LMFDB - Embedded newform 1638.2.m.h.1621.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1638,2,Mod(289,1638)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1638, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("1638.289");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1638 = 2 \cdot 3^{2} \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1638.m (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:	$13.0794958511$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(\zeta_{3})$
Coefficient field:	8.0.447703281.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - x^{7} - 2x^{6} + 2x^{5} + 3x^{4} + 4x^{3} - 8x^{2} - 8x + 16 $ x^8 - x^7 - 2x^6 + 2x^5 + 3x^4 + 4x^3 - 8x^2 - 8x + 16
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 3 $
Twist minimal:	no (minimal twist has level 546)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			1621.2
Root			$1.26359 - 0.635098i$ of defining polynomial
Character	$\chi$	$=$	1638.1621
Dual form			1638.2.m.h.289.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} +1.00000 q^{4} +(-0.611519 - 1.05918i) q^{5} +(1.15207 + 2.38175i) q^{7} -1.00000 q^{8} +O(q^{10})$	\(q-1.00000 q^{2} +1.00000 q^{4} +(-0.611519 - 1.05918i) q^{5} +(1.15207 + 2.38175i) q^{7} -1.00000 q^{8} +(0.611519 + 1.05918i) q^{10} +(0.0702857 + 0.121738i) q^{11} +(2.39335 + 2.69665i) q^{13} +(-1.15207 - 2.38175i) q^{14} +1.00000 q^{16} -0.186556 q^{17} +(-0.447955 + 0.775880i) q^{19} +(-0.611519 - 1.05918i) q^{20} +(-0.0702857 - 0.121738i) q^{22} -0.0364808 q^{23} +(1.75209 - 3.03471i) q^{25} +(-2.39335 - 2.69665i) q^{26} +(1.15207 + 2.38175i) q^{28} +(-2.99337 + 5.18466i) q^{29} +(-1.82050 + 3.15319i) q^{31} -1.00000 q^{32} +0.186556 q^{34} +(1.81820 - 2.67673i) q^{35} -0.363609 q^{37} +(0.447955 - 0.775880i) q^{38} +(0.611519 + 1.05918i) q^{40} +(-1.70480 + 2.95279i) q^{41} +(-2.06841 - 3.58258i) q^{43} +(0.0702857 + 0.121738i) q^{44} +0.0364808 q^{46} +(-0.358745 - 0.621364i) q^{47} +(-4.34548 + 5.48788i) q^{49} +(-1.75209 + 3.03471i) q^{50} +(2.39335 + 2.69665i) q^{52} +(-3.49556 + 6.05448i) q^{53} +(0.0859621 - 0.148891i) q^{55} +(-1.15207 - 2.38175i) q^{56} +(2.99337 - 5.18466i) q^{58} +6.99624 q^{59} +(-0.186556 + 0.323125i) q^{61} +(1.82050 - 3.15319i) q^{62} +1.00000 q^{64} +(1.39266 - 4.18404i) q^{65} +(2.42903 + 4.20720i) q^{67} -0.186556 q^{68} +(-1.81820 + 2.67673i) q^{70} +(5.31198 + 9.20062i) q^{71} +(-4.80900 + 8.32943i) q^{73} +0.363609 q^{74} +(-0.447955 + 0.775880i) q^{76} +(-0.208977 + 0.307654i) q^{77} +(-2.94837 - 5.10673i) q^{79} +(-0.611519 - 1.05918i) q^{80} +(1.70480 - 2.95279i) q^{82} +9.14057 q^{83} +(0.114083 + 0.197597i) q^{85} +(2.06841 + 3.58258i) q^{86} +(-0.0702857 - 0.121738i) q^{88} +6.35472 q^{89} +(-3.66544 + 8.80707i) q^{91} -0.0364808 q^{92} +(0.358745 + 0.621364i) q^{94} +1.09573 q^{95} +(3.24059 + 5.61287i) q^{97} +(4.34548 - 5.48788i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 8 q^{2} + 8 q^{4} - 2 q^{5} + 3 q^{7} - 8 q^{8}+O(q^{10}) $ 8 * q - 8 * q^2 + 8 * q^4 - 2 * q^5 + 3 * q^7 - 8 * q^8	$ 8 q - 8 q^{2} + 8 q^{4} - 2 q^{5} + 3 q^{7} - 8 q^{8} + 2 q^{10} - 4 q^{11} + 3 q^{13} - 3 q^{14} + 8 q^{16} - 4 q^{17} - 4 q^{19} - 2 q^{20} + 4 q^{22} + 8 q^{23} + 2 q^{25} - 3 q^{26} + 3 q^{28} - 2 q^{29} + 14 q^{31} - 8 q^{32} + 4 q^{34} + 22 q^{35} + 12 q^{37} + 4 q^{38} + 2 q^{40} - 12 q^{41} - 4 q^{44} - 8 q^{46} - 7 q^{47} + 5 q^{49} - 2 q^{50} + 3 q^{52} + q^{53} - 25 q^{55} - 3 q^{56} + 2 q^{58} + 32 q^{59} - 4 q^{61} - 14 q^{62} + 8 q^{64} - 10 q^{65} + 19 q^{67} - 4 q^{68} - 22 q^{70} - 20 q^{71} - 7 q^{73} - 12 q^{74} - 4 q^{76} + 24 q^{77} + 24 q^{79} - 2 q^{80} + 12 q^{82} + 64 q^{83} + 15 q^{85} + 4 q^{88} - 22 q^{89} - 38 q^{91} + 8 q^{92} + 7 q^{94} + 56 q^{95} + 11 q^{97} - 5 q^{98}+O(q^{100}) $ 8 * q - 8 * q^2 + 8 * q^4 - 2 * q^5 + 3 * q^7 - 8 * q^8 + 2 * q^10 - 4 * q^11 + 3 * q^13 - 3 * q^14 + 8 * q^16 - 4 * q^17 - 4 * q^19 - 2 * q^20 + 4 * q^22 + 8 * q^23 + 2 * q^25 - 3 * q^26 + 3 * q^28 - 2 * q^29 + 14 * q^31 - 8 * q^32 + 4 * q^34 + 22 * q^35 + 12 * q^37 + 4 * q^38 + 2 * q^40 - 12 * q^41 - 4 * q^44 - 8 * q^46 - 7 * q^47 + 5 * q^49 - 2 * q^50 + 3 * q^52 + q^53 - 25 * q^55 - 3 * q^56 + 2 * q^58 + 32 * q^59 - 4 * q^61 - 14 * q^62 + 8 * q^64 - 10 * q^65 + 19 * q^67 - 4 * q^68 - 22 * q^70 - 20 * q^71 - 7 * q^73 - 12 * q^74 - 4 * q^76 + 24 * q^77 + 24 * q^79 - 2 * q^80 + 12 * q^82 + 64 * q^83 + 15 * q^85 + 4 * q^88 - 22 * q^89 - 38 * q^91 + 8 * q^92 + 7 * q^94 + 56 * q^95 + 11 * q^97 - 5 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1638\mathbb{Z}\right)^\times$.

$n$	$379$	$703$	$911$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{2}{3}\right)$	$1$

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 $

$2$	−1.00000			−0.707107
$2$	−1.00000			−0.707107
$3$		0			0
$3$		0			0
$4$	1.00000			0.500000
$5$	−0.611519	−	1.05918i	−0.273479	−	0.473680i	0.696271	−	0.717779i	$-0.254841\pi$
$5$	−0.611519	−	1.05918i	−0.273479	−	0.473680i	−0.969750	+	0.244099i	$0.921508\pi$
$6$		0			0
$7$	1.15207	+	2.38175i	0.435441	+	0.900217i
$7$	1.15207	+	2.38175i	0.435441	+	0.900217i
$8$	−1.00000			−0.353553
$9$		0			0
$10$	0.611519	+	1.05918i	0.193379	+	0.334943i
$11$	0.0702857	+	0.121738i	0.0211919	+	0.0367055i	0.876427	−	0.481535i	$-0.159921\pi$
$11$	0.0702857	+	0.121738i	0.0211919	+	0.0367055i	−0.855235	+	0.518240i	$0.826587\pi$
$12$		0			0
$13$	2.39335	+	2.69665i	0.663795	+	0.747915i
$13$	2.39335	+	2.69665i	0.663795	+	0.747915i
$14$	−1.15207	−	2.38175i	−0.307903	−	0.636550i
$15$		0			0
$16$	1.00000			0.250000
$17$	−0.186556			−0.0452466			−0.0226233	−	0.999744i	$-0.507202\pi$
$17$	−0.186556			−0.0452466			−0.0226233	+	0.999744i	$0.507202\pi$
$18$		0			0
$19$	−0.447955	+	0.775880i	−0.102768	+	0.177999i	−0.912824	−	0.408353i	$-0.866103\pi$
$19$	−0.447955	+	0.775880i	−0.102768	+	0.177999i	0.810056	+	0.586352i	$0.199437\pi$
$20$	−0.611519	−	1.05918i	−0.136740	−	0.236840i
$21$		0			0
$22$	−0.0702857	−	0.121738i	−0.0149850	−	0.0259547i
$23$	−0.0364808			−0.00760678			−0.00380339	−	0.999993i	$-0.501211\pi$
$23$	−0.0364808			−0.00760678			−0.00380339	+	0.999993i	$0.501211\pi$
$24$		0			0
$25$	1.75209	−	3.03471i	0.350418	−	0.606942i
$26$	−2.39335	−	2.69665i	−0.469374	−	0.528856i
$27$		0			0
$28$	1.15207	+	2.38175i	0.217720	+	0.450109i
$29$	−2.99337	+	5.18466i	−0.555854	+	0.962768i	0.441982	+	0.897024i	$0.354275\pi$
$29$	−2.99337	+	5.18466i	−0.555854	+	0.962768i	−0.997837	+	0.0657442i	$0.979058\pi$
$30$		0			0
$31$	−1.82050	+	3.15319i	−0.326971	+	0.566330i	−0.981909	−	0.189352i	$-0.939361\pi$
$31$	−1.82050	+	3.15319i	−0.326971	+	0.566330i	0.654939	+	0.755682i	$0.272694\pi$
$32$	−1.00000			−0.176777
$33$		0			0
$34$	0.186556			0.0319941
$35$	1.81820	−	2.67673i	0.307331	−	0.452451i
$36$		0			0
$37$	−0.363609			−0.0597769			−0.0298884	−	0.999553i	$-0.509515\pi$
$37$	−0.363609			−0.0597769			−0.0298884	+	0.999553i	$0.509515\pi$
$38$	0.447955	−	0.775880i	0.0726678	−	0.125864i
$39$		0			0
$40$	0.611519	+	1.05918i	0.0966896	+	0.167471i
$41$	−1.70480	+	2.95279i	−0.266245	+	0.461149i	−0.967889	−	0.251378i	$-0.919116\pi$
$41$	−1.70480	+	2.95279i	−0.266245	+	0.461149i	0.701644	+	0.712527i	$0.252450\pi$
$42$		0			0
$43$	−2.06841	−	3.58258i	−0.315429	−	0.546339i	0.664100	−	0.747644i	$-0.268815\pi$
$43$	−2.06841	−	3.58258i	−0.315429	−	0.546339i	−0.979529	+	0.201305i	$0.935482\pi$
$44$	0.0702857	+	0.121738i	0.0105960	+	0.0183528i
$45$		0			0
$46$	0.0364808			0.00537880
$47$	−0.358745	−	0.621364i	−0.0523283	−	0.0906353i	0.838675	−	0.544633i	$-0.183331\pi$
$47$	−0.358745	−	0.621364i	−0.0523283	−	0.0906353i	−0.891003	+	0.453997i	$0.849998\pi$
$48$		0			0
$49$	−4.34548	+	5.48788i	−0.620783	+	0.783983i
$50$	−1.75209	+	3.03471i	−0.247783	+	0.429173i
$51$		0			0
$52$	2.39335	+	2.69665i	0.331897	+	0.373957i
$53$	−3.49556	+	6.05448i	−0.480151	+	0.831647i	−0.999741	−	0.0227694i	$-0.992752\pi$
$53$	−3.49556	+	6.05448i	−0.480151	+	0.831647i	0.519589	+	0.854416i	$0.326085\pi$
$54$		0			0
$55$	0.0859621	−	0.148891i	0.0115911	−	0.0200764i
$56$	−1.15207	−	2.38175i	−0.153952	−	0.318275i
$57$		0			0
$58$	2.99337	−	5.18466i	0.393048	−	0.680780i
$59$	6.99624			0.910833			0.455416	−	0.890279i	$-0.349490\pi$
$59$	6.99624			0.910833			0.455416	+	0.890279i	$0.349490\pi$
$60$		0			0
$61$	−0.186556	+	0.323125i	−0.0238861	+	0.0413719i	−0.877721	−	0.479171i	$-0.840937\pi$
$61$	−0.186556	+	0.323125i	−0.0238861	+	0.0413719i	0.853835	+	0.520543i	$0.174271\pi$
$62$	1.82050	−	3.15319i	0.231203	−	0.400456i
$63$		0			0
$64$	1.00000			0.125000
$65$	1.39266	−	4.18404i	0.172738	−	0.518966i
$66$		0			0
$67$	2.42903	+	4.20720i	0.296753	+	0.513992i	0.975391	−	0.220481i	$-0.0707628\pi$
$67$	2.42903	+	4.20720i	0.296753	+	0.513992i	−0.678638	+	0.734473i	$0.737429\pi$
$68$	−0.186556			−0.0226233
$69$		0			0
$70$	−1.81820	+	2.67673i	−0.217316	+	0.319931i
$71$	5.31198	+	9.20062i	0.630416	+	1.09191i	0.987467	+	0.157828i	$0.0504492\pi$
$71$	5.31198	+	9.20062i	0.630416	+	1.09191i	−0.357050	+	0.934085i	$0.616218\pi$
$72$		0			0
$73$	−4.80900	+	8.32943i	−0.562851	+	0.974886i	0.434395	+	0.900722i	$0.356962\pi$
$73$	−4.80900	+	8.32943i	−0.562851	+	0.974886i	−0.997246	+	0.0741638i	$0.976371\pi$
$74$	0.363609			0.0422686
$75$		0			0
$76$	−0.447955	+	0.775880i	−0.0513839	+	0.0889996i
$77$	−0.208977	+	0.307654i	−0.0238151	+	0.0350604i
$78$		0			0
$79$	−2.94837	−	5.10673i	−0.331718	−	0.574552i	0.651131	−	0.758966i	$-0.274295\pi$
$79$	−2.94837	−	5.10673i	−0.331718	−	0.574552i	−0.982849	+	0.184413i	$0.940962\pi$
$80$	−0.611519	−	1.05918i	−0.0683699	−	0.118420i
$81$		0			0
$82$	1.70480	−	2.95279i	0.188263	−	0.326082i
$83$	9.14057			1.00331			0.501654	−	0.865068i	$-0.332725\pi$
$83$	9.14057			1.00331			0.501654	+	0.865068i	$0.332725\pi$
$84$		0			0
$85$	0.114083	+	0.197597i	0.0123740	+	0.0214324i
$86$	2.06841	+	3.58258i	0.223042	+	0.386320i
$87$		0			0
$88$	−0.0702857	−	0.121738i	−0.00749249	−	0.0129774i
$89$	6.35472			0.673599			0.336799	−	0.941576i	$-0.390656\pi$
$89$	6.35472			0.673599			0.336799	+	0.941576i	$0.390656\pi$
$90$		0			0
$91$	−3.66544	+	8.80707i	−0.384243	+	0.923232i
$92$	−0.0364808			−0.00380339
$93$		0			0
$94$	0.358745	+	0.621364i	0.0370017	+	0.0640888i
$95$	1.09573			0.112420
$96$		0			0
$97$	3.24059	+	5.61287i	0.329032	+	0.569901i	0.982320	−	0.187209i	$-0.0599441\pi$
$97$	3.24059	+	5.61287i	0.329032	+	0.569901i	−0.653288	+	0.757110i	$0.726611\pi$
$98$	4.34548	−	5.48788i	0.438960	−	0.554359i
$99$		0			0
$100$	1.75209	−	3.03471i	0.175209	−	0.303471i
$101$	−1.50230	−	2.60206i	−0.149484	−	0.258915i	0.781553	−	0.623839i	$-0.214428\pi$
$101$	−1.50230	−	2.60206i	−0.149484	−	0.258915i	−0.931037	+	0.364925i	$0.881095\pi$
$102$		0			0
$103$	−4.12788	−	7.14970i	−0.406732	−	0.704480i	0.587789	−	0.809014i	$-0.299998\pi$
$103$	−4.12788	−	7.14970i	−0.406732	−	0.704480i	−0.994521	+	0.104534i	$0.966665\pi$
$104$	−2.39335	−	2.69665i	−0.234687	−	0.264428i
$105$		0			0
$106$	3.49556	−	6.05448i	0.339518	−	0.588063i
$107$	4.47283			0.432405			0.216202	−	0.976349i	$-0.430633\pi$
$107$	4.47283			0.432405			0.216202	+	0.976349i	$0.430633\pi$
$108$		0			0
$109$	−3.83686	+	6.64563i	−0.367504	+	0.636536i	−0.989175	−	0.146743i	$-0.953121\pi$
$109$	−3.83686	+	6.64563i	−0.367504	+	0.636536i	0.621671	+	0.783279i	$0.286454\pi$
$110$	−0.0859621	+	0.148891i	−0.00819616	+	0.0141962i
$111$		0			0
$112$	1.15207	+	2.38175i	0.108860	+	0.225054i
$113$	6.18222	+	10.7079i	0.581575	+	1.00732i	0.995293	+	0.0969119i	$0.0308965\pi$
$113$	6.18222	+	10.7079i	0.581575	+	1.00732i	−0.413718	+	0.910405i	$0.635770\pi$
$114$		0			0
$115$	0.0223087	+	0.0386398i	0.00208030	+	0.00360318i
$116$	−2.99337	+	5.18466i	−0.277927	+	0.481384i
$117$		0			0
$118$	−6.99624			−0.644056
$119$	−0.214926	−	0.444331i	−0.0197022	−	0.0407317i
$120$		0			0
$121$	5.49012	−	9.50917i	0.499102	−	0.864470i
$122$	0.186556	−	0.323125i	0.0168900	−	0.0292544i
$123$		0			0
$124$	−1.82050	+	3.15319i	−0.163485	+	0.283165i
$125$	−10.4009			−0.930287
$126$		0			0
$127$	−5.45432	+	9.44716i	−0.483993	+	0.838300i	−0.999831	−	0.0183858i	$-0.994147\pi$
$127$	−5.45432	+	9.44716i	−0.483993	+	0.838300i	0.515838	+	0.856686i	$0.327481\pi$
$128$	−1.00000			−0.0883883
$129$		0			0
$130$	−1.39266	+	4.18404i	−0.122144	+	0.366964i
$131$	10.9715	+	19.0032i	0.958583	+	1.66031i	0.725948	+	0.687749i	$0.241401\pi$
$131$	10.9715	+	19.0032i	0.958583	+	1.66031i	0.232634	+	0.972564i	$0.425265\pi$
$132$		0			0
$133$	−2.36403	−	0.173050i	−0.204987	−	0.0150053i
$134$	−2.42903	−	4.20720i	−0.209836	−	0.363447i
$135$		0			0
$136$	0.186556			0.0159971
$137$	−2.69210			−0.230002			−0.115001	−	0.993365i	$-0.536687\pi$
$137$	−2.69210			−0.230002			−0.115001	+	0.993365i	$0.536687\pi$
$138$		0			0
$139$	5.28925	+	9.16126i	0.448629	+	0.777048i	0.998297	−	0.0583352i	$-0.0185792\pi$
$139$	5.28925	+	9.16126i	0.448629	+	0.777048i	−0.549668	+	0.835383i	$0.685246\pi$
$140$	1.81820	−	2.67673i	0.153666	−	0.226225i
$141$		0			0
$142$	−5.31198	−	9.20062i	−0.445772	−	0.772099i
$143$	−0.160068	+	0.480898i	−0.0133855	+	0.0402147i
$144$		0			0
$145$	7.32200			0.608059
$146$	4.80900	−	8.32943i	0.397996	−	0.689349i
$147$		0			0
$148$	−0.363609			−0.0298884
$149$	−5.95244	+	10.3099i	−0.487643	+	0.844623i	−0.999899	−	0.0142102i	$-0.995477\pi$
$149$	−5.95244	+	10.3099i	−0.487643	+	0.844623i	0.512256	+	0.858833i	$0.328810\pi$
$150$		0			0
$151$	−3.66774	+	6.35272i	−0.298477	+	0.516977i	−0.975788	−	0.218720i	$-0.929812\pi$
$151$	−3.66774	+	6.35272i	−0.298477	+	0.516977i	0.677311	+	0.735697i	$0.263145\pi$
$152$	0.447955	−	0.775880i	0.0363339	−	0.0629322i
$153$		0			0
$154$	0.208977	−	0.307654i	0.0168398	−	0.0247915i
$155$	4.45307			0.357679
$156$		0			0
$157$	5.15138	−	8.92246i	0.411125	−	0.712090i	−0.583888	−	0.811834i	$-0.698469\pi$
$157$	5.15138	−	8.92246i	0.411125	−	0.712090i	0.995013	+	0.0997446i	$0.0318026\pi$
$158$	2.94837	+	5.10673i	0.234560	+	0.406270i
$159$		0			0
$160$	0.611519	+	1.05918i	0.0483448	+	0.0837356i
$161$	−0.0420284	−	0.0868883i	−0.00331230	−	0.00684775i
$162$		0			0
$163$	5.06852	−	8.77893i	0.396997	−	0.687619i	−0.596357	−	0.802719i	$-0.703386\pi$
$163$	5.06852	−	8.77893i	0.396997	−	0.687619i	0.993354	+	0.115101i	$0.0367190\pi$
$164$	−1.70480	+	2.95279i	−0.133122	+	0.230575i
$165$		0			0
$166$	−9.14057			−0.709446
$167$	4.28857	−	7.42802i	0.331860	−	0.574798i	−0.651017	−	0.759063i	$-0.725657\pi$
$167$	4.28857	−	7.42802i	0.331860	−	0.574798i	0.982876	+	0.184266i	$0.0589906\pi$
$168$		0			0
$169$	−1.54380	+	12.9080i	−0.118754	+	0.992924i
$170$	−0.114083	−	0.197597i	−0.00874974	−	0.0151550i
$171$		0			0
$172$	−2.06841	−	3.58258i	−0.157714	−	0.273169i
$173$	−5.33942	+	9.24815i	−0.405949	+	0.703124i	−0.994431	−	0.105386i	$-0.966392\pi$
$173$	−5.33942	+	9.24815i	−0.405949	+	0.703124i	0.588483	+	0.808510i	$0.299725\pi$
$174$		0			0
$175$	9.24645	+	0.676853i	0.698966	+	0.0511653i
$176$	0.0702857	+	0.121738i	0.00529799	+	0.00917638i
$177$		0			0
$178$	−6.35472			−0.476306
$179$	−6.48961	−	11.2403i	−0.485056	−	0.840142i	0.514797	−	0.857312i	$-0.327867\pi$
$179$	−6.48961	−	11.2403i	−0.485056	−	0.840142i	−0.999853	+	0.0171707i	$0.994534\pi$
$180$		0			0
$181$	23.7327			1.76403			0.882017	−	0.471217i	$-0.156185\pi$
$181$	23.7327			1.76403			0.882017	+	0.471217i	$0.156185\pi$
$182$	3.66544	−	8.80707i	0.271701	−	0.652824i
$183$		0			0
$184$	0.0364808			0.00268940
$185$	0.222353	+	0.385127i	0.0163477	+	0.0283151i
$186$		0			0
$187$	−0.0131122	−	0.0227111i	−0.000958863	−	0.00166080i
$188$	−0.358745	−	0.621364i	−0.0261642	−	0.0453176i
$189$		0			0
$190$	−1.09573			−0.0794926
$191$	−9.98892	+	17.3013i	−0.722773	+	1.25188i	0.237111	+	0.971483i	$0.423800\pi$
$191$	−9.98892	+	17.3013i	−0.722773	+	1.25188i	−0.959884	+	0.280397i	$0.909534\pi$
$192$		0			0
$193$	3.11194	+	5.39003i	0.224002	+	0.387983i	0.956020	−	0.293303i	$-0.0947544\pi$
$193$	3.11194	+	5.39003i	0.224002	+	0.387983i	−0.732017	+	0.681286i	$0.761421\pi$
$194$	−3.24059	−	5.61287i	−0.232661	−	0.402981i
$195$		0			0
$196$	−4.34548	+	5.48788i	−0.310391	+	0.391991i
$197$	−12.2503	+	21.2182i	−0.872799	+	1.51173i	−0.0137105	+	0.999906i	$0.504364\pi$
$197$	−12.2503	+	21.2182i	−0.872799	+	1.51173i	−0.859089	+	0.511827i	$0.828969\pi$
$198$		0			0
$199$	−19.6151			−1.39048			−0.695238	−	0.718780i	$-0.744701\pi$
$199$	−19.6151			−1.39048			−0.695238	+	0.718780i	$0.744701\pi$
$200$	−1.75209	+	3.03471i	−0.123891	+	0.214586i
$201$		0			0
$202$	1.50230	+	2.60206i	0.105701	+	0.183080i
$203$	−15.7971	−	1.15637i	−1.10874	−	0.0811615i
$204$		0			0
$205$	4.17006			0.291250
$206$	4.12788	+	7.14970i	0.287603	+	0.498143i
$207$		0			0
$208$	2.39335	+	2.69665i	0.165949	+	0.186979i
$209$	−0.125939			−0.00871140
$210$		0			0
$211$	−2.99635	+	5.18983i	−0.206277	+	0.357283i	−0.950539	−	0.310605i	$-0.899468\pi$
$211$	−2.99635	+	5.18983i	−0.206277	+	0.357283i	0.744262	+	0.667888i	$0.232802\pi$
$212$	−3.49556	+	6.05448i	−0.240076	+	0.415823i
$213$		0			0
$214$	−4.47283			−0.305756
$215$	−2.52974	+	4.38163i	−0.172527	+	0.298825i
$216$		0			0
$217$	−9.60745	−	0.703279i	−0.652196	−	0.0477417i
$218$	3.83686	−	6.64563i	0.259865	−	0.450099i
$219$		0			0
$220$	0.0859621	−	0.148891i	0.00579556	−	0.0100382i
$221$	−0.446494	−	0.503076i	−0.0300344	−	0.0338406i
$222$		0			0
$223$	13.8098	−	23.9193i	0.924775	−	1.60176i	0.132853	−	0.991136i	$-0.457586\pi$
$223$	13.8098	−	23.9193i	0.924775	−	1.60176i	0.791922	−	0.610622i	$-0.209080\pi$
$224$	−1.15207	−	2.38175i	−0.0769758	−	0.159137i
$225$		0			0
$226$	−6.18222	−	10.7079i	−0.411235	−	0.712281i
$227$	1.79129			0.118892			0.0594460	−	0.998232i	$-0.481067\pi$
$227$	1.79129			0.118892			0.0594460	+	0.998232i	$0.481067\pi$
$228$		0			0
$229$	12.6142	+	21.8485i	0.833572	+	1.44379i	0.895188	+	0.445690i	$0.147041\pi$
$229$	12.6142	+	21.8485i	0.833572	+	1.44379i	−0.0616153	+	0.998100i	$0.519625\pi$
$230$	−0.0223087	−	0.0386398i	−0.00147099	−	0.00254783i
$231$		0			0
$232$	2.99337	−	5.18466i	0.196524	−	0.340390i
$233$	−14.1852	−	24.5695i	−0.929304	−	1.60960i	−0.784489	−	0.620143i	$-0.787075\pi$
$233$	−14.1852	−	24.5695i	−0.929304	−	1.60960i	−0.144815	−	0.989459i	$-0.546259\pi$
$234$		0			0
$235$	−0.438758	+	0.759952i	−0.0286214	+	0.0495738i
$236$	6.99624			0.455416
$237$		0			0
$238$	0.214926	+	0.444331i	0.0139316	+	0.0288017i
$239$	28.9654			1.87362			0.936809	−	0.349842i	$-0.113765\pi$
$239$	28.9654			1.87362			0.936809	+	0.349842i	$0.113765\pi$
$240$		0			0
$241$	−13.1951			−0.849974			−0.424987	−	0.905200i	$-0.639721\pi$
$241$	−13.1951			−0.849974			−0.424987	+	0.905200i	$0.639721\pi$
$242$	−5.49012	+	9.50917i	−0.352918	+	0.611272i
$243$		0			0
$244$	−0.186556	+	0.323125i	−0.0119430	+	0.0206860i
$245$	8.47000	+	1.24671i	0.541128	+	0.0796495i
$246$		0			0
$247$	−3.16438	+	0.648974i	−0.201345	+	0.0412932i
$248$	1.82050	−	3.15319i	0.115602	−	0.200228i
$249$		0			0
$250$	10.4009			0.657812
$251$	−4.73276	−	8.19739i	−0.298729	−	0.517415i	0.677116	−	0.735876i	$-0.263229\pi$
$251$	−4.73276	−	8.19739i	−0.298729	−	0.517415i	−0.975846	+	0.218462i	$0.929896\pi$
$252$		0			0
$253$	−0.00256408	−	0.00444112i	−0.000161202	−	0.000279211i
$254$	5.45432	−	9.44716i	0.342235	−	0.592768i
$255$		0			0
$256$	1.00000			0.0625000
$257$	10.2358			0.638490			0.319245	−	0.947672i	$-0.396571\pi$
$257$	10.2358			0.638490			0.319245	+	0.947672i	$0.396571\pi$
$258$		0			0
$259$	−0.418902	−	0.866025i	−0.0260293	−	0.0538122i
$260$	1.39266	−	4.18404i	0.0863692	−	0.259483i
$261$		0			0
$262$	−10.9715	−	19.0032i	−0.677820	−	1.17402i
$263$	−2.42308	−	4.19690i	−0.149414	−	0.258792i	0.781597	−	0.623783i	$-0.214405\pi$
$263$	−2.42308	−	4.19690i	−0.149414	−	0.258792i	−0.931011	+	0.364991i	$0.881072\pi$
$264$		0			0
$265$	8.55039			0.525246
$266$	2.36403	+	0.173050i	0.144948	+	0.0106104i
$267$		0			0
$268$	2.42903	+	4.20720i	0.148377	+	0.256996i
$269$	0.897277			0.0547079			0.0273540	−	0.999626i	$-0.491292\pi$
$269$	0.897277			0.0547079			0.0273540	+	0.999626i	$0.491292\pi$
$270$		0			0
$271$	13.8751			0.842854			0.421427	−	0.906862i	$-0.361529\pi$
$271$	13.8751			0.842854			0.421427	+	0.906862i	$0.361529\pi$
$272$	−0.186556			−0.0113116
$273$		0			0
$274$	2.69210			0.162636
$275$	0.492588			0.0297042
$276$		0			0
$277$	−20.4739			−1.23016			−0.615078	−	0.788466i	$-0.710876\pi$
$277$	−20.4739			−1.23016			−0.615078	+	0.788466i	$0.710876\pi$
$278$	−5.28925	−	9.16126i	−0.317228	−	0.549456i
$279$		0			0
$280$	−1.81820	+	2.67673i	−0.108658	+	0.159965i
$281$	−5.11819			−0.305326			−0.152663	−	0.988278i	$-0.548785\pi$
$281$	−5.11819			−0.305326			−0.152663	+	0.988278i	$0.548785\pi$
$282$		0			0
$283$	−4.54066	−	7.86466i	−0.269914	−	0.467505i	0.698925	−	0.715195i	$-0.253662\pi$
$283$	−4.54066	−	7.86466i	−0.269914	−	0.467505i	−0.968839	+	0.247690i	$0.920329\pi$
$284$	5.31198	+	9.20062i	0.315208	+	0.545957i
$285$		0			0
$286$	0.160068	−	0.480898i	0.00946499	−	0.0284361i
$287$	−8.99686	−	0.658583i	−0.531068	−	0.0388749i
$288$		0			0
$289$	−16.9652			−0.997953
$290$	−7.32200			−0.429963
$291$		0			0
$292$	−4.80900	+	8.32943i	−0.281425	+	0.487443i
$293$	−3.13195	−	5.42469i	−0.182970	−	0.316914i	0.759920	−	0.650016i	$-0.225238\pi$
$293$	−3.13195	−	5.42469i	−0.182970	−	0.316914i	−0.942891	+	0.333102i	$0.891905\pi$
$294$		0			0
$295$	−4.27833	−	7.41029i	−0.249094	−	0.431443i
$296$	0.363609			0.0211343
$297$		0			0
$298$	5.95244	−	10.3099i	0.344816	−	0.597238i
$299$	−0.0873112	−	0.0983759i	−0.00504934	−	0.00568922i
$300$		0			0
$301$	6.14988	−	9.05381i	0.354473	−	0.521853i
$302$	3.66774	−	6.35272i	0.211055	−	0.365558i
$303$		0			0
$304$	−0.447955	+	0.775880i	−0.0256920	+	0.0444998i
$305$	0.456331			0.0261294
$306$		0			0
$307$	30.0806			1.71679			0.858395	−	0.512989i	$-0.171462\pi$
$307$	30.0806			1.71679			0.858395	+	0.512989i	$0.171462\pi$
$308$	−0.208977	+	0.307654i	−0.0119076	+	0.0175302i
$309$		0			0
$310$	−4.45307			−0.252917
$311$	13.8292	−	23.9528i	0.784180	−	1.35824i	−0.145308	−	0.989386i	$-0.546417\pi$
$311$	13.8292	−	23.9528i	0.784180	−	1.35824i	0.929488	−	0.368853i	$-0.120249\pi$
$312$		0			0
$313$	−3.43002	−	5.94097i	−0.193876	−	0.335804i	0.752655	−	0.658415i	$-0.228773\pi$
$313$	−3.43002	−	5.94097i	−0.193876	−	0.335804i	−0.946532	+	0.322611i	$0.895439\pi$
$314$	−5.15138	+	8.92246i	−0.290709	+	0.503523i
$315$		0			0
$316$	−2.94837	−	5.10673i	−0.165859	−	0.287276i
$317$	−3.37146	−	5.83953i	−0.189360	−	0.327981i	0.755677	−	0.654944i	$-0.227308\pi$
$317$	−3.37146	−	5.83953i	−0.189360	−	0.327981i	−0.945037	+	0.326963i	$0.893975\pi$
$318$		0			0
$319$	−0.841564			−0.0471186
$320$	−0.611519	−	1.05918i	−0.0341849	−	0.0592100i
$321$		0			0
$322$	0.0420284	+	0.0868883i	0.00234215	+	0.00484209i
$323$	0.0835688	−	0.144745i	0.00464989	−	0.00805385i
$324$		0			0
$325$	12.3769	−	2.53834i	0.686546	−	0.140802i
$326$	−5.06852	+	8.77893i	−0.280719	+	0.486220i
$327$		0			0
$328$	1.70480	−	2.95279i	0.0941317	−	0.163041i
$329$	1.06664	−	1.57029i	0.0588056	−	0.0865731i
$330$		0			0
$331$	5.54908	−	9.61129i	0.305005	−	0.528284i	−0.672257	−	0.740317i	$-0.734675\pi$
$331$	5.54908	−	9.61129i	0.305005	−	0.528284i	0.977262	+	0.212033i	$0.0680085\pi$
$332$	9.14057			0.501654
$333$		0			0
$334$	−4.28857	+	7.42802i	−0.234660	+	0.406443i
$335$	2.97079	−	5.14557i	0.162312	−	0.281132i
$336$		0			0
$337$	21.6470			1.17918			0.589592	−	0.807701i	$-0.299288\pi$
$337$	21.6470			1.17918			0.589592	+	0.807701i	$0.299288\pi$
$338$	1.54380	−	12.9080i	0.0839715	−	0.702103i
$339$		0			0
$340$	0.114083	+	0.197597i	0.00618700	+	0.0107162i
$341$	−0.511819			−0.0277166
$342$		0			0
$343$	−18.0770	−	4.02745i	−0.976069	−	0.217462i
$344$	2.06841	+	3.58258i	0.111521	+	0.193160i
$345$		0			0
$346$	5.33942	−	9.24815i	0.287049	−	0.497183i
$347$	−29.8675			−1.60337			−0.801685	−	0.597746i	$-0.796063\pi$
$347$	−29.8675			−1.60337			−0.801685	+	0.597746i	$0.796063\pi$
$348$		0			0
$349$	−6.47690	+	11.2183i	−0.346700	+	0.600503i	−0.985661	−	0.168737i	$-0.946031\pi$
$349$	−6.47690	+	11.2183i	−0.346700	+	0.600503i	0.638961	+	0.769239i	$0.279365\pi$
$350$	−9.24645	−	0.676853i	−0.494243	−	0.0361793i
$351$		0			0
$352$	−0.0702857	−	0.121738i	−0.00374624	−	0.00648868i
$353$	3.07853	+	5.33218i	0.163854	+	0.283803i	0.936248	−	0.351341i	$-0.114274\pi$
$353$	3.07853	+	5.33218i	0.163854	+	0.283803i	−0.772394	+	0.635144i	$0.780941\pi$
$354$		0			0
$355$	6.49675	−	11.2527i	0.344812	−	0.597232i
$356$	6.35472			0.336799
$357$		0			0
$358$	6.48961	+	11.2403i	0.342986	+	0.594070i
$359$	−12.4203	−	21.5125i	−0.655516	−	1.13539i	−0.981764	−	0.190103i	$-0.939118\pi$
$359$	−12.4203	−	21.5125i	−0.655516	−	1.13539i	0.326248	−	0.945284i	$-0.394215\pi$
$360$		0			0
$361$	9.09867	+	15.7594i	0.478878	+	0.829440i
$362$	−23.7327			−1.24736
$363$		0			0
$364$	−3.66544	+	8.80707i	−0.192121	+	0.461616i
$365$	11.7632			0.615712
$366$		0			0
$367$	−18.0306	−	31.2299i	−0.941188	−	1.63019i	−0.763209	−	0.646152i	$-0.776377\pi$
$367$	−18.0306	−	31.2299i	−0.941188	−	1.63019i	−0.177980	−	0.984034i	$-0.556956\pi$
$368$	−0.0364808			−0.00190169
$369$		0			0
$370$	−0.222353	−	0.385127i	−0.0115596	−	0.0200218i
$371$	−18.4474	−	1.35037i	−0.957740	−	0.0701079i
$372$		0			0
$373$	7.37092	−	12.7668i	0.381652	−	0.661041i	−0.609647	−	0.792673i	$-0.708689\pi$
$373$	7.37092	−	12.7668i	0.381652	−	0.661041i	0.991299	+	0.131633i	$0.0420219\pi$
$374$	0.0131122	+	0.0227111i	0.000678018	+	0.00117436i
$375$		0			0
$376$	0.358745	+	0.621364i	0.0185009	+	0.0320444i
$377$	−21.1454	+	4.33664i	−1.08904	+	0.223348i
$378$		0			0
$379$	5.33674	−	9.24351i	0.274130	−	0.474807i	−0.695785	−	0.718250i	$-0.744943\pi$
$379$	5.33674	−	9.24351i	0.274130	−	0.474807i	0.969915	+	0.243443i	$0.0782768\pi$
$380$	1.09573			0.0562098
$381$		0			0
$382$	9.98892	−	17.3013i	0.511078	−	0.885213i
$383$	−10.2017	+	17.6698i	−0.521281	+	0.902884i	0.478413	+	0.878135i	$0.341212\pi$
$383$	−10.2017	+	17.6698i	−0.521281	+	0.902884i	−0.999694	+	0.0247495i	$0.992121\pi$
$384$		0			0
$385$	0.453655	+	0.0332082i	0.0231204	+	0.00169244i
$386$	−3.11194	−	5.39003i	−0.158393	−	0.274346i
$387$		0			0
$388$	3.24059	+	5.61287i	0.164516	+	0.284950i
$389$	15.8455	−	27.4453i	0.803400	−	1.39153i	−0.113966	−	0.993485i	$-0.536356\pi$
$389$	15.8455	−	27.4453i	0.803400	−	1.39153i	0.917366	−	0.398045i	$-0.130311\pi$
$390$		0			0
$391$	0.00680573			0.000344181
$392$	4.34548	−	5.48788i	0.219480	−	0.277180i
$393$		0			0
$394$	12.2503	−	21.2182i	0.617162	−	1.06896i
$395$	−3.60597	+	6.24573i	−0.181436	+	0.314257i
$396$		0			0
$397$	1.30524	−	2.26074i	0.0655080	−	0.113463i	−0.831411	−	0.555658i	$-0.812467\pi$
$397$	1.30524	−	2.26074i	0.0655080	−	0.113463i	0.896919	+	0.442194i	$0.145800\pi$
$398$	19.6151			0.983215
$399$		0			0
$400$	1.75209	−	3.03471i	0.0876045	−	0.151735i
$401$	16.3696			0.817458			0.408729	−	0.912656i	$-0.365972\pi$
$401$	16.3696			0.817458			0.408729	+	0.912656i	$0.365972\pi$
$402$		0			0
$403$	−12.8601	+	2.63744i	−0.640608	+	0.131380i
$404$	−1.50230	−	2.60206i	−0.0747422	−	0.129457i
$405$		0			0
$406$	15.7971	+	1.15637i	0.783999	+	0.0573898i
$407$	−0.0255565	−	0.0442652i	−0.00126679	−	0.00219414i
$408$		0			0
$409$	22.7307			1.12396			0.561980	−	0.827151i	$-0.310040\pi$
$409$	22.7307			1.12396			0.561980	+	0.827151i	$0.310040\pi$
$410$	−4.17006			−0.205945
$411$		0			0
$412$	−4.12788	−	7.14970i	−0.203366	−	0.352240i
$413$	8.06014	+	16.6633i	0.396614	+	0.819948i
$414$		0			0
$415$	−5.58963	−	9.68152i	−0.274384	−	0.475247i
$416$	−2.39335	−	2.69665i	−0.117343	−	0.132214i
$417$		0			0
$418$	0.125939			0.00615989
$419$	11.4491	−	19.8303i	0.559323	−	0.968776i	−0.438230	−	0.898863i	$-0.644394\pi$
$419$	11.4491	−	19.8303i	0.559323	−	0.968776i	0.997553	−	0.0699131i	$-0.0222722\pi$
$420$		0			0
$421$	8.33173			0.406064			0.203032	−	0.979172i	$-0.434921\pi$
$421$	8.33173			0.406064			0.203032	+	0.979172i	$0.434921\pi$
$422$	2.99635	−	5.18983i	0.145860	−	0.252637i
$423$		0			0
$424$	3.49556	−	6.05448i	0.169759	−	0.294032i
$425$	−0.326863	+	0.566144i	−0.0158552	+	0.0274620i
$426$		0			0
$427$	−0.984529	−	0.0720689i	−0.0476447	−	0.00348766i
$428$	4.47283			0.216202
$429$		0			0
$430$	2.52974	−	4.38163i	0.121995	−	0.211301i
$431$	−13.7933	−	23.8907i	−0.664401	−	1.15078i	−0.979447	−	0.201700i	$-0.935353\pi$
$431$	−13.7933	−	23.8907i	−0.664401	−	1.15078i	0.315046	−	0.949076i	$-0.397980\pi$
$432$		0			0
$433$	−15.7254	−	27.2372i	−0.755714	−	1.30893i	−0.945019	−	0.327016i	$-0.893957\pi$
$433$	−15.7254	−	27.2372i	−0.755714	−	1.30893i	0.189305	−	0.981918i	$-0.439376\pi$
$434$	9.60745	+	0.703279i	0.461172	+	0.0337585i
$435$		0			0
$436$	−3.83686	+	6.64563i	−0.183752	+	0.318268i
$437$	0.0163418	−	0.0283048i	0.000781732	−	0.00135400i
$438$		0			0
$439$	−15.2460			−0.727653			−0.363827	−	0.931467i	$-0.618530\pi$
$439$	−15.2460			−0.727653			−0.363827	+	0.931467i	$0.618530\pi$
$440$	−0.0859621	+	0.148891i	−0.00409808	+	0.00709808i
$441$		0			0
$442$	0.446494	+	0.503076i	0.0212375	+	0.0239289i
$443$	−10.7666	−	18.6482i	−0.511535	−	0.886005i	−0.999911	−	0.0133713i	$-0.995744\pi$
$443$	−10.7666	−	18.6482i	−0.511535	−	0.886005i	0.488375	−	0.872634i	$-0.337590\pi$
$444$		0			0
$445$	−3.88603	−	6.73080i	−0.184215	−	0.319071i
$446$	−13.8098	+	23.9193i	−0.653915	+	1.13261i
$447$		0			0
$448$	1.15207	+	2.38175i	0.0544301	+	0.112527i
$449$	−2.76290	−	4.78549i	−0.130389	−	0.225841i	0.793437	−	0.608652i	$-0.208289\pi$
$449$	−2.76290	−	4.78549i	−0.130389	−	0.225841i	−0.923827	+	0.382811i	$0.874956\pi$
$450$		0			0
$451$	−0.479292			−0.0225690
$452$	6.18222	+	10.7079i	0.290787	+	0.503658i
$453$		0			0
$454$	−1.79129			−0.0840694
$455$	11.5698	−	1.50332i	0.542399	−	0.0704767i
$456$		0			0
$457$	−32.0373			−1.49864			−0.749321	−	0.662207i	$-0.769620\pi$
$457$	−32.0373			−1.49864			−0.749321	+	0.662207i	$0.769620\pi$
$458$	−12.6142	−	21.8485i	−0.589425	−	1.02091i
$459$		0			0
$460$	0.0223087	+	0.0386398i	0.00104015	+	0.00180159i
$461$	6.48516	+	11.2326i	0.302044	+	0.523156i	0.976599	−	0.215069i	$-0.0689977\pi$
$461$	6.48516	+	11.2326i	0.302044	+	0.523156i	−0.674555	+	0.738225i	$0.735664\pi$
$462$		0			0
$463$	−11.6453			−0.541202			−0.270601	−	0.962692i	$-0.587222\pi$
$463$	−11.6453			−0.541202			−0.270601	+	0.962692i	$0.587222\pi$
$464$	−2.99337	+	5.18466i	−0.138964	+	0.240692i
$465$		0			0
$466$	14.1852	+	24.5695i	0.657117	+	1.13816i
$467$	−2.99029	−	5.17934i	−0.138374	−	0.239671i	0.788507	−	0.615026i	$-0.210854\pi$
$467$	−2.99029	−	5.17934i	−0.138374	−	0.239671i	−0.926881	+	0.375354i	$0.877521\pi$
$468$		0			0
$469$	−7.22211	+	10.6323i	−0.333486	+	0.490955i
$470$	0.438758	−	0.759952i	0.0202384	−	0.0350539i
$471$		0			0
$472$	−6.99624			−0.322028
$473$	0.290759	−	0.503609i	0.0133691	−	0.0231560i
$474$		0			0
$475$	1.56971	+	2.71882i	0.0720234	+	0.124748i
$476$	−0.214926	−	0.444331i	−0.00985109	−	0.0203659i
$477$		0			0
$478$	−28.9654			−1.32485
$479$	3.33079	+	5.76911i	0.152188	+	0.263597i	0.932032	−	0.362377i	$-0.118035\pi$
$479$	3.33079	+	5.76911i	0.152188	+	0.263597i	−0.779844	+	0.625974i	$0.784701\pi$
$480$		0			0
$481$	−0.870241	−	0.980524i	−0.0396796	−	0.0447080i
$482$	13.1951			0.601022
$483$		0			0
$484$	5.49012	−	9.50917i	0.249551	−	0.432235i
$485$	3.96337	−	6.86475i	0.179967	−	0.311712i
$486$		0			0
$487$	−18.9362			−0.858079			−0.429039	−	0.903286i	$-0.641148\pi$
$487$	−18.9362			−0.858079			−0.429039	+	0.903286i	$0.641148\pi$
$488$	0.186556	−	0.323125i	0.00844501	−	0.0146272i
$489$		0			0
$490$	−8.47000	−	1.24671i	−0.382636	−	0.0563207i
$491$	19.5234	−	33.8155i	0.881079	−	1.52607i	0.0309367	−	0.999521i	$-0.490151\pi$
$491$	19.5234	−	33.8155i	0.881079	−	1.52607i	0.850143	−	0.526553i	$-0.176516\pi$
$492$		0			0
$493$	0.558432	−	0.967232i	0.0251505	−	0.0435619i
$494$	3.16438	−	0.648974i	0.142372	−	0.0291987i
$495$		0			0
$496$	−1.82050	+	3.15319i	−0.0817427	+	0.141582i
$497$	−15.7938	+	23.2516i	−0.708450	+	1.04298i
$498$		0			0
$499$	−16.6602	−	28.8563i	−0.745812	−	1.29178i	−0.949814	−	0.312814i	$-0.898728\pi$
$499$	−16.6602	−	28.8563i	−0.745812	−	1.29178i	0.204002	−	0.978970i	$-0.434605\pi$
$500$	−10.4009			−0.465144
$501$		0			0
$502$	4.73276	+	8.19739i	0.211234	+	0.365867i
$503$	−5.86768	−	10.1631i	−0.261627	−	0.453151i	0.705048	−	0.709160i	$-0.250926\pi$
$503$	−5.86768	−	10.1631i	−0.261627	−	0.453151i	−0.966674	+	0.256009i	$0.917592\pi$
$504$		0			0
$505$	−1.83737	+	3.18242i	−0.0817618	+	0.141616i
$506$	0.00256408	+	0.00444112i	0.000113987	+	0.000197432i
$507$		0			0
$508$	−5.45432	+	9.44716i	−0.241996	+	0.419150i
$509$	34.6529			1.53596			0.767982	−	0.640471i	$-0.221261\pi$
$509$	34.6529			1.53596			0.767982	+	0.640471i	$0.221261\pi$
$510$		0			0
$511$	−25.3789	−	1.85777i	−1.12270	−	0.0821830i
$512$	−1.00000			−0.0441942
$513$		0			0
$514$	−10.2358			−0.451481
$515$	−5.04855	+	8.74434i	−0.222466	+	0.385322i
$516$		0			0
$517$	0.0504293	−	0.0873461i	0.00221788	−	0.00384148i
$518$	0.418902	+	0.866025i	0.0184055	+	0.0380510i
$519$		0			0
$520$	−1.39266	+	4.18404i	−0.0610722	+	0.183482i
$521$	−2.62165	+	4.54083i	−0.114856	+	0.198937i	−0.917722	−	0.397222i	$-0.869974\pi$
$521$	−2.62165	+	4.54083i	−0.114856	+	0.198937i	0.802866	+	0.596160i	$0.203307\pi$
$522$		0			0
$523$	−15.9800			−0.698757			−0.349379	−	0.936982i	$-0.613607\pi$
$523$	−15.9800			−0.698757			−0.349379	+	0.936982i	$0.613607\pi$
$524$	10.9715	+	19.0032i	0.479291	+	0.830157i
$525$		0			0
$526$	2.42308	+	4.19690i	0.105651	+	0.182994i
$527$	0.339625	−	0.588248i	0.0147943	−	0.0256245i
$528$		0			0
$529$	−22.9987			−0.999942
$530$	−8.55039			−0.371405
$531$		0			0
$532$	−2.36403	−	0.173050i	−0.102494	−	0.00750267i
$533$	−12.0428	+	2.46982i	−0.521632	+	0.106980i
$534$		0			0
$535$	−2.73522	−	4.73753i	−0.118254	−	0.204821i
$536$	−2.42903	−	4.20720i	−0.104918	−	0.181724i
$537$		0			0
$538$	−0.897277			−0.0386843
$539$	−0.973511	−	0.143293i	−0.0419321	−	0.00617205i
$540$		0			0
$541$	−0.886405	−	1.53530i	−0.0381095	−	0.0660077i	0.846342	−	0.532641i	$-0.178800\pi$
$541$	−0.886405	−	1.53530i	−0.0381095	−	0.0660077i	−0.884451	+	0.466633i	$0.845467\pi$
$542$	−13.8751			−0.595988
$543$		0			0
$544$	0.186556			0.00799854
$545$	9.38523			0.402019
$546$		0			0
$547$	9.88287			0.422561			0.211280	−	0.977425i	$-0.432237\pi$
$547$	9.88287			0.422561			0.211280	+	0.977425i	$0.432237\pi$
$548$	−2.69210			−0.115001
$549$		0			0
$550$	−0.492588			−0.0210040
$551$	−2.68179	−	4.64499i	−0.114248	−	0.197883i
$552$		0			0
$553$	8.76624	−	12.9056i	0.372779	−	0.548802i
$554$	20.4739			0.869852
$555$		0			0
$556$	5.28925	+	9.16126i	0.224314	+	0.388524i
$557$	10.0865	+	17.4704i	0.427380	+	0.740244i	0.996639	−	0.0819139i	$-0.0261033\pi$
$557$	10.0865	+	17.4704i	0.427380	+	0.740244i	−0.569259	+	0.822158i	$0.692770\pi$
$558$		0			0
$559$	4.71055	−	14.1521i	0.199235	−	0.598571i
$560$	1.81820	−	2.67673i	0.0768328	−	0.113113i
$561$		0			0
$562$	5.11819			0.215898
$563$	0.106297			0.00447988			0.00223994	−	0.999997i	$-0.499287\pi$
$563$	0.106297			0.00447988			0.00223994	+	0.999997i	$0.499287\pi$
$564$		0			0
$565$	7.56109	−	13.0962i	0.318097	−	0.550961i
$566$	4.54066	+	7.86466i	0.190858	+	0.330576i
$567$		0			0
$568$	−5.31198	−	9.20062i	−0.222886	−	0.386050i
$569$	7.66181			0.321200			0.160600	−	0.987020i	$-0.448657\pi$
$569$	7.66181			0.321200			0.160600	+	0.987020i	$0.448657\pi$
$570$		0			0
$571$	−1.44075	+	2.49545i	−0.0602935	+	0.104431i	−0.894597	−	0.446875i	$-0.852537\pi$
$571$	−1.44075	+	2.49545i	−0.0602935	+	0.104431i	0.834303	+	0.551306i	$0.185870\pi$
$572$	−0.160068	+	0.480898i	−0.00669276	+	0.0201074i
$573$		0			0
$574$	8.99686	+	0.658583i	0.375522	+	0.0274887i
$575$	−0.0639177	+	0.110709i	−0.00266555	+	0.00461687i
$576$		0			0
$577$	17.3055	−	29.9740i	0.720438	−	1.24783i	−0.240387	−	0.970677i	$-0.577274\pi$
$577$	17.3055	−	29.9740i	0.720438	−	1.24783i	0.960825	−	0.277157i	$-0.0893923\pi$
$578$	16.9652			0.705659
$579$		0			0
$580$	7.32200			0.304029
$581$	10.5306	+	21.7706i	0.436881	+	0.903195i
$582$		0			0
$583$	−0.982751			−0.0407014
$584$	4.80900	−	8.32943i	0.198998	−	0.344674i
$585$		0			0
$586$	3.13195	+	5.42469i	0.129380	+	0.224092i
$587$	5.21346	−	9.02999i	0.215183	−	0.372707i	−0.738146	−	0.674641i	$-0.764299\pi$
$587$	5.21346	−	9.02999i	0.215183	−	0.372707i	0.953329	+	0.301933i	$0.0976320\pi$
$588$		0			0
$589$	−1.63100	−	2.82497i	−0.0672041	−	0.116401i
$590$	4.27833	+	7.41029i	0.176136	+	0.305077i
$591$		0			0
$592$	−0.363609			−0.0149442
$593$	−10.9551	−	18.9748i	−0.449873	−	0.779203i	0.548505	−	0.836148i	$-0.315197\pi$
$593$	−10.9551	−	18.9748i	−0.449873	−	0.779203i	−0.998377	+	0.0569451i	$0.981864\pi$
$594$		0			0
$595$	−0.339196	+	0.499362i	−0.0139057	+	0.0204718i
$596$	−5.95244	+	10.3099i	−0.243822	+	0.422311i
$597$		0			0
$598$	0.0873112	+	0.0983759i	0.00357042	+	0.00402289i
$599$	7.67924	−	13.3008i	0.313765	−	0.543457i	−0.665409	−	0.746479i	$-0.731743\pi$
$599$	7.67924	−	13.3008i	0.313765	−	0.543457i	0.979174	+	0.203022i	$0.0650762\pi$
$600$		0			0
$601$	1.63801	−	2.83711i	0.0668157	−	0.115728i	−0.830682	−	0.556747i	$-0.812049\pi$
$601$	1.63801	−	2.83711i	0.0668157	−	0.115728i	0.897498	+	0.441019i	$0.145383\pi$
$602$	−6.14988	+	9.05381i	−0.250650	+	0.369006i
$603$		0			0
$604$	−3.66774	+	6.35272i	−0.149238	+	0.258488i
$605$	−13.4292			−0.545976
$606$		0			0
$607$	−16.5768	+	28.7118i	−0.672830	+	1.16538i	0.304268	+	0.952587i	$0.401588\pi$
$607$	−16.5768	+	28.7118i	−0.672830	+	1.16538i	−0.977098	+	0.212790i	$0.931745\pi$
$608$	0.447955	−	0.775880i	0.0181670	−	0.0314661i
$609$		0			0
$610$	−0.456331			−0.0184763
$611$	0.816999	−	2.45455i	0.0330522	−	0.0993003i
$612$		0			0
$613$	17.1792	+	29.7553i	0.693863	+	1.20181i	0.970562	+	0.240849i	$0.0774260\pi$
$613$	17.1792	+	29.7553i	0.693863	+	1.20181i	−0.276700	+	0.960956i	$0.589241\pi$
$614$	−30.0806			−1.21395
$615$		0			0
$616$	0.208977	−	0.307654i	0.00841992	−	0.0123957i
$617$	10.2155	+	17.6938i	0.411261	+	0.712325i	0.995028	−	0.0995961i	$-0.0317551\pi$
$617$	10.2155	+	17.6938i	0.411261	+	0.712325i	−0.583767	+	0.811921i	$0.698422\pi$
$618$		0			0
$619$	−6.14114	+	10.6368i	−0.246833	+	0.427528i	−0.962645	−	0.270765i	$-0.912723\pi$
$619$	−6.14114	+	10.6368i	−0.246833	+	0.427528i	0.715812	+	0.698293i	$0.246057\pi$
$620$	4.45307			0.178839
$621$		0			0
$622$	−13.8292	+	23.9528i	−0.554499	+	0.960420i
$623$	7.32107	+	15.1354i	0.293312	+	0.606386i
$624$		0			0
$625$	−2.40009	−	4.15708i	−0.0960036	−	0.166283i
$626$	3.43002	+	5.94097i	0.137091	+	0.237449i
$627$		0			0
$628$	5.15138	−	8.92246i	0.205563	−	0.356045i
$629$	0.0678335			0.00270470
$630$		0			0
$631$	−0.272895	−	0.472667i	−0.0108638	−	0.0188166i	0.860542	−	0.509379i	$-0.170125\pi$
$631$	−0.272895	−	0.472667i	−0.0108638	−	0.0188166i	−0.871406	+	0.490562i	$0.836791\pi$
$632$	2.94837	+	5.10673i	0.117280	+	0.203135i
$633$		0			0
$634$	3.37146	+	5.83953i	0.133898	+	0.231917i
$635$	13.3417			0.529448
$636$		0			0
$637$	−25.1991	+	1.41617i	−0.998425	+	0.0561105i
$638$	0.841564			0.0333178
$639$		0			0
$640$	0.611519	+	1.05918i	0.0241724	+	0.0418678i
$641$	36.0597			1.42427			0.712136	−	0.702041i	$-0.247728\pi$
$641$	36.0597			1.42427			0.712136	+	0.702041i	$0.247728\pi$
$642$		0			0
$643$	13.7343	+	23.7885i	0.541627	+	0.938125i	0.998811	+	0.0487529i	$0.0155247\pi$
$643$	13.7343	+	23.7885i	0.541627	+	0.938125i	−0.457184	+	0.889372i	$0.651142\pi$
$644$	−0.0420284	−	0.0868883i	−0.00165615	−	0.00342388i
$645$		0			0
$646$	−0.0835688	+	0.144745i	−0.00328797	+	0.00569493i
$647$	3.07080	+	5.31878i	0.120726	+	0.209103i	0.920054	−	0.391792i	$-0.128145\pi$
$647$	3.07080	+	5.31878i	0.120726	+	0.209103i	−0.799328	+	0.600894i	$0.794811\pi$
$648$		0			0
$649$	0.491736	+	0.851712i	0.0193023	+	0.0334326i
$650$	−12.3769	+	2.53834i	−0.485462	+	0.0995619i
$651$		0			0
$652$	5.06852	−	8.77893i	0.198498	−	0.343809i
$653$	24.3606			0.953304			0.476652	−	0.879092i	$-0.341850\pi$
$653$	24.3606			0.953304			0.476652	+	0.879092i	$0.341850\pi$
$654$		0			0
$655$	13.4185	−	23.2416i	0.524305	−	0.908123i
$656$	−1.70480	+	2.95279i	−0.0665611	+	0.115287i
$657$		0			0
$658$	−1.06664	+	1.57029i	−0.0415818	+	0.0612165i
$659$	−5.44539	−	9.43169i	−0.212122	−	0.367407i	0.740256	−	0.672325i	$-0.234704\pi$
$659$	−5.44539	−	9.43169i	−0.212122	−	0.367407i	−0.952379	+	0.304918i	$0.901371\pi$
$660$		0			0
$661$	18.6363	+	32.2789i	0.724866	+	1.25551i	0.959029	+	0.283308i	$0.0914319\pi$
$661$	18.6363	+	32.2789i	0.724866	+	1.25551i	−0.234163	+	0.972197i	$0.575235\pi$
$662$	−5.54908	+	9.61129i	−0.215671	+	0.373553i
$663$		0			0
$664$	−9.14057			−0.354723
$665$	1.26236	+	2.60976i	0.0489521	+	0.101202i
$666$		0			0
$667$	0.109201	−	0.189141i	0.00422826	−	0.00732356i
$668$	4.28857	−	7.42802i	0.165930	−	0.287399i
$669$		0			0
$670$	−2.97079	+	5.14557i	−0.114772	+	0.198791i
$671$	−0.0524490			−0.00202477
$672$		0			0
$673$	−21.9417	+	38.0042i	−0.845792	+	1.46495i	0.0391397	+	0.999234i	$0.487538\pi$
$673$	−21.9417	+	38.0042i	−0.845792	+	1.46495i	−0.884932	+	0.465721i	$0.845795\pi$
$674$	−21.6470			−0.833810
$675$		0			0
$676$	−1.54380	+	12.9080i	−0.0593768	+	0.496462i
$677$	20.6518	+	35.7700i	0.793713	+	1.37475i	0.923653	+	0.383230i	$0.125188\pi$
$677$	20.6518	+	35.7700i	0.793713	+	1.37475i	−0.129940	+	0.991522i	$0.541478\pi$
$678$		0			0
$679$	−9.63509	+	14.1847i	−0.369761	+	0.544359i
$680$	−0.114083	−	0.197597i	−0.00437487	−	0.00757750i
$681$		0			0
$682$	0.511819			0.0195986
$683$	−27.5816			−1.05538			−0.527690	−	0.849437i	$-0.676942\pi$
$683$	−27.5816			−1.05538			−0.527690	+	0.849437i	$0.676942\pi$
$684$		0			0
$685$	1.64627	+	2.85143i	0.0629008	+	0.108947i
$686$	18.0770	+	4.02745i	0.690185	+	0.153769i
$687$		0			0
$688$	−2.06841	−	3.58258i	−0.0788572	−	0.136585i
$689$	−24.6929	+	5.06419i	−0.940723	+	0.192930i
$690$		0			0
$691$	29.3993			1.11840			0.559202	−	0.829032i	$-0.311108\pi$
$691$	29.3993			1.11840			0.559202	+	0.829032i	$0.311108\pi$
$692$	−5.33942	+	9.24815i	−0.202974	+	0.351562i
$693$		0			0
$694$	29.8675			1.13375
$695$	6.46895	−	11.2046i	0.245381	−	0.425013i
$696$		0			0
$697$	0.318041	−	0.550863i	0.0120466	−	0.0208654i
$698$	6.47690	−	11.2183i	0.245154	−	0.424619i
$699$		0			0
$700$	9.24645	+	0.676853i	0.349483	+	0.0255826i
$701$	−19.0498			−0.719500			−0.359750	−	0.933049i	$-0.617138\pi$
$701$	−19.0498			−0.719500			−0.359750	+	0.933049i	$0.617138\pi$
$702$		0			0
$703$	0.162880	−	0.282117i	0.00614314	−	0.0106402i
$704$	0.0702857	+	0.121738i	0.00264899	+	0.00458819i
$705$		0			0
$706$	−3.07853	−	5.33218i	−0.115862	−	0.200679i
$707$	4.46671	−	6.57585i	0.167988	−	0.247310i
$708$		0			0
$709$	−8.95282	+	15.5067i	−0.336230	+	0.582368i	−0.983720	−	0.179706i	$-0.942485\pi$
$709$	−8.95282	+	15.5067i	−0.336230	+	0.582368i	0.647490	+	0.762074i	$0.275819\pi$
$710$	−6.49675	+	11.2527i	−0.243819	+	0.422306i
$711$		0			0
$712$	−6.35472			−0.238153
$713$	0.0664132	−	0.115031i	0.00248719	−	0.00430794i
$714$		0			0
$715$	0.607242	−	0.124538i	0.0227096	−	0.00465744i
$716$	−6.48961	−	11.2403i	−0.242528	−	0.420071i
$717$		0			0
$718$	12.4203	+	21.5125i	0.463520	+	0.802840i
$719$	17.1583	−	29.7191i	0.639897	−	1.10833i	−0.345558	−	0.938397i	$-0.612310\pi$
$719$	17.1583	−	29.7191i	0.639897	−	1.10833i	0.985455	−	0.169936i	$-0.0543562\pi$
$720$		0			0
$721$	12.2732	−	18.0685i	0.457078	−	0.672907i
$722$	−9.09867	−	15.7594i	−0.338618	−	0.586503i
$723$		0			0
$724$	23.7327			0.882017
$725$	10.4893	+	18.1680i	0.389563	+	0.674743i
$726$		0			0
$727$	20.6482			0.765800			0.382900	−	0.923790i	$-0.374925\pi$
$727$	20.6482			0.765800			0.382900	+	0.923790i	$0.374925\pi$
$728$	3.66544	−	8.80707i	0.135850	−	0.326412i
$729$		0			0
$730$	−11.7632			−0.435374
$731$	0.385874	+	0.668354i	0.0142721	+	0.0247199i
$732$		0			0
$733$	14.5834	+	25.2592i	0.538650	+	0.932969i	0.998977	+	0.0452199i	$0.0143988\pi$
$733$	14.5834	+	25.2592i	0.538650	+	0.932969i	−0.460327	+	0.887749i	$0.652268\pi$
$734$	18.0306	+	31.2299i	0.665521	+	1.15272i
$735$		0			0
$736$	0.0364808			0.00134470
$737$	−0.341452	+	0.591413i	−0.0125776	+	0.0217850i
$738$		0			0
$739$	21.1080	+	36.5602i	0.776471	+	1.34489i	0.933964	+	0.357367i	$0.116326\pi$
$739$	21.1080	+	36.5602i	0.776471	+	1.34489i	−0.157493	+	0.987520i	$0.550341\pi$
$740$	0.222353	+	0.385127i	0.00817387	+	0.0141576i
$741$		0			0
$742$	18.4474	+	1.35037i	0.677225	+	0.0495738i
$743$	−8.87311	+	15.3687i	−0.325523	+	0.563822i	−0.981618	−	0.190856i	$-0.938874\pi$
$743$	−8.87311	+	15.3687i	−0.325523	+	0.563822i	0.656095	+	0.754678i	$0.272207\pi$
$744$		0			0
$745$	14.5601			0.533441
$746$	−7.37092	+	12.7668i	−0.269869	+	0.467426i
$747$		0			0
$748$	−0.0131122	−	0.0227111i	−0.000479431	−	0.000830399i
$749$	5.15300	+	10.6532i	0.188287	+	0.389258i
$750$		0			0
$751$	31.3274			1.14315			0.571576	−	0.820549i	$-0.306332\pi$
$751$	31.3274			1.14315			0.571576	+	0.820549i	$0.306332\pi$
$752$	−0.358745	−	0.621364i	−0.0130821	−	0.0226588i
$753$		0			0
$754$	21.1454	−	4.33664i	0.770069	−	0.157931i
$755$	8.97157			0.326509
$756$		0			0
$757$	12.9370	−	22.4076i	0.470204	−	0.814417i	−0.529216	−	0.848487i	$-0.677514\pi$
$757$	12.9370	−	22.4076i	0.470204	−	0.814417i	0.999419	+	0.0340705i	$0.0108471\pi$
$758$	−5.33674	+	9.24351i	−0.193839	+	0.335739i
$759$		0			0
$760$	−1.09573			−0.0397463
$761$	−0.477691	+	0.827386i	−0.0173163	+	0.0299927i	−0.874554	−	0.484929i	$-0.838846\pi$
$761$	−0.477691	+	0.827386i	−0.0173163	+	0.0299927i	0.857237	+	0.514921i	$0.172179\pi$
$762$		0			0
$763$	−20.2486	−	1.48222i	−0.733047	−	0.0536600i
$764$	−9.98892	+	17.3013i	−0.361387	+	0.625940i
$765$		0			0
$766$	10.2017	−	17.6698i	0.368601	−	0.638436i
$767$	16.7444	+	18.8664i	0.604606	+	0.681225i
$768$		0			0
$769$	0.0702857	−	0.121738i	0.00253457	−	0.00439000i	−0.864755	−	0.502193i	$-0.832527\pi$
$769$	0.0702857	−	0.121738i	0.00253457	−	0.00439000i	0.867290	+	0.497803i	$0.165860\pi$
$770$	−0.453655	−	0.0332082i	−0.0163486	−	0.00119674i
$771$		0			0
$772$	3.11194	+	5.39003i	0.112001	+	0.193992i
$773$	−16.3472			−0.587968			−0.293984	−	0.955810i	$-0.594981\pi$
$773$	−16.3472			−0.587968			−0.293984	+	0.955810i	$0.594981\pi$
$774$		0			0
$775$	6.37934	+	11.0493i	0.229153	+	0.396904i
$776$	−3.24059	−	5.61287i	−0.116331	−	0.201490i
$777$		0			0
$778$	−15.8455	+	27.4453i	−0.568090	+	0.983960i
$779$	−1.52734	−	2.64544i	−0.0547228	−	0.0947826i
$780$		0			0
$781$	−0.746713	+	1.29335i	−0.0267195	+	0.0462795i
$782$	−0.00680573			−0.000243372
$783$		0			0
$784$	−4.34548	+	5.48788i	−0.155196	+	0.195996i
$785$	−12.6007			−0.449737
$786$		0			0
$787$	35.7105			1.27294			0.636471	−	0.771301i	$-0.280394\pi$
$787$	35.7105			1.27294			0.636471	+	0.771301i	$0.280394\pi$
$788$	−12.2503	+	21.2182i	−0.436400	+	0.755866i
$789$		0			0
$790$	3.60597	−	6.24573i	0.128295	−	0.222213i
$791$	−18.3813	+	27.0608i	−0.653563	+	0.962170i
$792$		0			0
$793$	−1.31785	+	0.270273i	−0.0467981	+	0.00959769i
$794$	−1.30524	+	2.26074i	−0.0463212	+	0.0802306i
$795$		0			0
$796$	−19.6151			−0.695238
$797$	−2.01756	−	3.49451i	−0.0714655	−	0.123782i	0.828078	−	0.560612i	$-0.189434\pi$
$797$	−2.01756	−	3.49451i	−0.0714655	−	0.123782i	−0.899544	+	0.436831i	$0.856101\pi$
$798$		0			0
$799$	0.0669261	+	0.115919i	0.00236768	+	0.00410093i
$800$	−1.75209	+	3.03471i	−0.0619457	+	0.107293i
$801$		0			0
$802$	−16.3696			−0.578030
$803$	−1.35202			−0.0477116
$804$		0			0
$805$	−0.0663293	+	0.0976495i	−0.00233780	+	0.00344169i
$806$	12.8601	−	2.63744i	0.452978	−	0.0928999i
$807$		0			0
$808$	1.50230	+	2.60206i	0.0528507	+	0.0915401i
$809$	−13.9783	−	24.2112i	−0.491452	−	0.851220i	0.508499	−	0.861062i	$-0.330200\pi$
$809$	−13.9783	−	24.2112i	−0.491452	−	0.851220i	−0.999952	+	0.00984234i	$0.996867\pi$
$810$		0			0
$811$	49.6578			1.74372			0.871861	−	0.489754i	$-0.162913\pi$
$811$	49.6578			1.74372			0.871861	+	0.489754i	$0.162913\pi$
$812$	−15.7971	−	1.15637i	−0.554371	−	0.0405807i
$813$		0			0
$814$	0.0255565	+	0.0442652i	0.000895755	+	0.00155149i
$815$	−12.3980			−0.434282
$816$		0			0
$817$	3.70621			0.129664
$818$	−22.7307			−0.794759
$819$		0			0
$820$	4.17006			0.145625
$821$	40.7269			1.42138			0.710690	−	0.703506i	$-0.248383\pi$
$821$	40.7269			1.42138			0.710690	+	0.703506i	$0.248383\pi$
$822$		0			0
$823$	−53.6630			−1.87058			−0.935288	−	0.353889i	$-0.884859\pi$
$823$	−53.6630			−1.87058			−0.935288	+	0.353889i	$0.884859\pi$
$824$	4.12788	+	7.14970i	0.143801	+	0.249071i
$825$		0			0
$826$	−8.06014	−	16.6633i	−0.280448	−	0.579790i
$827$	−55.5393			−1.93129			−0.965646	−	0.259862i	$-0.916323\pi$
$827$	−55.5393			−1.93129			−0.965646	+	0.259862i	$0.916323\pi$
$828$		0			0
$829$	16.6472	+	28.8337i	0.578180	+	1.00144i	0.995688	+	0.0927638i	$0.0295701\pi$
$829$	16.6472	+	28.8337i	0.578180	+	1.00144i	−0.417508	+	0.908673i	$0.637097\pi$
$830$	5.58963	+	9.68152i	0.194019	+	0.336051i
$831$		0			0
$832$	2.39335	+	2.69665i	0.0829743	+	0.0934894i
$833$	0.810677	−	1.02380i	0.0280883	−	0.0354725i
$834$		0			0
$835$	−10.4902			−0.363027
$836$	−0.125939			−0.00435570
$837$		0			0
$838$	−11.4491	+	19.8303i	−0.395501	+	0.685028i
$839$	−2.98552	−	5.17107i	−0.103072	−	0.178525i	0.809877	−	0.586600i	$-0.199534\pi$
$839$	−2.98552	−	5.17107i	−0.103072	−	0.178525i	−0.912949	+	0.408074i	$0.866200\pi$
$840$		0			0
$841$	−3.42050	−	5.92448i	−0.117948	−	0.204292i
$842$	−8.33173			−0.287130
$843$		0			0
$844$	−2.99635	+	5.18983i	−0.103139	+	0.178641i
$845$	14.6160	−	6.25833i	0.502805	−	0.215293i
$846$		0			0
$847$	28.9735	+	2.12090i	0.995540	+	0.0728749i
$848$	−3.49556	+	6.05448i	−0.120038	+	0.207912i
$849$		0			0
$850$	0.326863	−	0.566144i	0.0112113	−	0.0194186i
$851$	0.0132647			0.000454710
$852$		0			0
$853$	−24.0993			−0.825143			−0.412572	−	0.910925i	$-0.635369\pi$
$853$	−24.0993			−0.825143			−0.412572	+	0.910925i	$0.635369\pi$
$854$	0.984529	+	0.0720689i	0.0336899	+	0.00246615i
$855$		0			0
$856$	−4.47283			−0.152878
$857$	−0.639263	+	1.10724i	−0.0218368	+	0.0378225i	−0.876737	−	0.480970i	$-0.840285\pi$
$857$	−0.639263	+	1.10724i	−0.0218368	+	0.0378225i	0.854900	+	0.518792i	$0.173618\pi$
$858$		0			0
$859$	−3.92591	−	6.79988i	−0.133950	−	0.232009i	0.791246	−	0.611498i	$-0.209433\pi$
$859$	−3.92591	−	6.79988i	−0.133950	−	0.232009i	−0.925196	+	0.379490i	$0.876100\pi$
$860$	−2.52974	+	4.38163i	−0.0862633	+	0.149412i
$861$		0			0
$862$	13.7933	+	23.8907i	0.469802	+	0.813722i
$863$	−19.2024	−	33.2595i	−0.653656	−	1.13217i	−0.982229	−	0.187687i	$-0.939901\pi$
$863$	−19.2024	−	33.2595i	−0.653656	−	1.13217i	0.328573	−	0.944479i	$-0.393432\pi$
$864$		0			0
$865$	13.0606			0.444074
$866$	15.7254	+	27.2372i	0.534370	+	0.925556i
$867$		0			0
$868$	−9.60745	−	0.703279i	−0.326098	−	0.0238708i
$869$	0.414457	−	0.717861i	0.0140595	−	0.0243518i
$870$		0			0
$871$	−5.53183	+	16.6195i	−0.187439	+	0.563131i
$872$	3.83686	−	6.64563i	0.129932	−	0.225049i
$873$		0			0
$874$	−0.0163418	+	0.0283048i	−0.000552768	+	0.000957423i
$875$	−11.9826	−	24.7724i	−0.405085	−	0.837461i
$876$		0			0
$877$	−9.55295	+	16.5462i	−0.322580	+	0.558725i	−0.981020	−	0.193908i	$-0.937884\pi$
$877$	−9.55295	+	16.5462i	−0.322580	+	0.558725i	0.658439	+	0.752634i	$0.271217\pi$
$878$	15.2460			0.514529
$879$		0			0
$880$	0.0859621	−	0.148891i	0.00289778	−	0.00501910i
$881$	−13.6438	+	23.6317i	−0.459671	+	0.796173i	−0.998943	−	0.0459583i	$-0.985366\pi$
$881$	−13.6438	+	23.6317i	−0.459671	+	0.796173i	0.539273	+	0.842131i	$0.318699\pi$
$882$		0			0
$883$	35.8526			1.20654			0.603268	−	0.797538i	$-0.293865\pi$
$883$	35.8526			1.20654			0.603268	+	0.797538i	$0.293865\pi$
$884$	−0.446494	−	0.503076i	−0.0150172	−	0.0169203i
$885$		0			0
$886$	10.7666	+	18.6482i	0.361710	+	0.626500i
$887$	7.43855			0.249762			0.124881	−	0.992172i	$-0.460145\pi$
$887$	7.43855			0.249762			0.124881	+	0.992172i	$0.460145\pi$
$888$		0			0
$889$	−28.7845	−	2.10707i	−0.965403	−	0.0706688i
$890$	3.88603	+	6.73080i	0.130260	+	0.225617i
$891$		0			0
$892$	13.8098	−	23.9193i	0.462388	−	0.800879i
$893$	0.642806			0.0215107
$894$		0			0
$895$	−7.93703	+	13.7473i	−0.265306	+	0.459523i
$896$	−1.15207	−	2.38175i	−0.0384879	−	0.0795687i
$897$		0			0
$898$	2.76290	+	4.78549i	0.0921993	+	0.159694i
$899$	−10.8988	−	18.8773i	−0.363496	−	0.629594i
$900$		0			0
$901$	0.652118	−	1.12950i	0.0217252	−	0.0376292i
$902$	0.479292			0.0159587
$903$		0			0
$904$	−6.18222	−	10.7079i	−0.205618	−	0.356140i
$905$	−14.5130	−	25.1372i	−0.482427	−	0.835588i
$906$		0			0
$907$	−3.64524	−	6.31374i	−0.121038	−	0.209644i	0.799139	−	0.601146i	$-0.205289\pi$
$907$	−3.64524	−	6.31374i	−0.121038	−	0.209644i	−0.920177	+	0.391502i	$0.871956\pi$
$908$	1.79129			0.0594460
$909$		0			0
$910$	−11.5698	+	1.50332i	−0.383534	+	0.0498345i
$911$	−8.89914			−0.294842			−0.147421	−	0.989074i	$-0.547097\pi$
$911$	−8.89914			−0.294842			−0.147421	+	0.989074i	$0.547097\pi$
$912$		0			0
$913$	0.642452	+	1.11276i	0.0212621	+	0.0368270i
$914$	32.0373			1.05970
$915$		0			0
$916$	12.6142	+	21.8485i	0.416786	+	0.721895i
$917$	−32.6209	+	48.0243i	−1.07724	+	1.58590i
$918$		0			0
$919$	3.63489	−	6.29581i	0.119904	−	0.207680i	−0.799826	−	0.600233i	$-0.795075\pi$
$919$	3.63489	−	6.29581i	0.119904	−	0.207680i	0.919729	+	0.392553i	$0.128408\pi$
$920$	−0.0223087	−	0.0386398i	−0.000735496	−	0.00127392i
$921$		0			0
$922$	−6.48516	−	11.2326i	−0.213577	−	0.369927i
$923$	−12.0974	+	36.3448i	−0.398191	+	1.19630i
$924$		0			0
$925$	−0.637075	+	1.10345i	−0.0209469	+	0.0362811i
$926$	11.6453			0.382688
$927$		0			0
$928$	2.99337	−	5.18466i	0.0982621	−	0.170195i
$929$	3.30467	−	5.72385i	0.108423	−	0.187793i	−0.806709	−	0.590949i	$-0.798753\pi$
$929$	3.30467	−	5.72385i	0.108423	−	0.187793i	0.915131	+	0.403156i	$0.132087\pi$
$930$		0			0
$931$	−2.31136	−	5.82989i	−0.0757517	−	0.191067i
$932$	−14.1852	−	24.5695i	−0.464652	−	0.804801i
$933$		0			0
$934$	2.99029	+	5.17934i	0.0978453	+	0.169473i
$935$	−0.0160368	+	0.0277765i	−0.000524458	+	0.000908389i
$936$		0			0
$937$	−44.3217			−1.44793			−0.723963	−	0.689838i	$-0.757682\pi$
$937$	−44.3217			−1.44793			−0.723963	+	0.689838i	$0.757682\pi$
$938$	7.22211	−	10.6323i	0.235810	−	0.347158i
$939$		0			0
$940$	−0.438758	+	0.759952i	−0.0143107	+	0.0247869i
$941$	−8.06612	+	13.9709i	−0.262948	+	0.455440i	−0.967024	−	0.254685i	$-0.918028\pi$
$941$	−8.06612	+	13.9709i	−0.262948	+	0.455440i	0.704076	+	0.710125i	$0.251361\pi$
$942$		0			0
$943$	0.0621924	−	0.107720i	0.00202526	−	0.00350786i
$944$	6.99624			0.227708
$945$		0			0
$946$	−0.290759	+	0.503609i	−0.00945338	+	0.0163737i
$947$	−7.96489			−0.258824			−0.129412	−	0.991591i	$-0.541309\pi$
$947$	−7.96489			−0.258824			−0.129412	+	0.991591i	$0.541309\pi$
$948$		0			0
$949$	−33.9711	+	6.96704i	−1.10275	+	0.226160i
$950$	−1.56971	−	2.71882i	−0.0509282	−	0.0882103i
$951$		0			0
$952$	0.214926	+	0.444331i	0.00696578	+	0.0144008i
$953$	−21.7224	−	37.6243i	−0.703658	−	1.21877i	−0.967174	−	0.254116i	$-0.918215\pi$
$953$	−21.7224	−	37.6243i	−0.703658	−	1.21877i	0.263516	−	0.964655i	$-0.415118\pi$
$954$		0			0
$955$	24.4336			0.790654
$956$	28.9654			0.936809
$957$		0			0
$958$	−3.33079	−	5.76911i	−0.107613	−	0.186391i
$959$	−3.10149	−	6.41192i	−0.100152	−	0.207052i
$960$		0			0
$961$	8.87159	+	15.3660i	0.286180	+	0.495679i
$962$	0.870241	+	0.980524i	0.0280577	+	0.0316134i
$963$		0			0
$964$	−13.1951			−0.424987
$965$	3.80602	−	6.59221i	0.122520	−	0.212211i
$966$		0			0
$967$	−8.68636			−0.279335			−0.139667	−	0.990198i	$-0.544603\pi$
$967$	−8.68636			−0.279335			−0.139667	+	0.990198i	$0.544603\pi$
$968$	−5.49012	+	9.50917i	−0.176459	+	0.305636i
$969$		0			0
$970$	−3.96337	+	6.86475i	−0.127256	+	0.220414i
$971$	13.9015	−	24.0781i	0.446120	−	0.772703i	−0.552009	−	0.833838i	$-0.686139\pi$
$971$	13.9015	−	24.0781i	0.446120	−	0.772703i	0.998130	+	0.0611349i	$0.0194720\pi$
$972$		0			0
$973$	−15.7263	+	23.1521i	−0.504161	+	0.742222i
$974$	18.9362			0.606753
$975$		0			0
$976$	−0.186556	+	0.323125i	−0.00597152	+	0.0103430i
$977$	−21.1398	−	36.6152i	−0.676322	−	1.17142i	−0.976081	−	0.217409i	$-0.930239\pi$
$977$	−21.1398	−	36.6152i	−0.676322	−	1.17142i	0.299759	−	0.954015i	$-0.403094\pi$
$978$		0			0
$979$	0.446646	+	0.773614i	0.0142749	+	0.0247248i
$980$	8.47000	+	1.24671i	0.270564	+	0.0398247i
$981$		0			0
$982$	−19.5234	+	33.8155i	−0.623017	+	1.07910i
$983$	20.5285	−	35.5564i	0.654757	−	1.13407i	−0.327197	−	0.944956i	$-0.606104\pi$
$983$	20.5285	−	35.5564i	0.654757	−	1.13407i	0.981955	−	0.189117i	$-0.0605626\pi$
$984$		0			0
$985$	29.9652			0.954771
$986$	−0.558432	+	0.967232i	−0.0177841	+	0.0308029i
$987$		0			0
$988$	−3.16438	+	0.648974i	−0.100672	+	0.0206466i
$989$	0.0754571	+	0.130696i	0.00239940	+	0.00415588i
$990$		0			0
$991$	13.7587	+	23.8308i	0.437061	+	0.757012i	0.997461	−	0.0712102i	$-0.0226861\pi$
$991$	13.7587	+	23.8308i	0.437061	+	0.757012i	−0.560401	+	0.828222i	$0.689353\pi$
$992$	1.82050	−	3.15319i	0.0578008	−	0.100114i
$993$		0			0
$994$	15.7938	−	23.2516i	0.500950	−	0.737495i
$995$	11.9950	+	20.7759i	0.380267	+	0.658641i
$996$		0			0
$997$	36.8679			1.16762			0.583810	−	0.811891i	$-0.301561\pi$
$997$	36.8679			1.16762			0.583810	+	0.811891i	$0.301561\pi$
$998$	16.6602	+	28.8563i	0.527369	+	0.913430i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1638.2.m.h.1621.2		8
3.2	odd	2		546.2.j.c.529.3	yes	8
7.2	even	3		1638.2.p.h.919.2		8
13.3	even	3		1638.2.p.h.991.2		8
21.2	odd	6		546.2.k.c.373.3	yes	8
39.29	odd	6		546.2.k.c.445.3	yes	8
91.16	even	3	inner	1638.2.m.h.289.2		8
273.107	odd	6		546.2.j.c.289.3	✓	8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
546.2.j.c.289.3	✓	8	273.107	odd	6
546.2.j.c.529.3	yes	8	3.2	odd	2
546.2.k.c.373.3	yes	8	21.2	odd	6
546.2.k.c.445.3	yes	8	39.29	odd	6
1638.2.m.h.289.2		8	91.16	even	3	inner
1638.2.m.h.1621.2		8	1.1	even	1	trivial
1638.2.p.h.919.2		8	7.2	even	3
1638.2.p.h.991.2		8	13.3	even	3

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 1638 = 2 \cdot 3^{2} \cdot 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1638.m (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} +1.00000 q^{4} +(-0.611519 - 1.05918i) q^{5} +(1.15207 + 2.38175i) q^{7} -1.00000 q^{8} +O(q^{10})\)	\(q-1.00000 q^{2} +1.00000 q^{4} +(-0.611519 - 1.05918i) q^{5} +(1.15207 + 2.38175i) q^{7} -1.00000 q^{8} +(0.611519 + 1.05918i) q^{10} +(0.0702857 + 0.121738i) q^{11} +(2.39335 + 2.69665i) q^{13} +(-1.15207 - 2.38175i) q^{14} +1.00000 q^{16} -0.186556 q^{17} +(-0.447955 + 0.775880i) q^{19} +(-0.611519 - 1.05918i) q^{20} +(-0.0702857 - 0.121738i) q^{22} -0.0364808 q^{23} +(1.75209 - 3.03471i) q^{25} +(-2.39335 - 2.69665i) q^{26} +(1.15207 + 2.38175i) q^{28} +(-2.99337 + 5.18466i) q^{29} +(-1.82050 + 3.15319i) q^{31} -1.00000 q^{32} +0.186556 q^{34} +(1.81820 - 2.67673i) q^{35} -0.363609 q^{37} +(0.447955 - 0.775880i) q^{38} +(0.611519 + 1.05918i) q^{40} +(-1.70480 + 2.95279i) q^{41} +(-2.06841 - 3.58258i) q^{43} +(0.0702857 + 0.121738i) q^{44} +0.0364808 q^{46} +(-0.358745 - 0.621364i) q^{47} +(-4.34548 + 5.48788i) q^{49} +(-1.75209 + 3.03471i) q^{50} +(2.39335 + 2.69665i) q^{52} +(-3.49556 + 6.05448i) q^{53} +(0.0859621 - 0.148891i) q^{55} +(-1.15207 - 2.38175i) q^{56} +(2.99337 - 5.18466i) q^{58} +6.99624 q^{59} +(-0.186556 + 0.323125i) q^{61} +(1.82050 - 3.15319i) q^{62} +1.00000 q^{64} +(1.39266 - 4.18404i) q^{65} +(2.42903 + 4.20720i) q^{67} -0.186556 q^{68} +(-1.81820 + 2.67673i) q^{70} +(5.31198 + 9.20062i) q^{71} +(-4.80900 + 8.32943i) q^{73} +0.363609 q^{74} +(-0.447955 + 0.775880i) q^{76} +(-0.208977 + 0.307654i) q^{77} +(-2.94837 - 5.10673i) q^{79} +(-0.611519 - 1.05918i) q^{80} +(1.70480 - 2.95279i) q^{82} +9.14057 q^{83} +(0.114083 + 0.197597i) q^{85} +(2.06841 + 3.58258i) q^{86} +(-0.0702857 - 0.121738i) q^{88} +6.35472 q^{89} +(-3.66544 + 8.80707i) q^{91} -0.0364808 q^{92} +(0.358745 + 0.621364i) q^{94} +1.09573 q^{95} +(3.24059 + 5.61287i) q^{97} +(4.34548 - 5.48788i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 8 q^{2} + 8 q^{4} - 2 q^{5} + 3 q^{7} - 8 q^{8}+O(q^{10}) \) 8 * q - 8 * q^2 + 8 * q^4 - 2 * q^5 + 3 * q^7 - 8 * q^8	\( 8 q - 8 q^{2} + 8 q^{4} - 2 q^{5} + 3 q^{7} - 8 q^{8} + 2 q^{10} - 4 q^{11} + 3 q^{13} - 3 q^{14} + 8 q^{16} - 4 q^{17} - 4 q^{19} - 2 q^{20} + 4 q^{22} + 8 q^{23} + 2 q^{25} - 3 q^{26} + 3 q^{28} - 2 q^{29} + 14 q^{31} - 8 q^{32} + 4 q^{34} + 22 q^{35} + 12 q^{37} + 4 q^{38} + 2 q^{40} - 12 q^{41} - 4 q^{44} - 8 q^{46} - 7 q^{47} + 5 q^{49} - 2 q^{50} + 3 q^{52} + q^{53} - 25 q^{55} - 3 q^{56} + 2 q^{58} + 32 q^{59} - 4 q^{61} - 14 q^{62} + 8 q^{64} - 10 q^{65} + 19 q^{67} - 4 q^{68} - 22 q^{70} - 20 q^{71} - 7 q^{73} - 12 q^{74} - 4 q^{76} + 24 q^{77} + 24 q^{79} - 2 q^{80} + 12 q^{82} + 64 q^{83} + 15 q^{85} + 4 q^{88} - 22 q^{89} - 38 q^{91} + 8 q^{92} + 7 q^{94} + 56 q^{95} + 11 q^{97} - 5 q^{98}+O(q^{100}) \) 8 * q - 8 * q^2 + 8 * q^4 - 2 * q^5 + 3 * q^7 - 8 * q^8 + 2 * q^10 - 4 * q^11 + 3 * q^13 - 3 * q^14 + 8 * q^16 - 4 * q^17 - 4 * q^19 - 2 * q^20 + 4 * q^22 + 8 * q^23 + 2 * q^25 - 3 * q^26 + 3 * q^28 - 2 * q^29 + 14 * q^31 - 8 * q^32 + 4 * q^34 + 22 * q^35 + 12 * q^37 + 4 * q^38 + 2 * q^40 - 12 * q^41 - 4 * q^44 - 8 * q^46 - 7 * q^47 + 5 * q^49 - 2 * q^50 + 3 * q^52 + q^53 - 25 * q^55 - 3 * q^56 + 2 * q^58 + 32 * q^59 - 4 * q^61 - 14 * q^62 + 8 * q^64 - 10 * q^65 + 19 * q^67 - 4 * q^68 - 22 * q^70 - 20 * q^71 - 7 * q^73 - 12 * q^74 - 4 * q^76 + 24 * q^77 + 24 * q^79 - 2 * q^80 + 12 * q^82 + 64 * q^83 + 15 * q^85 + 4 * q^88 - 22 * q^89 - 38 * q^91 + 8 * q^92 + 7 * q^94 + 56 * q^95 + 11 * q^97 - 5 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more