0.850997i	$0.675998\pi$
$59$	−11.7118	+	6.76178i	−1.52474	+	0.880309i	−0.999570	+	0.0293119i	$0.990668\pi$
$60$		0			0
$61$	5.40657	+	9.36446i	0.692241	+	1.19900i	0.971102	+	0.238665i	$0.0767097\pi$
$61$	5.40657	+	9.36446i	0.692241	+	1.19900i	−0.278861	+	0.960331i	$0.589957\pi$
$62$		0			0
$63$	2.96254	+	1.71042i	0.373244	+	0.215493i
$64$		0			0
$65$	−0.959638	−	12.3749i	−0.119028	−	1.53491i
$66$		0			0
$67$	−0.882772	−	0.509669i	−0.107848	−	0.0622659i	0.445106	−	0.895478i	$-0.353166\pi$
$67$	−0.882772	−	0.509669i	−0.107848	−	0.0622659i	−0.552954	+	0.833212i	$0.686499\pi$
$68$		0			0
$69$	−0.961204	−	1.66485i	−0.115715	−	0.200425i
$70$		0			0
$71$	11.5439	−	6.66485i	1.37000	−	0.790973i	0.379077	−	0.925365i	$-0.376242\pi$
$71$	11.5439	−	6.66485i	1.37000	−	0.790973i	0.990928	+	0.134393i	$0.0429084\pi$
$72$		0			0
$73$			5.33055i			0.623893i	0.950100	+	0.311947i	$0.100981\pi$
$73$			5.33055i			0.623893i	−0.950100	+	0.311947i	$0.899019\pi$
$74$		0			0
$75$	4.74922	−	8.22589i	0.548392	−	0.949843i
$76$		0			0
$77$	−10.0776			−1.14845
$78$		0			0
$79$	11.1521			1.25470			0.627352	−	0.778736i	$-0.284139\pi$
$79$	11.1521			1.25470			0.627352	+	0.778736i	$0.284139\pi$
$80$		0			0
$81$	2.30301	−	3.98893i	0.255890	−	0.443214i
$82$		0			0
$83$			14.3490i			1.57501i	0.616307	+	0.787506i	$0.288628\pi$
$83$			14.3490i			1.57501i	−0.616307	+	0.787506i	$0.711372\pi$
$84$		0			0
$85$	5.28584	−	3.05178i	0.573330	−	0.331012i
$86$		0			0
$87$	−3.54387	−	6.13815i	−0.379942	−	0.658079i
$88$		0			0
$89$	4.00567	+	2.31268i	0.424601	+	0.245143i	0.697044	−	0.717029i	$-0.254498\pi$
$89$	4.00567	+	2.31268i	0.424601	+	0.245143i	−0.272443	+	0.962172i	$0.587832\pi$
$90$		0			0
$91$	9.44030	−	6.47220i	0.989612	−	0.678471i
$92$		0			0
$93$	−1.62363	−	0.937403i	−0.168362	−	0.0972041i
$94$		0			0
$95$	−11.0185	−	19.0846i	−1.13047	−	1.95804i
$96$		0			0
$97$	−10.2385	+	5.91117i	−1.03956	+	0.600189i	−0.919708	−	0.392603i	$-0.871575\pi$
$97$	−10.2385	+	5.91117i	−1.03956	+	0.600189i	−0.119849	+	0.992792i	$0.538241\pi$
$98$		0			0
$99$		−	3.42084i		−	0.343808i
$100$		0			0
$101$	3.16945	−	5.48965i	0.315372	−	0.546241i	−0.664144	−	0.747605i	$-0.731204\pi$
$101$	3.16945	−	5.48965i	0.315372	−	0.546241i	0.979517	+	0.201363i	$0.0645372\pi$
$102$		0			0
$103$	−6.88494			−0.678394			−0.339197	−	0.940715i	$-0.610155\pi$
$103$	−6.88494			−0.678394			−0.339197	+	0.940715i	$0.610155\pi$
$104$		0			0
$105$	15.1521			1.47869
$106$		0			0
$107$	0.0797637	−	0.138155i	0.00771104	−	0.0133559i	−0.862144	−	0.506663i	$-0.830879\pi$
$107$	0.0797637	−	0.138155i	0.00771104	−	0.0133559i	0.869855	+	0.493307i	$0.164212\pi$
$108$		0			0
$109$			10.9282i			1.04673i	0.852108	+	0.523366i	$0.175324\pi$
$109$			10.9282i			1.04673i	−0.852108	+	0.523366i	$0.824676\pi$
$110$		0			0
$111$	13.5782	−	7.83938i	1.28879	−	0.744081i
$112$		0			0
$113$	−5.99843	−	10.3896i	−0.564285	−	0.977371i	−0.997116	−	0.0758954i	$-0.975819\pi$
$113$	−5.99843	−	10.3896i	−0.564285	−	0.977371i	0.432831	−	0.901475i	$-0.357515\pi$
$114$		0			0
$115$	4.13356	+	2.38651i	0.385456	+	0.222543i
$116$		0			0
$117$	2.19699	+	3.20451i	0.203112	+	0.296257i
$118$		0			0
$119$	4.87441	+	2.81424i	0.446837	+	0.257981i
$120$		0			0
$121$	−0.461204	−	0.798828i	−0.0419276	−	0.0726208i
$122$		0			0
$123$	2.72324	−	1.57227i	0.245547	−	0.141766i
$124$		0			0
$125$			6.37067i			0.569810i
$126$		0			0
$127$	−6.26928	+	10.8587i	−0.556309	+	0.963555i	0.441492	+	0.897265i	$0.354449\pi$
$127$	−6.26928	+	10.8587i	−0.556309	+	0.963555i	−0.997800	+	0.0662897i	$0.978884\pi$
$128$		0			0
$129$	−5.92241			−0.521439
$130$		0			0
$131$	9.33891			0.815944			0.407972	−	0.912994i	$-0.366236\pi$
$131$	9.33891			0.815944			0.407972	+	0.912994i	$0.366236\pi$
$132$		0			0
$133$	10.1609	−	17.5991i	0.881058	−	1.52604i
$134$		0			0
$135$			19.4624i			1.67506i
$136$		0			0
$137$	−4.46254	+	2.57645i	−0.381260	+	0.220121i	−0.678366	−	0.734724i	$-0.737312\pi$
$137$	−4.46254	+	2.57645i	−0.381260	+	0.220121i	0.297106	+	0.954844i	$0.403978\pi$
$138$		0			0
$139$	1.59983	+	2.77098i	0.135696	+	0.235032i	0.925863	−	0.377859i	$-0.123340\pi$
$139$	1.59983	+	2.77098i	0.135696	+	0.235032i	−0.790167	+	0.612891i	$0.790006\pi$
$140$		0			0
$141$	−1.89242	−	1.09259i	−0.159370	−	0.0920125i
$142$		0			0
$143$	−10.3252	−	4.93944i	−0.863440	−	0.413057i
$144$		0			0
$145$	15.2400	+	8.79883i	1.26561	+	0.730703i
$146$		0			0
$147$	2.13356	+	3.69543i	0.175973	+	0.304794i
$148$		0			0
$149$	6.59922	−	3.81006i	0.540629	−	0.312133i	−0.204705	−	0.978824i	$-0.565623\pi$
$149$	6.59922	−	3.81006i	0.540629	−	0.312133i	0.745334	+	0.666691i	$0.232290\pi$
$150$		0			0
$151$		−	12.5042i		−	1.01758i	−0.860891	−	0.508790i	$-0.830093\pi$
$151$		−	12.5042i		−	1.01758i	0.860891	−	0.508790i	$-0.169907\pi$
$152$		0			0
$153$	−0.955296	+	1.65462i	−0.0772311	+	0.133768i
$154$		0			0
$155$	4.65483			0.373885
$156$		0			0
$157$	1.80735			0.144242			0.0721211	−	0.997396i	$-0.477023\pi$
$157$	1.80735			0.144242			0.0721211	+	0.997396i	$0.477023\pi$
$158$		0			0
$159$	−2.59186	+	4.48923i	−0.205548	+	0.356019i
$160$		0			0
$161$			4.40150i			0.346887i
$162$		0			0
$163$	−10.1790	+	5.87684i	−0.797280	+	0.460310i	−0.842519	−	0.538667i	$-0.818928\pi$
$163$	−10.1790	+	5.87684i	−0.797280	+	0.460310i	0.0452393	+	0.998976i	$0.485595\pi$
$164$		0			0
$165$	−7.57603	−	13.1221i	−0.589793	−	1.02155i
$166$		0			0
$167$	−14.7492	−	8.51546i	−1.14133	−	0.658946i	−0.194569	−	0.980889i	$-0.562331\pi$
$167$	−14.7492	−	8.51546i	−1.14133	−	0.658946i	−0.946759	+	0.321942i	$0.895664\pi$
$168$		0			0
$169$	12.8446	−	2.00418i	0.988045	−	0.154168i
$170$		0			0
$171$	5.97403	+	3.44911i	0.456845	+	0.263760i
$172$		0			0
$173$	−7.66243	−	13.2717i	−0.582563	−	1.00903i	−0.995174	−	0.0981221i	$-0.968716\pi$
$173$	−7.66243	−	13.2717i	−0.582563	−	1.00903i	0.412611	−	0.910907i	$-0.364617\pi$
$174$		0			0
$175$	−18.8338	+	10.8737i	−1.42370	+	0.821975i
$176$		0			0
$177$		−	18.7505i		−	1.40938i
$178$		0			0
$179$	0.637292	−	1.10382i	0.0476334	−	0.0825035i	−0.841226	−	0.540684i	$-0.818165\pi$
$179$	0.637292	−	1.10382i	0.0476334	−	0.0825035i	0.888859	+	0.458181i	$0.151499\pi$
$180$		0			0
$181$	−2.41650			−0.179617			−0.0898085	−	0.995959i	$-0.528625\pi$
$181$	−2.41650			−0.179617			−0.0898085	+	0.995959i	$0.528625\pi$
$182$		0			0
$183$	−14.9925			−1.10828
$184$		0			0
$185$	−19.4639	+	33.7124i	−1.43101	+	2.47859i
$186$		0			0
$187$		−	5.62849i		−	0.411596i
$188$		0			0
$189$	−15.5430	+	8.97377i	−1.13059	+	0.652746i
$190$		0			0
$191$	3.35435	+	5.80990i	0.242712	+	0.420390i	0.961486	−	0.274854i	$-0.0886296\pi$
$191$	3.35435	+	5.80990i	0.242712	+	0.420390i	−0.718774	+	0.695244i	$0.755296\pi$
$192$		0			0
$193$	−4.64192	−	2.68001i	−0.334132	−	0.192911i	0.323542	−	0.946214i	$-0.395126\pi$
$193$	−4.64192	−	2.68001i	−0.334132	−	0.192911i	−0.657674	+	0.753302i	$0.728460\pi$
$194$		0			0
$195$	15.5244	+	7.42664i	1.11173	+	0.531833i
$196$		0			0
$197$	7.46978	+	4.31268i	0.532199	+	0.307266i	0.741912	−	0.670498i	$-0.233919\pi$
$197$	7.46978	+	4.31268i	0.532199	+	0.307266i	−0.209712	+	0.977763i	$0.567253\pi$
$198$		0			0
$199$	−5.43194	−	9.40840i	−0.385060	−	0.666944i	0.606717	−	0.794918i	$-0.292486\pi$
$199$	−5.43194	−	9.40840i	−0.385060	−	0.666944i	−0.991778	+	0.127974i	$0.959153\pi$
$200$		0			0
$201$	1.22397	−	0.706660i	0.0863323	−	0.0498440i
$202$		0			0
$203$			16.2279i			1.13898i
$204$		0			0
$205$	−3.90368	+	6.76136i	−0.272645	+	0.472234i
$206$		0			0
$207$	−1.49409			−0.103847
$208$		0			0
$209$	−20.3217			−1.40568
$210$		0			0
$211$	5.41867	−	9.38541i	0.373037	−	0.646118i	−0.616994	−	0.786968i	$-0.711650\pi$
$211$	5.41867	−	9.38541i	0.373037	−	0.646118i	0.990031	+	0.140849i	$0.0449832\pi$
$212$		0			0
$213$			18.4818i			1.26635i
$214$		0			0
$215$	12.7343	−	7.35218i	0.868475	−	0.501414i
$216$		0			0
$217$	2.14626	+	3.71743i	0.145697	+	0.252355i
$218$		0			0
$219$	−6.40067	−	3.69543i	−0.432517	−	0.249714i
$220$		0			0
$221$	3.61482	+	5.27255i	0.243159	+	0.354670i
$222$		0			0
$223$	−6.27821	−	3.62473i	−0.420420	−	0.242730i	0.274837	−	0.961491i	$-0.411376\pi$
$223$	−6.27821	−	3.62473i	−0.420420	−	0.242730i	−0.695257	+	0.718761i	$0.744709\pi$
$224$		0			0
$225$	−3.69108	−	6.39314i	−0.246072	−	0.426210i
$226$		0			0
$227$	−8.31254	+	4.79925i	−0.551723	+	0.318537i	−0.749817	−	0.661646i	$-0.769858\pi$
$227$	−8.31254	+	4.79925i	−0.551723	+	0.318537i	0.198094	+	0.980183i	$0.436525\pi$
$228$		0			0
$229$		−	2.92820i		−	0.193501i	−0.995309	−	0.0967506i	$-0.969155\pi$
$229$		−	2.92820i		−	0.193501i	0.995309	−	0.0967506i	$-0.0308449\pi$
$230$		0			0
$231$	6.98634	−	12.1007i	0.459667	−	0.796167i
$232$		0			0
$233$	13.1521			0.861620			0.430810	−	0.902443i	$-0.358228\pi$
$233$	13.1521			0.861620			0.430810	+	0.902443i	$0.358228\pi$
$234$		0			0
$235$	5.42543			0.353916
$236$		0			0
$237$	−7.73121	+	13.3909i	−0.502196	+	0.869829i
$238$		0			0
$239$		−	9.02686i		−	0.583899i	−0.956434	−	0.291949i	$-0.905696\pi$
$239$		−	9.02686i		−	0.583899i	0.956434	−	0.291949i	$-0.0943039\pi$
$240$		0			0
$241$	14.5846	−	8.42042i	0.939477	−	0.542407i	0.0496804	−	0.998765i	$-0.484180\pi$
$241$	14.5846	−	8.42042i	0.939477	−	0.542407i	0.889796	+	0.456358i	$0.150846\pi$
$242$		0			0
$243$	−5.28729	−	9.15785i	−0.339180	−	0.587476i
$244$		0			0
$245$	−9.17513	−	5.29726i	−0.586177	−	0.338430i
$246$		0			0
$247$	19.0366	−	13.0514i	1.21127	−	0.830438i
$248$		0			0
$249$	−17.2296	−	9.94754i	−1.09188	−	0.630400i
$250$		0			0
$251$	14.9604	+	25.9121i	0.944290	+	1.63556i	0.757167	+	0.653221i	$0.226583\pi$
$251$	14.9604	+	25.9121i	0.944290	+	1.63556i	0.187123	+	0.982337i	$0.440084\pi$
$252$		0			0
$253$	3.81181	−	2.20075i	0.239647	−	0.138360i
$254$		0			0
$255$			8.46265i			0.529952i
$256$		0			0
$257$	2.07603	−	3.59578i	0.129499	−	0.224299i	−0.793984	−	0.607939i	$-0.791996\pi$
$257$	2.07603	−	3.59578i	0.129499	−	0.224299i	0.923483	+	0.383640i	$0.125330\pi$
$258$		0			0
$259$	−35.8977			−2.23058
$260$		0			0
$261$	−5.50857			−0.340972
$262$		0			0
$263$	4.90440	−	8.49467i	0.302418	−	0.523804i	−0.674265	−	0.738490i	$-0.735539\pi$
$263$	4.90440	−	8.49467i	0.302418	−	0.523804i	0.976683	+	0.214686i	$0.0688727\pi$
$264$		0			0
$265$		−	12.8703i		−	0.790617i
$266$		0			0
$267$	−5.55390	+	3.20655i	−0.339893	+	0.196238i
$268$		0			0
$269$	3.45964	+	5.99227i	0.210938	+	0.365355i	0.952008	−	0.306072i	$-0.0990149\pi$
$269$	3.45964	+	5.99227i	0.210938	+	0.365355i	−0.741070	+	0.671427i	$0.765682\pi$
$270$		0			0
$271$	−11.0163	−	6.36028i	−0.669194	−	0.386359i	0.126577	−	0.991957i	$-0.459601\pi$
$271$	−11.0163	−	6.36028i	−0.669194	−	0.386359i	−0.795771	+	0.605597i	$0.792934\pi$
$272$		0			0
$273$	1.22698	+	15.8223i	0.0742603	+	0.957612i
$274$		0			0
$275$	18.8338	+	10.8737i	1.13572	+	0.655709i
$276$		0			0
$277$	4.09766	+	7.09735i	0.246204	+	0.426438i	0.962470	−	0.271390i	$-0.0874832\pi$
$277$	4.09766	+	7.09735i	0.246204	+	0.426438i	−0.716265	+	0.697828i	$0.754150\pi$
$278$		0			0
$279$	−1.26188	+	0.728548i	−0.0755469	+	0.0436170i
$280$		0			0
$281$		−	8.00836i		−	0.477739i	−0.971052	−	0.238869i	$-0.923223\pi$
$281$		−	8.00836i		−	0.477739i	0.971052	−	0.238869i	$-0.0767768\pi$
$282$		0			0
$283$	11.0163	−	19.0808i	0.654853	−	1.13424i	−0.327078	−	0.944997i	$-0.606064\pi$
$283$	11.0163	−	19.0808i	0.654853	−	1.13424i	0.981931	−	0.189241i	$-0.0606027\pi$
$284$		0			0
$285$	30.5545			1.80989
$286$		0			0
$287$	−7.19966			−0.424982
$288$		0			0
$289$	6.92820	−	12.0000i	0.407541	−	0.705882i
$290$		0			0
$291$		−	16.3918i		−	0.960904i
$292$		0			0
$293$	6.97246	−	4.02555i	0.407336	−	0.235175i	−0.282309	−	0.959324i	$-0.591100\pi$
$293$	6.97246	−	4.02555i	0.407336	−	0.235175i	0.689644	+	0.724148i	$0.257767\pi$
$294$		0			0
$295$	23.2772	+	40.3174i	1.35525	+	2.34737i
$296$		0			0
$297$	15.5430	+	8.97377i	0.901898	+	0.520711i
$298$		0			0
$299$	−2.15736	+	4.50967i	−0.124763	+	0.260801i
$300$		0			0
$301$	11.7431	+	6.77991i	0.676864	+	0.390788i
$302$		0			0
$303$	4.39448	+	7.61146i	0.252456	+	0.437267i
$304$		0			0
$305$	32.2369	−	18.6120i	1.84588	−	1.06572i
$306$		0			0
$307$			16.7281i			0.954722i	0.878707	+	0.477361i	$0.158407\pi$
$307$			16.7281i			0.954722i	−0.878707	+	0.477361i	$0.841593\pi$
$308$		0			0
$309$	4.77302	−	8.26711i	0.271528	−	0.470299i
$310$		0			0
$311$	3.79287			0.215074			0.107537	−	0.994201i	$-0.465704\pi$
$311$	3.79287			0.215074			0.107537	+	0.994201i	$0.465704\pi$
$312$		0			0
$313$	−26.6981			−1.50907			−0.754533	−	0.656263i	$-0.772136\pi$
$313$	−26.6981			−1.50907			−0.754533	+	0.656263i	$0.772136\pi$
$314$		0			0
$315$	5.88808	−	10.1984i	0.331755	−	0.574617i
$316$		0			0
$317$		−	18.6378i		−	1.04680i	−0.852086	−	0.523401i	$-0.824663\pi$
$317$		−	18.6378i		−	1.04680i	0.852086	−	0.523401i	$-0.175337\pi$
$318$		0			0
$319$	14.0538	−	8.11396i	0.786861	−	0.454295i
$320$		0			0
$321$	0.110593	+	0.191553i	0.00617270	+	0.0106914i
$322$		0			0
$323$	9.82937	+	5.67499i	0.546921	+	0.315765i
$324$		0			0
$325$	−24.6263	+	1.90971i	−1.36602	+	0.105931i
$326$		0			0
$327$	−13.1221	−	7.57603i	−0.725652	−	0.418955i
$328$		0			0
$329$	2.50157	+	4.33284i	0.137916	+	0.238877i
$330$		0			0
$331$	−11.5179	+	6.64986i	−0.633081	+	0.365509i	−0.781944	−	0.623348i	$-0.785772\pi$
$331$	−11.5179	+	6.64986i	−0.633081	+	0.365509i	0.148864	+	0.988858i	$0.452438\pi$
$332$		0			0
$333$		−	12.1855i		−	0.667761i
$334$		0			0
$335$	−1.75452	+	3.03892i	−0.0958597	+	0.166034i
$336$		0			0
$337$	−20.6174			−1.12310			−0.561550	−	0.827443i	$-0.689795\pi$
$337$	−20.6174			−1.12310			−0.561550	+	0.827443i	$0.689795\pi$
$338$		0			0
$339$	16.6338			0.903422
$340$		0			0
$341$	2.14626	−	3.71743i	0.116226	−	0.201310i
$342$		0			0
$343$			12.4518i			0.672332i
$344$		0			0
$345$	−5.73121	+	3.30892i	−0.308558	+	0.178146i
$346$		0			0
$347$	−5.30675	−	9.19155i	−0.284881	−	0.493428i	0.687699	−	0.725996i	$-0.258621\pi$
$347$	−5.30675	−	9.19155i	−0.284881	−	0.493428i	−0.972580	+	0.232567i	$0.925287\pi$
$348$		0			0
$349$	10.4164	+	6.01390i	0.557576	+	0.321917i	0.752172	−	0.658967i	$-0.229006\pi$
$349$	10.4164	+	6.01390i	0.557576	+	0.321917i	−0.194596	+	0.980883i	$0.562340\pi$
$350$		0			0
$351$	−20.3234	+	1.57603i	−1.08478	+	0.0841221i
$352$		0			0
$353$	20.7265	+	11.9665i	1.10316	+	0.636910i	0.937049	−	0.349197i	$-0.113545\pi$
$353$	20.7265	+	11.9665i	1.10316	+	0.636910i	0.166112	+	0.986107i	$0.446879\pi$
$354$		0			0
$355$	−22.9436	−	39.7394i	−1.21772	−	2.10915i
$356$		0			0
$357$	−6.75842	+	3.90197i	−0.357693	+	0.206514i
$358$		0			0
$359$			0.104919i			0.00553740i	0.999996	+	0.00276870i	$0.000881306\pi$
$359$			0.104919i			0.00553740i	−0.999996	+	0.00276870i	$0.999119\pi$
$360$		0			0
$361$	10.9896	−	19.0346i	0.578401	−	1.00182i
$362$		0			0
$363$	1.27893			0.0671262
$364$		0			0
$365$	18.3503			0.960496
$366$		0			0
$367$	−6.07542	+	10.5229i	−0.317134	+	0.549293i	−0.979889	−	0.199544i	$-0.936054\pi$
$367$	−6.07542	+	10.5229i	−0.317134	+	0.549293i	0.662754	+	0.748837i	$0.269387\pi$
$368$		0			0
$369$		−	2.44393i		−	0.127226i
$370$		0			0
$371$	10.2785	−	5.93427i	0.533631	−	0.308092i
$372$		0			0
$373$	−17.0602	−	29.5491i	−0.883343	−	1.53000i	−0.847601	−	0.530634i	$-0.821954\pi$
$373$	−17.0602	−	29.5491i	−0.883343	−	1.53000i	−0.0357425	−	0.999361i	$-0.511380\pi$
$374$		0			0
$375$	−7.64960	−	4.41650i	−0.395024	−	0.228067i
$376$		0			0
$377$	−7.95396	+	16.6267i	−0.409650	+	0.856319i
$378$		0			0
$379$	−28.2719	−	16.3228i	−1.45223	−	0.838447i	−0.453624	−	0.891193i	$-0.649869\pi$
$379$	−28.2719	−	16.3228i	−1.45223	−	0.838447i	−0.998608	+	0.0527463i	$0.983203\pi$
$380$		0			0
$381$	−8.69242	−	15.0557i	−0.445326	−	0.771327i
$382$		0			0
$383$	26.6743	−	15.4004i	1.36299	−	0.786924i	0.372971	−	0.927843i	$-0.378339\pi$
$383$	26.6743	−	15.4004i	1.36299	−	0.786924i	0.990021	+	0.140919i	$0.0450056\pi$
$384$		0			0
$385$			34.6918i			1.76806i
$386$		0			0
$387$	−2.30144	+	3.98622i	−0.116989	+	0.202631i
$388$		0			0
$389$	1.41963			0.0719782			0.0359891	−	0.999352i	$-0.488542\pi$
$389$	1.41963			0.0719782			0.0359891	+	0.999352i	$0.488542\pi$
$390$		0			0
$391$	−2.45831			−0.124322
$392$		0			0
$393$	−6.47424	+	11.2137i	−0.326582	+	0.565657i
$394$		0			0
$395$		−	38.3906i		−	1.93164i
$396$		0			0
$397$	−18.0400	+	10.4154i	−0.905402	+	0.522734i	−0.878949	−	0.476916i	$-0.841755\pi$
$397$	−18.0400	+	10.4154i	−0.905402	+	0.522734i	−0.0264531	+	0.999650i	$0.508421\pi$
$398$		0			0
$399$	14.0881	+	24.4013i	0.705288	+	1.22160i
$400$		0			0
$401$	7.26868	+	4.19657i	0.362980	+	0.209567i	0.670387	−	0.742011i	$-0.266128\pi$
$401$	7.26868	+	4.19657i	0.362980	+	0.209567i	−0.307407	+	0.951578i	$0.599461\pi$
$402$		0			0
$403$	0.376938	+	4.86075i	0.0187766	+	0.242131i
$404$		0			0
$405$	−13.7318	−	7.92804i	−0.682337	−	0.393948i
$406$		0			0
$407$	17.9489	+	31.0884i	0.889693	+	1.54099i
$408$		0			0
$409$	−4.71684	+	2.72327i	−0.233233	+	0.134657i	−0.612063	−	0.790809i	$-0.709660\pi$
$409$	−4.71684	+	2.72327i	−0.233233	+	0.134657i	0.378830	+	0.925466i	$0.376327\pi$
$410$		0			0
$411$		−	7.14453i		−	0.352414i
$412$		0			0
$413$	−21.4654	+	37.1792i	−1.05624	+	1.82947i
$414$		0			0
$415$	49.3962			2.42476
$416$		0			0
$417$	−4.43635			−0.217249
$418$		0			0
$419$	−6.22602	+	10.7838i	−0.304161	+	0.526822i	−0.977074	−	0.212899i	$-0.931709\pi$
$419$	−6.22602	+	10.7838i	−0.304161	+	0.526822i	0.672913	+	0.739721i	$0.265043\pi$
$420$		0			0
$421$			18.7584i			0.914228i	0.889408	+	0.457114i	$0.151117\pi$
$421$			18.7584i			0.914228i	−0.889408	+	0.457114i	$0.848883\pi$
$422$		0			0
$423$	−1.47078	+	0.849157i	−0.0715119	+	0.0412874i
$424$		0			0
$425$	−6.07313	−	10.5190i	−0.294590	−	0.510245i
$426$		0			0
$427$	29.7277	+	17.1633i	1.43862	+	0.830590i
$428$		0			0
$429$	13.0891	−	8.97377i	0.631946	−	0.433258i
$430$		0			0
$431$	−14.9431	−	8.62739i	−0.719783	−	0.415567i	0.0948900	−	0.995488i	$-0.469750\pi$
$431$	−14.9431	−	8.62739i	−0.719783	−	0.415567i	−0.814673	+	0.579921i	$0.803083\pi$
$432$		0			0
$433$	8.96097	+	15.5209i	0.430637	+	0.745885i	0.996928	−	0.0783203i	$-0.0249557\pi$
$433$	8.96097	+	15.5209i	0.430637	+	0.745885i	−0.566292	+	0.824205i	$0.691622\pi$
$434$		0			0
$435$	−21.1304	+	12.1997i	−1.01313	+	0.584929i
$436$		0			0
$437$			8.87574i			0.424584i
$438$		0			0
$439$	−13.7550	+	23.8244i	−0.656491	+	1.13708i	0.325027	+	0.945705i	$0.394627\pi$
$439$	−13.7550	+	23.8244i	−0.656491	+	1.13708i	−0.981518	+	0.191371i	$0.938707\pi$
$440$		0			0
$441$	3.31639			0.157923
$442$		0			0
$443$	0.223850			0.0106354			0.00531772	−	0.999986i	$-0.498307\pi$
$443$	0.223850			0.0106354			0.00531772	+	0.999986i	$0.498307\pi$
$444$		0			0
$445$	7.96133	−	13.7894i	0.377403	−	0.653681i
$446$		0			0
$447$			10.5654i			0.499725i
$448$		0			0
$449$	−24.3636	+	14.0664i	−1.14979	+	0.663832i	−0.948836	−	0.315768i	$-0.897738\pi$
$449$	−24.3636	+	14.0664i	−1.14979	+	0.663832i	−0.200955	+	0.979600i	$0.564405\pi$
$450$		0			0
$451$	3.59983	+	6.23508i	0.169509	+	0.293599i
$452$		0			0
$453$	15.0145	+	8.66861i	0.705442	+	0.407287i
$454$		0			0
$455$	−22.2804	−	32.4980i	−1.04452	−	1.52353i
$456$		0			0
$457$	−7.22976	−	4.17410i	−0.338194	−	0.195256i	0.321279	−	0.946985i	$-0.395887\pi$
$457$	−7.22976	−	4.17410i	−0.338194	−	0.195256i	−0.659473	+	0.751728i	$0.729221\pi$
$458$		0			0
$459$	−5.01198	−	8.68101i	−0.233939	−	0.405195i
$460$		0			0
$461$	10.5260	−	6.07717i	0.490243	−	0.283042i	−0.234432	−	0.972133i	$-0.575323\pi$
$461$	10.5260	−	6.07717i	0.490243	−	0.283042i	0.724675	+	0.689090i	$0.241990\pi$
$462$		0			0
$463$		−	30.3490i		−	1.41044i	−0.708989	−	0.705220i	$-0.750848\pi$
$463$		−	30.3490i		−	1.41044i	0.708989	−	0.705220i	$-0.249152\pi$
$464$		0			0
$465$	−3.22698	+	5.58930i	−0.149648	+	0.259197i
$466$		0			0
$467$	−35.7902			−1.65617			−0.828086	−	0.560602i	$-0.810570\pi$
$467$	−35.7902			−1.65617			−0.828086	+	0.560602i	$0.810570\pi$
$468$		0			0
$469$	−3.23591			−0.149420
$470$		0			0
$471$	−1.25295	+	2.17018i	−0.0577331	+	0.0999966i
$472$		0			0
$473$		−	13.5598i		−	0.623481i
$474$		0			0
$475$	−37.9789	+	21.9271i	−1.74259	+	1.00608i
$476$		0			0
$477$	2.01439	+	3.48903i	0.0922326	+	0.159752i
$478$		0			0
$479$	14.7003	+	8.48720i	0.671672	+	0.387790i	0.796710	−	0.604362i	$-0.206572\pi$
$479$	14.7003	+	8.48720i	0.671672	+	0.387790i	−0.125038	+	0.992152i	$0.539905\pi$
$480$		0			0
$481$	−36.7799	−	17.5949i	−1.67702	−	0.802260i
$482$		0			0
$483$	−5.28512	−	3.05136i	−0.240481	−	0.138842i
$484$		0			0
$485$	20.3490	+	35.2456i	0.924003	+	1.60042i
$486$		0			0
$487$	7.19347	−	4.15315i	0.325967	−	0.188197i	−0.328082	−	0.944649i	$-0.606402\pi$
$487$	7.19347	−	4.15315i	0.325967	−	0.188197i	0.654049	+	0.756452i	$0.273069\pi$
$488$		0			0
$489$		−	16.2966i		−	0.736957i
$490$		0			0
$491$	−19.5249	+	33.8181i	−0.881146	+	1.52619i	−0.0310786	+	0.999517i	$0.509894\pi$
$491$	−19.5249	+	33.8181i	−0.881146	+	1.52619i	−0.850068	+	0.526673i	$0.823439\pi$
$492$		0			0
$493$	−9.06354			−0.408201
$494$		0			0
$495$	−11.7762			−0.529299
$496$		0			0
$497$	21.1577	−	36.6463i	0.949054	−	1.64381i
$498$		0			0
$499$		−	32.7546i		−	1.46630i	−0.680068	−	0.733149i	$-0.738050\pi$
$499$		−	32.7546i		−	1.46630i	0.680068	−	0.733149i	$-0.261950\pi$
$500$		0			0
$501$	20.4499	−	11.8068i	0.913635	−	0.527488i
$502$		0			0
$503$	−5.06827	−	8.77850i	−0.225983	−	0.391414i	0.730631	−	0.682773i	$-0.239226\pi$
$503$	−5.06827	−	8.77850i	−0.225983	−	0.391414i	−0.956614	+	0.291359i	$0.905893\pi$
$504$		0			0
$505$	−18.8980	−	10.9108i	−0.840949	−	0.485522i
$506$		0			0
$507$	−6.49804	+	16.8126i	−0.288588	+	0.746672i
$508$		0			0
$509$	−35.9478	−	20.7545i	−1.59336	−	0.919926i	−0.992725	−	0.120401i	$-0.961582\pi$
$509$	−35.9478	−	20.7545i	−1.59336	−	0.919926i	−0.600633	−	0.799525i	$-0.705085\pi$
$510$		0			0
$511$	8.46097	+	14.6548i	0.374291	+	0.648291i
$512$		0			0
$513$	−31.3429	+	18.0958i	−1.38382	+	0.798951i
$514$		0			0
$515$			23.7012i			1.04440i
$516$		0			0
$517$	2.50157	−	4.33284i	0.110019	−	0.190558i
$518$		0			0
$519$	21.2480			0.932686
$520$		0			0
$521$	38.8591			1.70245			0.851223	−	0.524804i	$-0.175861\pi$
$521$	38.8591			1.70245			0.851223	+	0.524804i	$0.175861\pi$
$522$		0			0
$523$	14.1701	−	24.5433i	0.619613	−	1.07320i	−0.369943	−	0.929055i	$-0.620623\pi$
$523$	14.1701	−	24.5433i	0.619613	−	1.07320i	0.989556	−	0.144147i	$-0.0460439\pi$
$524$		0			0
$525$		−	30.1530i		−	1.31598i
$526$		0			0
$527$	−2.07624	+	1.19872i	−0.0904424	+	0.0522169i
$528$		0			0
$529$	10.5388	+	18.2537i	0.458209	+	0.793640i
$530$		0			0
$531$	−12.6205	−	7.28645i	−0.547683	−	0.316205i
$532$		0			0
$533$	−7.37658	−	3.52884i	−0.319515	−	0.152851i
$534$		0			0
$535$	−0.475594	−	0.274584i	−0.0205617	−	0.0118713i
$536$		0			0
$537$	0.883611	+	1.53046i	0.0381306	+	0.0660442i
$538$		0			0
$539$	−8.46097	+	4.88494i	−0.364440	+	0.210409i
$540$		0			0
$541$		−	34.4879i		−	1.48275i	−0.671090	−	0.741376i	$-0.734174\pi$
$541$		−	34.4879i		−	1.48275i	0.671090	−	0.741376i	$-0.265826\pi$
$542$		0			0
$543$	1.67525	−	2.90162i	0.0718918	−	0.124520i
$544$		0			0
$545$	37.6200			1.61147
$546$		0			0
$547$	27.7469			1.18637			0.593186	−	0.805065i	$-0.297870\pi$
$547$	27.7469			1.18637			0.593186	+	0.805065i	$0.297870\pi$
$548$		0			0
$549$	−5.82608	+	10.0911i	−0.248651	+	0.430676i
$550$		0			0
$551$			32.7240i			1.39409i
$552$		0			0
$553$	30.6594	−	17.7012i	1.30377	−	0.752733i
$554$		0			0
$555$	−26.9868	−	46.7426i	−1.14553	−	1.98411i
$556$		0			0
$557$	12.1511	+	7.01541i	0.514857	+	0.297253i	0.734828	−	0.678254i	$-0.237263\pi$
$557$	12.1511	+	7.01541i	0.514857	+	0.297253i	−0.219971	+	0.975506i	$0.570596\pi$
$558$		0			0
$559$	8.70862	+	12.7023i	0.368335	+	0.537251i
$560$		0			0
$561$	6.75842	+	3.90197i	0.285341	+	0.164741i
$562$		0			0
$563$	20.8268	+	36.0731i	0.877745	+	1.52030i	0.853809	+	0.520586i	$0.174287\pi$
$563$	20.8268	+	36.0731i	0.877745	+	1.52030i	0.0239362	+	0.999713i	$0.492380\pi$
$564$		0			0
$565$	−35.7659	+	20.6494i	−1.50468	+	0.868728i
$566$		0			0
$567$		−	14.6219i		−	0.614062i
$568$		0			0
$569$	−18.0801	+	31.3157i	−0.757959	+	1.31282i	0.185931	+	0.982563i	$0.440470\pi$
$569$	−18.0801	+	31.3157i	−0.757959	+	1.31282i	−0.943890	+	0.330260i	$0.892864\pi$
$570$		0			0
$571$	23.1786			0.969994			0.484997	−	0.874516i	$-0.338821\pi$
$571$	23.1786			0.969994			0.484997	+	0.874516i	$0.338821\pi$
$572$		0			0
$573$	−9.30167			−0.388583
$574$		0			0
$575$	4.74922	−	8.22589i	0.198056	−	0.343043i
$576$		0			0
$577$		−	2.75597i		−	0.114733i	−0.998353	−	0.0573663i	$-0.981730\pi$
$577$		−	2.75597i		−	0.114733i	0.998353	−	0.0573663i	$-0.0182703\pi$
$578$		0			0
$579$	6.43606	−	3.71586i	0.267473	−	0.154426i
$580$		0			0
$581$	22.7757	+	39.4486i	0.944895	+	1.63661i
$582$		0			0
$583$	−10.2785	−	5.93427i	−0.425690	−	0.245772i
$584$		0			0
$585$	11.0314	−	7.56308i	0.456094	−	0.312695i
$586$		0			0
$587$	13.9789	+	8.07070i	0.576969	+	0.333113i	0.759928	−	0.650007i	$-0.225234\pi$
$587$	13.9789	+	8.07070i	0.576969	+	0.333113i	−0.182959	+	0.983121i	$0.558567\pi$
$588$		0			0
$589$	4.32798	+	7.49628i	0.178331	+	0.308879i
$590$		0			0
$591$	−10.3569	+	5.97957i	−0.426026	+	0.245966i
$592$		0			0
$593$			13.0028i			0.533961i	0.963702	+	0.266981i	$0.0860260\pi$
$593$			13.0028i			0.533961i	−0.963702	+	0.266981i	$0.913974\pi$
$594$		0			0
$595$	9.68795	−	16.7800i	0.397167	−	0.687914i
$596$		0			0
$597$	15.0629			0.616482
$598$		0			0
$599$	9.58930			0.391808			0.195904	−	0.980623i	$-0.437236\pi$
$599$	9.58930			0.391808			0.195904	+	0.980623i	$0.437236\pi$
$600$		0			0
$601$	10.4758	−	18.1446i	0.427317	−	0.740135i	−0.569317	−	0.822118i	$-0.692792\pi$
$601$	10.4758	−	18.1446i	0.427317	−	0.740135i	0.996634	+	0.0819835i	$0.0261255\pi$
$602$		0			0
$603$		−	1.09843i		−	0.0447315i
$604$		0			0
$605$	−2.74994	+	1.58768i	−0.111801	+	0.0645484i
$606$		0			0
$607$	−3.76772	−	6.52587i	−0.152927	−	0.264877i	0.779375	−	0.626557i	$-0.215537\pi$
$607$	−3.76772	−	6.52587i	−0.152927	−	0.264877i	−0.932302	+	0.361680i	$0.882203\pi$
$608$		0			0
$609$	−19.4857	−	11.2501i	−0.789601	−	0.455876i
$610$		0			0
$611$	0.439340	+	5.66544i	0.0177738	+	0.229199i
$612$		0			0
$613$	6.77010	+	3.90872i	0.273442	+	0.157872i	0.630451	−	0.776229i	$-0.282870\pi$
$613$	6.77010	+	3.90872i	0.273442	+	0.157872i	−0.357009	+	0.934101i	$0.616203\pi$
$614$		0			0
$615$	−5.41248	−	9.37469i	−0.218252	−	0.378024i
$616$		0			0
$617$	9.26409	−	5.34863i	0.372958	−	0.215328i	−0.301792	−	0.953374i	$-0.597585\pi$
$617$	9.26409	−	5.34863i	0.372958	−	0.215328i	0.674750	+	0.738046i	$0.264251\pi$
$618$		0			0
$619$		−	2.18518i		−	0.0878296i	−0.999035	−	0.0439148i	$-0.986017\pi$
$619$		−	2.18518i		−	0.0878296i	0.999035	−	0.0439148i	$-0.0139830\pi$
$620$		0			0
$621$	3.91940	−	6.78860i	0.157280	−	0.272417i
$622$		0			0
$623$	14.6833			0.588274
$624$		0			0
$625$	−12.3222			−0.492887
$626$		0			0
$627$	14.0881	−	24.4013i	0.562625	−	0.974496i
$628$		0			0
$629$		−	20.0494i		−	0.799423i
$630$		0			0
$631$	−11.3010	+	6.52466i	−0.449888	+	0.259743i	−0.707783	−	0.706430i	$-0.750304\pi$
$631$	−11.3010	+	6.52466i	−0.449888	+	0.259743i	0.257895	+	0.966173i	$0.416971\pi$
$632$		0			0
$633$	7.51304	+	13.0130i	0.298616	+	0.517219i
$634$		0			0
$635$	37.3808	+	21.5818i	1.48341	+	0.856448i
$636$		0			0
$637$	4.78862	−	10.0100i	0.189732	−	0.396610i
$638$		0			0
$639$	12.4396	+	7.18200i	0.492102	+	0.284115i
$640$		0			0
$641$	−1.43255	−	2.48124i	−0.0565821	−	0.0980032i	0.836347	−	0.548201i	$-0.184687\pi$
$641$	−1.43255	−	2.48124i	−0.0565821	−	0.0980032i	−0.892929	+	0.450197i	$0.851354\pi$
$642$		0			0
$643$	29.4589	−	17.0081i	1.16175	−	0.670734i	0.210024	−	0.977696i	$-0.432646\pi$
$643$	29.4589	−	17.0081i	1.16175	−	0.670734i	0.951722	+	0.306962i	$0.0993125\pi$
$644$		0			0
$645$			20.3877i			0.802766i
$646$		0			0
$647$	4.58399	−	7.93971i	0.180215	−	0.312142i	−0.761738	−	0.647885i	$-0.775654\pi$
$647$	4.58399	−	7.93971i	0.180215	−	0.312142i	0.941954	+	0.335742i	$0.108987\pi$
$648$		0			0
$649$	42.9309			1.68518
$650$		0			0
$651$	−5.95161			−0.233262
$652$		0			0
$653$	−6.46543	+	11.1985i	−0.253012	+	0.438230i	−0.964354	−	0.264617i	$-0.914755\pi$
$653$	−6.46543	+	11.1985i	−0.253012	+	0.438230i	0.711342	+	0.702846i	$0.248088\pi$
$654$		0			0
$655$		−	32.1489i		−	1.25616i
$656$		0			0
$657$	−4.97459	+	2.87208i	−0.194077	+	0.112050i
$658$		0			0
$659$	−22.6056	−	39.1541i	−0.880590	−	1.52523i	−0.850686	−	0.525674i	$-0.823813\pi$
$659$	−22.6056	−	39.1541i	−0.880590	−	1.52523i	−0.0299039	−	0.999553i	$-0.509520\pi$
$660$		0			0
$661$	15.4709	+	8.93213i	0.601748	+	0.347419i	0.769729	−	0.638371i	$-0.220391\pi$
$661$	15.4709	+	8.93213i	0.601748	+	0.347419i	−0.167981	+	0.985790i	$0.553725\pi$
$662$		0			0
$663$	−8.83702	+	0.685288i	−0.343201	+	0.0266144i
$664$		0			0
$665$	−60.5845	−	34.9785i	−2.34937	−	1.35641i
$666$		0			0
$667$	−3.54387	−	6.13815i	−0.137219	−	0.237670i
$668$		0			0
$669$	8.70479	−	5.02571i	0.336547	−	0.194305i
$670$		0			0
$671$		−	34.3266i		−	1.32516i
$672$		0			0
$673$	−15.9165	+	27.5682i	−0.613536	+	1.06268i	0.377104	+	0.926171i	$0.376920\pi$
$673$	−15.9165	+	27.5682i	−0.613536	+	1.06268i	−0.990639	+	0.136504i	$0.956413\pi$
$674$		0			0
$675$	38.7307			1.49075
$676$		0			0
$677$	13.6123			0.523162			0.261581	−	0.965181i	$-0.415756\pi$
$677$	13.6123			0.523162			0.261581	+	0.965181i	$0.415756\pi$
$678$		0			0
$679$	−18.7652	+	32.5022i	−0.720140	+	1.24732i
$680$		0			0
$681$		−	13.3084i		−	0.509979i
$682$		0			0
$683$	7.62925	−	4.40475i	0.291925	−	0.168543i	−0.346885	−	0.937908i	$-0.612760\pi$
$683$	7.62925	−	4.40475i	0.291925	−	0.168543i	0.638810	+	0.769365i	$0.279427\pi$
$684$		0			0
$685$	8.86934	+	15.3622i	0.338880	+	0.586958i
$686$		0			0
$687$	3.51605	+	2.02999i	0.134146	+	0.0774490i
$688$		0			0
$689$	13.4397	−	1.04221i	0.512011	−	0.0397051i
$690$		0			0
$691$	17.3881	+	10.0390i	0.661475	+	0.381903i	0.792839	−	0.609431i	$-0.208602\pi$
$691$	17.3881	+	10.0390i	0.661475	+	0.381903i	−0.131364	+	0.991334i	$0.541936\pi$
$692$		0			0
$693$	−5.42977	−	9.40464i	−0.206260	−	0.357253i
$694$		0			0
$695$	9.53903	−	5.50736i	0.361836	−	0.208906i
$696$		0			0
$697$		−	4.02112i		−	0.152311i
$698$		0			0
$699$	−9.11772	+	15.7924i	−0.344864	+	0.597322i
$700$		0			0
$701$	−48.6918			−1.83906			−0.919532	−	0.393014i	$-0.871432\pi$
$701$	−48.6918			−1.83906			−0.919532	+	0.393014i	$0.871432\pi$
$702$		0			0
$703$	−72.3887			−2.73019
$704$		0			0
$705$	−3.76120	+	6.51459i	−0.141655	+	0.245354i
$706$		0			0
$707$		−	20.1230i		−	0.756803i
$708$		0			0
$709$	−1.47403	+	0.851030i	−0.0553583	+	0.0319611i	−0.527424	−	0.849602i	$-0.676842\pi$
$709$	−1.47403	+	0.851030i	−0.0553583	+	0.0319611i	0.472065	+	0.881564i	$0.343509\pi$
$710$		0			0
$711$	6.00868	+	10.4073i	0.225343	+	0.390306i
$712$		0			0
$713$	−1.62363	−	0.937403i	−0.0608054	−	0.0351060i
$714$		0			0
$715$	−17.0039	+	35.5444i	−0.635909	+	1.32928i
$716$		0			0
$717$	10.8390	+	6.25791i	0.404791	+	0.233706i
$718$		0			0
$719$	−5.67742	−	9.83358i	−0.211732	−	0.366731i	0.740525	−	0.672029i	$-0.234577\pi$
$719$	−5.67742	−	9.83358i	−0.211732	−	0.366731i	−0.952257	+	0.305299i	$0.901244\pi$
$720$		0			0
$721$	−18.9282	+	10.9282i	−0.704923	+	0.406988i
$722$		0			0
$723$			23.3500i			0.868395i
$724$		0			0
$725$	17.5099	−	30.3280i	0.650302	−	1.12636i
$726$		0			0
$727$	14.9882			0.555881			0.277940	−	0.960598i	$-0.410348\pi$
$727$	14.9882			0.555881			0.277940	+	0.960598i	$0.410348\pi$
$728$		0			0
$729$	28.4798			1.05481
$730$		0			0
$731$	−3.78668	+	6.55872i	−0.140055	+	0.242583i
$732$		0			0
$733$		−	35.0688i		−	1.29529i	−0.761940	−	0.647647i	$-0.775753\pi$
$733$		−	35.0688i		−	1.29529i	0.761940	−	0.647647i	$-0.224247\pi$
$734$		0			0
$735$	12.7214	−	7.34470i	0.469236	−	0.270913i
$736$		0			0
$737$	1.61795	+	2.80238i	0.0595981	+	0.103227i
$738$		0			0
$739$	27.8353	+	16.0707i	1.02394	+	0.591170i	0.915242	−	0.402905i	$-0.131999\pi$
$739$	27.8353	+	16.0707i	1.02394	+	0.591170i	0.108695	+	0.994075i	$0.465333\pi$
$740$		0			0
$741$	2.47424	+	31.9062i	0.0908935	+	1.17210i
$742$		0			0
$743$	−17.2332	−	9.94958i	−0.632224	−	0.365015i	0.149389	−	0.988778i	$-0.452269\pi$
$743$	−17.2332	−	9.94958i	−0.632224	−	0.365015i	−0.781613	+	0.623764i	$0.785603\pi$
$744$		0			0
$745$	−13.1160	−	22.7176i	−0.480534	−	0.832310i
$746$		0			0
$747$	−13.3909	+	7.73121i	−0.489946	+	0.282870i
$748$		0			0
$749$		−	0.506423i		−	0.0185043i
$750$		0			0
$751$	−12.0608	+	20.8899i	−0.440105	+	0.762284i	−0.997697	−	0.0678313i	$-0.978392\pi$
$751$	−12.0608	+	20.8899i	−0.440105	+	0.762284i	0.557592	+	0.830115i	$0.311725\pi$
$752$		0			0
$753$	−41.4854			−1.51181
$754$		0			0
$755$	−43.0455			−1.56658
$756$		0			0
$757$	−1.38205	+	2.39377i	−0.0502313	+	0.0870031i	−0.890048	−	0.455867i	$-0.849329\pi$
$757$	−1.38205	+	2.39377i	−0.0502313	+	0.0870031i	0.839816	+	0.542870i	$0.182663\pi$
$758$		0			0
$759$			6.10273i			0.221515i
$760$		0			0
$761$	−3.86287	+	2.23023i	−0.140029	+	0.0808457i	−0.568378	−	0.822768i	$-0.692429\pi$
$761$	−3.86287	+	2.23023i	−0.140029	+	0.0808457i	0.428349	+	0.903613i	$0.359095\pi$
$762$		0			0
$763$	17.3459	+	30.0440i	0.627964	+	1.08767i
$764$		0			0
$765$	5.69598	+	3.28858i	0.205939	+	0.118899i
$766$		0			0
$767$	−40.2160	+	27.5718i	−1.45211	+	0.995560i
$768$		0			0
$769$	27.7369	+	16.0139i	1.00022	+	0.577476i	0.908313	−	0.418292i	$-0.137371\pi$
$769$	27.7369	+	16.0139i	1.00022	+	0.577476i	0.0919050	+	0.995768i	$0.470704\pi$
$770$		0			0
$771$	2.87843	+	4.98559i	0.103664	+	0.179552i
$772$		0			0
$773$	−21.8277	+	12.6023i	−0.785090	+	0.453272i	−0.838231	−	0.545315i	$-0.816410\pi$
$773$	−21.8277	+	12.6023i	−0.785090	+	0.453272i	0.0531414	+	0.998587i	$0.483077\pi$
$774$		0			0
$775$		−	9.26324i		−	0.332745i
$776$		0			0
$777$	24.8863	−	43.1043i	0.892790	−	1.54636i
$778$		0			0
$779$	−14.5183			−0.520172
$780$		0			0
$781$	−42.3155			−1.51417
$782$		0			0
$783$	14.4504	−	25.0289i	0.516417	−	0.894460i
$784$		0			0
$785$		−	6.22175i		−	0.222064i
$786$		0			0
$787$	−33.0239	+	19.0664i	−1.17717	+	0.679642i	−0.955359	−	0.295446i	$-0.904532\pi$
$787$	−33.0239	+	19.0664i	−1.17717	+	0.679642i	−0.221816	+	0.975089i	$0.571198\pi$
$788$		0			0
$789$	6.80000	+	11.7779i	0.242086	+	0.419306i
$790$		0			0
$791$	−32.9820	−	19.0422i	−1.17270	−	0.677061i
$792$		0			0
$793$	22.0458	+	32.1558i	0.782869	+	1.14189i
$794$		0			0
$795$	15.4541	+	8.92241i	0.548099	+	0.316445i
$796$		0			0
$797$	2.65663	+	4.60142i	0.0941026	+	0.162991i	0.909234	−	0.416286i	$-0.136668\pi$
$797$	2.65663	+	4.60142i	0.0941026	+	0.162991i	−0.815131	+	0.579277i	$0.803335\pi$
$798$		0			0
$799$	−2.41996	+	1.39716i	−0.0856119	+	0.0494280i
$800$		0			0
$801$			4.98425i			0.176110i
$802$		0			0
$803$	8.46097	−	14.6548i	0.298581	−	0.517158i
$804$		0			0
$805$	15.1521			0.534040
$806$		0			0
$807$	−9.59364			−0.337712
$808$		0			0
$809$	8.58773	−	14.8744i	0.301929	−	0.522956i	−0.674644	−	0.738143i	$-0.735703\pi$
$809$	8.58773	−	14.8744i	0.301929	−	0.522956i	0.976573	+	0.215188i	$0.0690363\pi$
$810$		0			0
$811$			12.7281i			0.446943i	0.974710	+	0.223472i	$0.0717390\pi$
$811$			12.7281i			0.446943i	−0.974710	+	0.223472i	$0.928261\pi$
$812$		0			0
$813$	15.2742	−	8.81859i	0.535691	−	0.309281i
$814$		0			0
$815$	20.2309	+	35.0409i	0.708656	+	1.22743i
$816$		0			0
$817$	23.6804	+	13.6719i	0.828471	+	0.478318i
$818$		0			0
$819$	11.1264	+	5.32270i	0.388788	+	0.185990i
$820$		0			0
$821$	−16.5302	−	9.54373i	−0.576909	−	0.333078i	0.182995	−	0.983114i	$-0.441421\pi$
$821$	−16.5302	−	9.54373i	−0.576909	−	0.333078i	−0.759904	+	0.650035i	$0.774754\pi$
$822$		0			0
$823$	−22.4372	−	38.8623i	−0.782111	−	1.35466i	−0.930710	−	0.365758i	$-0.880810\pi$
$823$	−22.4372	−	38.8623i	−0.782111	−	1.35466i	0.148600	−	0.988897i	$-0.452523\pi$
$824$		0			0
$825$	−26.1133	+	15.0765i	−0.909147	+	0.524896i
$826$		0			0
$827$		−	29.7249i		−	1.03364i	−0.856095	−	0.516819i	$-0.827116\pi$
$827$		−	29.7249i		−	1.03364i	0.856095	−	0.516819i	$-0.172884\pi$
$828$		0			0
$829$	23.4955	−	40.6954i	0.816033	−	1.41341i	−0.0925509	−	0.995708i	$-0.529502\pi$
$829$	23.4955	−	40.6954i	0.816033	−	1.41341i	0.908584	−	0.417703i	$-0.137165\pi$
$830$		0			0
$831$	−11.3629			−0.394174
$832$		0			0
$833$	5.45663			0.189061
$834$		0			0
$835$	−29.3142	+	50.7738i	−1.01446	+	1.75710i
$836$		0			0
$837$		−	7.64469i		−	0.264239i
$838$		0			0
$839$	39.6444	−	22.8887i	1.36868	−	0.790206i	0.377918	−	0.925839i	$-0.376640\pi$
$839$	39.6444	−	22.8887i	1.36868	−	0.790206i	0.990759	+	0.135633i	$0.0433070\pi$
$840$		0			0
$841$	1.43411	+	2.48395i	0.0494521	+	0.0856536i
$842$		0			0
$843$	9.61606	+	5.55183i	0.331195	+	0.191215i
$844$		0			0
$845$	−6.89933	−	44.2171i	−0.237344	−	1.52111i
$846$		0			0
$847$	−2.53590	−	1.46410i	−0.0871345	−	0.0503071i
$848$		0			0
$849$	15.2742	+	26.4558i	0.524210	+	0.907959i
$850$		0			0
$851$	13.5782	−	7.83938i	0.465455	−	0.268730i
$852$		0			0
$853$			35.3624i			1.21079i	0.795927	+	0.605393i	$0.206984\pi$
$853$			35.3624i			1.21079i	−0.795927	+	0.605393i	$0.793016\pi$
$854$		0			0
$855$	11.8735	−	20.5654i	0.406063	−	0.703323i
$856$		0			0
$857$	−43.3068			−1.47933			−0.739666	−	0.672975i	$-0.765016\pi$
$857$	−43.3068			−1.47933			−0.739666	+	0.672975i	$0.765016\pi$
$858$		0			0
$859$	−10.2009			−0.348049			−0.174025	−	0.984741i	$-0.555677\pi$
$859$	−10.2009			−0.348049			−0.174025	+	0.984741i	$0.555677\pi$
$860$		0			0
$861$	4.99119	−	8.64500i	0.170099	−	0.294621i
$862$		0			0
$863$		−	4.26879i		−	0.145311i	−0.997357	−	0.0726556i	$-0.976853\pi$
$863$		−	4.26879i		−	0.145311i	0.997357	−	0.0726556i	$-0.0231474\pi$
$864$		0			0
$865$	−45.6875	+	26.3777i	−1.55342	+	0.896868i
$866$		0			0
$867$	9.60602	+	16.6381i	0.326237	+	0.565060i
$868$		0			0
$869$	−30.6594	−	17.7012i	−1.04005	−	0.600473i
$870$		0			0
$871$	−3.31543	−	1.58605i	−0.112339	−	0.0537413i
$872$		0			0
$873$	−11.0329	−	6.36984i	−0.373406	−	0.215586i
$874$		0			0
$875$	10.1119	+	17.5144i	0.341845	+	0.592094i
$876$		0			0
$877$	−7.34659	+	4.24156i	−0.248077	+	0.143227i	−0.618883	−	0.785483i	$-0.712415\pi$
$877$	−7.34659	+	4.24156i	−0.248077	+	0.143227i	0.370807	+	0.928710i	$0.379081\pi$
$878$		0			0
$879$			11.1629i			0.376516i
$880$		0			0
$881$	−25.5503	+	44.2544i	−0.860810	+	1.49097i	0.0103376	+	0.999947i	$0.496709\pi$
$881$	−25.5503	+	44.2544i	−0.860810	+	1.49097i	−0.871148	+	0.491021i	$0.836624\pi$
$882$		0			0
$883$	21.5628			0.725645			0.362822	−	0.931858i	$-0.381813\pi$
$883$	21.5628			0.725645			0.362822	+	0.931858i	$0.381813\pi$
$884$		0			0
$885$	−64.5482			−2.16977
$886$		0			0
$887$	3.53551	−	6.12367i	0.118711	−	0.205613i	−0.800546	−	0.599271i	$-0.795457\pi$
$887$	3.53551	−	6.12367i	0.118711	−	0.205613i	0.919257	+	0.393658i	$0.128791\pi$
$888$		0			0
$889$			39.8039i			1.33498i
$890$		0			0
$891$	−12.6629	+	7.31095i	−0.424224	+	0.244926i
$892$		0			0
$893$	5.04447	+	8.73728i	0.168807	+	0.292382i
$894$		0			0
$895$	−3.79988	−	2.19386i	−0.127016	−	0.0733326i
$896$		0			0
$897$	−3.91940	−	5.71680i	−0.130865	−	0.190878i
$898$		0			0
$899$	−5.98616	−	3.45611i	−0.199650	−	0.115268i
$900$		0			0
$901$	3.31438	+	5.74067i	0.110418	+	0.191250i
$902$		0			0
$903$	−16.2820	+	9.40041i	−0.541830	+	0.312826i
$904$		0			0
$905$			8.31873i			0.276524i
$906$		0			0
$907$	20.2203	−	35.0226i	0.671405	−	1.16291i	−0.306101	−	0.951999i	$-0.599025\pi$
$907$	20.2203	−	35.0226i	0.671405	−	1.16291i	0.977506	−	0.210908i	$-0.0676421\pi$
$908$		0			0
$909$	6.83076			0.226562
$910$		0			0
$911$	5.91974			0.196130			0.0980649	−	0.995180i	$-0.468735\pi$
$911$	5.91974			0.196130			0.0980649	+	0.995180i	$0.468735\pi$
$912$		0			0
$913$	22.7757	−	39.4486i	0.753765	−	1.30556i
$914$		0			0
$915$			51.6113i			1.70622i
$916$		0			0
$917$	25.6747	−	14.8233i	0.847853	−	0.489508i
$918$		0			0
$919$	−25.2088	−	43.6630i	−0.831563	−	1.44031i	−0.896799	−	0.442439i	$-0.854113\pi$
$919$	−25.2088	−	43.6630i	−0.831563	−	1.44031i	0.0652360	−	0.997870i	$-0.479220\pi$
$920$		0			0
$921$	−20.0863	−	11.5968i	−0.661865	−	0.382128i
$922$		0			0
$923$	39.6395	−	27.1766i	1.30475	−	0.894527i
$924$		0			0
$925$	67.0886	+	38.7336i	2.20586	+	1.27355i
$926$		0			0
$927$	−3.70958	−	6.42518i	−0.121839	−	0.211031i
$928$		0			0
$929$	35.8923	−	20.7224i	1.17759	−	0.679881i	0.222133	−	0.975016i	$-0.428698\pi$
$929$	35.8923	−	20.7224i	1.17759	−	0.679881i	0.955455	+	0.295135i	$0.0953648\pi$
$930$		0			0
$931$		−	19.7012i		−	0.645681i
$932$		0			0
$933$	−2.62942	+	4.55430i	−0.0860835	+	0.149101i
$934$		0			0
$935$	−19.3759			−0.633660
$936$		0			0
$937$	5.67515			0.185399			0.0926995	−	0.995694i	$-0.470450\pi$
$937$	5.67515			0.185399			0.0926995	+	0.995694i	$0.470450\pi$
$938$		0			0
$939$	18.5086	−	32.0578i	0.604004	−	1.04617i
$940$		0			0
$941$		−	18.7044i		−	0.609744i	−0.952393	−	0.304872i	$-0.901386\pi$
$941$		−	18.7044i		−	0.609744i	0.952393	−	0.304872i	$-0.0986138\pi$
$942$		0			0
$943$	2.72324	−	1.57227i	0.0886811	−	0.0512000i
$944$		0			0
$945$	30.8919	+	53.5064i	1.00492	+	1.74056i
$946$		0			0
$947$	−31.8550	−	18.3915i	−1.03515	−	0.597643i	−0.116693	−	0.993168i	$-0.537229\pi$
$947$	−31.8550	−	18.3915i	−1.03515	−	0.597643i	−0.918455	+	0.395525i	$0.870563\pi$
$948$		0			0
$949$	1.48597	+	19.1620i	0.0482365	+	0.622026i
$950$		0			0
$951$	22.3794	+	12.9207i	0.725700	+	0.418983i
$952$		0			0
$953$	−9.16979	−	15.8825i	−0.297039	−	0.514486i	0.678419	−	0.734676i	$-0.262666\pi$
$953$	−9.16979	−	15.8825i	−0.297039	−	0.514486i	−0.975457	+	0.220190i	$0.929332\pi$
$954$		0			0
$955$	20.0004	−	11.5472i	0.647198	−	0.373660i
$956$		0			0
$957$			22.5002i			0.727327i
$958$		0			0
$959$	−8.17899	+	14.1664i	−0.264113	+	0.457458i
$960$		0			0
$961$	29.1716			0.941020
$962$		0			0
$963$	0.171905			0.00553957
$964$		0			0
$965$	−9.22586	+	15.9797i	−0.296991	+	0.514403i
$966$		0			0
$967$		−	17.0558i		−	0.548478i	−0.961662	−	0.274239i	$-0.911574\pi$
$967$		−	17.0558i		−	0.548478i	0.961662	−	0.274239i	$-0.0884260\pi$
$968$		0			0
$969$	−13.6285	+	7.86843i	−0.437811	+	0.252770i
$970$		0			0
$971$	9.32268	+	16.1474i	0.299179	+	0.518193i	0.975948	−	0.218002i	$-0.0699539\pi$
$971$	9.32268	+	16.1474i	0.299179	+	0.518193i	−0.676769	+	0.736195i	$0.736621\pi$
$972$		0			0
$973$	8.79655	+	5.07869i	0.282004	+	0.162815i
$974$		0			0
$975$	14.7792	−	30.8940i	0.473313	−	0.989399i
$976$		0			0
$977$	−14.0081	−	8.08758i	−0.448159	−	0.258745i	0.258893	−	0.965906i	$-0.416642\pi$
$977$	−14.0081	−	8.08758i	−0.448159	−	0.258745i	−0.707052	+	0.707161i	$0.749975\pi$
$978$		0			0
$979$	−7.34165	−	12.7161i	−0.234640	−	0.406408i
$980$		0			0
$981$	−10.1984	+	5.88808i	−0.325611	+	0.187992i
$982$		0			0
$983$			55.0587i			1.75610i	0.478568	+	0.878050i	$0.341156\pi$
$983$			55.0587i			1.75610i	−0.478568	+	0.878050i	$0.658844\pi$
$984$		0			0
$985$	14.8463	−	25.7145i	0.473041	−	0.819332i
$986$		0			0
$987$	−6.93689			−0.220804
$988$		0			0
$989$	−5.92241			−0.188322
$990$		0			0
$991$	−18.5364	+	32.1060i	−0.588828	+	1.01988i	0.405558	+	0.914069i	$0.367077\pi$
$991$	−18.5364	+	32.1060i	−0.588828	+	1.01988i	−0.994386	+	0.105811i	$0.966256\pi$
$992$		0			0
$993$		−	18.4402i		−	0.585181i
$994$		0			0
$995$	−32.3881	+	18.6993i	−1.02677	+	0.592808i
$996$		0			0
$997$	−24.3316	−	42.1436i	−0.770591	−	1.33470i	−0.937240	−	0.348686i	$-0.886628\pi$
$997$	−24.3316	−	42.1436i	−0.770591	−	1.33470i	0.166649	−	0.986016i	$-0.446705\pi$
$998$		0			0
$999$	55.3664	+	31.9658i	1.75171	+	1.01135i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	208.2.w.c.17.2		8
3.2	odd	2		1872.2.by.n.433.4		8
4.3	odd	2		104.2.o.a.17.3	✓	8
8.3	odd	2		832.2.w.g.641.2		8
8.5	even	2		832.2.w.i.641.3		8
12.11	even	2		936.2.bi.b.433.4		8
13.4	even	6		2704.2.f.q.337.6		8
13.6	odd	12		2704.2.a.bd.1.3		4
13.7	odd	12		2704.2.a.be.1.3		4
13.9	even	3		2704.2.f.q.337.5		8
13.10	even	6	inner	208.2.w.c.49.2		8
39.23	odd	6		1872.2.by.n.1297.1		8
52.3	odd	6		1352.2.o.f.361.3		8
52.7	even	12		1352.2.a.l.1.2		4
52.11	even	12		1352.2.i.l.1329.3		8
52.15	even	12		1352.2.i.k.1329.3		8
52.19	even	12		1352.2.a.k.1.2		4
52.23	odd	6		104.2.o.a.49.3	yes	8
52.31	even	4		1352.2.i.k.529.3		8
52.35	odd	6		1352.2.f.f.337.3		8
52.43	odd	6		1352.2.f.f.337.4		8
52.47	even	4		1352.2.i.l.529.3		8
52.51	odd	2		1352.2.o.f.1161.3		8
104.75	odd	6		832.2.w.g.257.2		8
104.101	even	6		832.2.w.i.257.3		8
156.23	even	6		936.2.bi.b.361.1		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
104.2.o.a.17.3	✓	8	4.3	odd	2
104.2.o.a.49.3	yes	8	52.23	odd	6
208.2.w.c.17.2		8	1.1	even	1	trivial
208.2.w.c.49.2		8	13.10	even	6	inner
832.2.w.g.257.2		8	104.75	odd	6
832.2.w.g.641.2		8	8.3	odd	2
832.2.w.i.257.3		8	104.101	even	6
832.2.w.i.641.3		8	8.5	even	2
936.2.bi.b.361.1		8	156.23	even	6
936.2.bi.b.433.4		8	12.11	even	2
1352.2.a.k.1.2		4	52.19	even	12
1352.2.a.l.1.2		4	52.7	even	12
1352.2.f.f.337.3		8	52.35	odd	6
1352.2.f.f.337.4		8	52.43	odd	6
1352.2.i.k.529.3		8	52.31	even	4
1352.2.i.k.1329.3		8	52.15	even	12
1352.2.i.l.529.3		8	52.47	even	4
1352.2.i.l.1329.3		8	52.11	even	12
1352.2.o.f.361.3		8	52.3	odd	6
1352.2.o.f.1161.3		8	52.51	odd	2
1872.2.by.n.433.4		8	3.2	odd	2
1872.2.by.n.1297.1		8	39.23	odd	6
2704.2.a.bd.1.3		4	13.6	odd	12
2704.2.a.be.1.3		4	13.7	odd	12
2704.2.f.q.337.5		8	13.9	even	3
2704.2.f.q.337.6		8	13.4	even	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 208 = 2^{4} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	208.w (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.693255 + 1.20075i) q^{3} -3.44247i q^{5} +(2.74922 - 1.58726i) q^{7} +(0.538796 + 0.933222i) q^{9} +O(q^{10})\)	\(q+(-0.693255 + 1.20075i) q^{3} -3.44247i q^{5} +(2.74922 - 1.58726i) q^{7} +(0.538796 + 0.933222i) q^{9} +(-2.74922 - 1.58726i) q^{11} +(3.59476 - 0.278764i) q^{13} +(4.13356 + 2.38651i) q^{15} +(0.886509 + 1.53548i) q^{17} +(5.54387 - 3.20075i) q^{19} +4.40150i q^{21} +(-0.693255 + 1.20075i) q^{23} -6.85061 q^{25} -5.65362 q^{27} +(-2.55596 + 4.42706i) q^{29} +1.35218i q^{31} +(3.81181 - 2.20075i) q^{33} +(-5.46410 - 9.46410i) q^{35} +(-9.79308 - 5.65404i) q^{37} +(-2.15736 + 4.50967i) q^{39} +(-1.96410 - 1.13397i) q^{41} +(2.13573 + 3.69919i) q^{43} +(3.21259 - 1.85479i) q^{45} +1.57603i q^{47} +(1.53880 - 2.66527i) q^{49} -2.45831 q^{51} +3.73869 q^{53} +(-5.46410 + 9.46410i) q^{55} +8.87574i q^{57} +(-11.7118 + 6.76178i) q^{59} +(5.40657 + 9.36446i) q^{61} +(2.96254 + 1.71042i) q^{63} +(-0.959638 - 12.3749i) q^{65} +(-0.882772 - 0.509669i) q^{67} +(-0.961204 - 1.66485i) q^{69} +(11.5439 - 6.66485i) q^{71} +5.33055i q^{73} +(4.74922 - 8.22589i) q^{75} -10.0776 q^{77} +11.1521 q^{79} +(2.30301 - 3.98893i) q^{81} +14.3490i q^{83} +(5.28584 - 3.05178i) q^{85} +(-3.54387 - 6.13815i) q^{87} +(4.00567 + 2.31268i) q^{89} +(9.44030 - 6.47220i) q^{91} +(-1.62363 - 0.937403i) q^{93} +(-11.0185 - 19.0846i) q^{95} +(-10.2385 + 5.91117i) q^{97} -3.42084i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 2 q^{3} + 6 q^{7} - 6 q^{9}+O(q^{10}) \) 8 * q - 2 * q^3 + 6 * q^7 - 6 * q^9	\( 8 q - 2 q^{3} + 6 q^{7} - 6 q^{9} - 6 q^{11} + 6 q^{13} + 6 q^{19} - 2 q^{23} - 20 q^{25} + 28 q^{27} - 8 q^{29} + 6 q^{33} - 16 q^{35} - 24 q^{37} + 14 q^{39} + 12 q^{41} - 6 q^{43} + 30 q^{45} + 2 q^{49} - 68 q^{51} + 20 q^{53} - 16 q^{55} - 18 q^{59} - 4 q^{61} - 36 q^{63} + 14 q^{65} + 42 q^{67} - 18 q^{69} + 54 q^{71} + 22 q^{75} - 60 q^{77} - 16 q^{79} - 20 q^{81} + 6 q^{85} + 10 q^{87} - 18 q^{89} + 46 q^{91} + 36 q^{93} - 16 q^{95} + 30 q^{97}+O(q^{100}) \) 8 * q - 2 * q^3 + 6 * q^7 - 6 * q^9 - 6 * q^11 + 6 * q^13 + 6 * q^19 - 2 * q^23 - 20 * q^25 + 28 * q^27 - 8 * q^29 + 6 * q^33 - 16 * q^35 - 24 * q^37 + 14 * q^39 + 12 * q^41 - 6 * q^43 + 30 * q^45 + 2 * q^49 - 68 * q^51 + 20 * q^53 - 16 * q^55 - 18 * q^59 - 4 * q^61 - 36 * q^63 + 14 * q^65 + 42 * q^67 - 18 * q^69 + 54 * q^71 + 22 * q^75 - 60 * q^77 - 16 * q^79 - 20 * q^81 + 6 * q^85 + 10 * q^87 - 18 * q^89 + 46 * q^91 + 36 * q^93 - 16 * q^95 + 30 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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