LMFDB - Embedded newform 1008.2.t.k.193.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1008,2,Mod(193,1008)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1008, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 0, 2, 4]))

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

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

chi := DirichletCharacter("1008.193");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1008 = 2^{4} \cdot 3^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1008.t (of order $3$, degree $2$, not minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$8.04892052375$
Analytic rank:	$0$
Dimension:	$22$
Relative dimension:	$11$ over $\Q(\zeta_{3})$
Twist minimal:	no (minimal twist has level 504)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			193.8
Character	$\chi$	$=$	1008.193
Dual form			1008.2.t.k.961.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.849966 + 1.50916i) q^{3} -1.58188 q^{5} +(1.80922 - 1.93047i) q^{7} +(-1.55512 + 2.56547i) q^{9} +O(q^{10})$	\(q+(0.849966 + 1.50916i) q^{3} -1.58188 q^{5} +(1.80922 - 1.93047i) q^{7} +(-1.55512 + 2.56547i) q^{9} -5.17139 q^{11} +(-0.681985 + 1.18123i) q^{13} +(-1.34454 - 2.38730i) q^{15} +(-2.30781 + 3.99724i) q^{17} +(-0.0321742 - 0.0557274i) q^{19} +(4.45116 + 1.08957i) q^{21} -6.74395 q^{23} -2.49767 q^{25} +(-5.19349 - 0.166357i) q^{27} +(4.70787 + 8.15427i) q^{29} +(-1.33139 - 2.30604i) q^{31} +(-4.39550 - 7.80444i) q^{33} +(-2.86196 + 3.05376i) q^{35} +(0.880766 + 1.52553i) q^{37} +(-2.36233 - 0.0252156i) q^{39} +(-0.858924 + 1.48770i) q^{41} +(5.12012 + 8.86831i) q^{43} +(2.46000 - 4.05825i) q^{45} +(2.60417 - 4.51056i) q^{47} +(-0.453429 - 6.98530i) q^{49} +(-7.99402 - 0.0853284i) q^{51} +(-0.479996 + 0.831377i) q^{53} +8.18049 q^{55} +(0.0567545 - 0.0959224i) q^{57} +(-4.66676 - 8.08307i) q^{59} +(-7.19512 + 12.4623i) q^{61} +(2.13900 + 7.64360i) q^{63} +(1.07882 - 1.86856i) q^{65} +(-6.24903 - 10.8236i) q^{67} +(-5.73213 - 10.1777i) q^{69} +4.49160 q^{71} +(-0.941655 + 1.63099i) q^{73} +(-2.12293 - 3.76938i) q^{75} +(-9.35619 + 9.98321i) q^{77} +(3.26752 - 5.65951i) q^{79} +(-4.16323 - 7.97919i) q^{81} +(5.08661 + 8.81026i) q^{83} +(3.65066 - 6.32314i) q^{85} +(-8.30455 + 14.0358i) q^{87} +(-4.12369 - 7.14243i) q^{89} +(1.04647 + 3.45366i) q^{91} +(2.34854 - 3.96933i) q^{93} +(0.0508957 + 0.0881539i) q^{95} +(-7.26638 - 12.5857i) q^{97} +(8.04210 - 13.2670i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 22 q - 2 q^{3} - 6 q^{5} - 7 q^{7} - 8 q^{9}+O(q^{10}) $ 22 * q - 2 * q^3 - 6 * q^5 - 7 * q^7 - 8 * q^9	$ 22 q - 2 q^{3} - 6 q^{5} - 7 q^{7} - 8 q^{9} - 6 q^{11} - 3 q^{13} + q^{15} + 7 q^{17} + q^{19} - 15 q^{21} + 4 q^{23} + 20 q^{25} + 4 q^{27} + 9 q^{29} + 4 q^{31} - 31 q^{33} - 14 q^{35} + 2 q^{37} - 8 q^{39} + 16 q^{41} + 22 q^{45} - 5 q^{47} - 15 q^{49} - 7 q^{51} + 11 q^{53} - 22 q^{55} + 7 q^{57} + 19 q^{59} - 13 q^{61} - 21 q^{63} + 13 q^{65} - 26 q^{67} - 4 q^{69} + 48 q^{71} - 35 q^{73} + 8 q^{75} - 4 q^{77} - 10 q^{79} - 8 q^{81} + 28 q^{83} - 20 q^{85} - 9 q^{87} + 6 q^{89} + 37 q^{91} - 32 q^{93} - 12 q^{95} - 29 q^{97} + 56 q^{99}+O(q^{100}) $ 22 * q - 2 * q^3 - 6 * q^5 - 7 * q^7 - 8 * q^9 - 6 * q^11 - 3 * q^13 + q^15 + 7 * q^17 + q^19 - 15 * q^21 + 4 * q^23 + 20 * q^25 + 4 * q^27 + 9 * q^29 + 4 * q^31 - 31 * q^33 - 14 * q^35 + 2 * q^37 - 8 * q^39 + 16 * q^41 + 22 * q^45 - 5 * q^47 - 15 * q^49 - 7 * q^51 + 11 * q^53 - 22 * q^55 + 7 * q^57 + 19 * q^59 - 13 * q^61 - 21 * q^63 + 13 * q^65 - 26 * q^67 - 4 * q^69 + 48 * q^71 - 35 * q^73 + 8 * q^75 - 4 * q^77 - 10 * q^79 - 8 * q^81 + 28 * q^83 - 20 * q^85 - 9 * q^87 + 6 * q^89 + 37 * q^91 - 32 * q^93 - 12 * q^95 - 29 * q^97 + 56 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1008\mathbb{Z}\right)^\times$.

$n$	$127$	$577$	$757$	$785$
$\chi(n)$	$1$	$e\left(\frac{2}{3}\right)$	$1$	$e\left(\frac{1}{3}\right)$

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
$3$	0.849966	+	1.50916i	0.490728	+	0.871313i
$3$	0.849966	+	1.50916i	0.490728	+	0.871313i
$4$		0			0
$5$	−1.58188			−0.707436			−0.353718	−	0.935352i	$-0.615083\pi$
$5$	−1.58188			−0.707436			−0.353718	+	0.935352i	$0.615083\pi$
$6$		0			0
$7$	1.80922	−	1.93047i	0.683822	−	0.729649i
$7$	1.80922	−	1.93047i	0.683822	−	0.729649i
$8$		0			0
$9$	−1.55512	+	2.56547i	−0.518372	+	0.855155i
$10$		0			0
$11$	−5.17139			−1.55923			−0.779616	−	0.626258i	$-0.784586\pi$
$11$	−5.17139			−1.55923			−0.779616	+	0.626258i	$0.784586\pi$
$12$		0			0
$13$	−0.681985	+	1.18123i	−0.189149	+	0.327615i	−0.944967	−	0.327167i	$-0.893906\pi$
$13$	−0.681985	+	1.18123i	−0.189149	+	0.327615i	0.755818	+	0.654782i	$0.227239\pi$
$14$		0			0
$15$	−1.34454	−	2.38730i	−0.347159	−	0.616398i
$16$		0			0
$17$	−2.30781	+	3.99724i	−0.559726	+	0.969473i	0.437794	+	0.899076i	$0.355760\pi$
$17$	−2.30781	+	3.99724i	−0.559726	+	0.969473i	−0.997519	+	0.0703975i	$0.977573\pi$
$18$		0			0
$19$	−0.0321742	−	0.0557274i	−0.00738128	−	0.0127847i	0.862311	−	0.506379i	$-0.169016\pi$
$19$	−0.0321742	−	0.0557274i	−0.00738128	−	0.0127847i	−0.869692	+	0.493594i	$0.835683\pi$
$20$		0			0
$21$	4.45116	+	1.08957i	0.971323	+	0.237763i
$22$		0			0
$23$	−6.74395			−1.40621			−0.703105	−	0.711086i	$-0.748204\pi$
$23$	−6.74395			−1.40621			−0.703105	+	0.711086i	$0.748204\pi$
$24$		0			0
$25$	−2.49767			−0.499534
$26$		0			0
$27$	−5.19349	−	0.166357i	−0.999487	−	0.0320154i
$28$		0			0
$29$	4.70787	+	8.15427i	0.874229	+	1.51421i	0.857582	+	0.514348i	$0.171966\pi$
$29$	4.70787	+	8.15427i	0.874229	+	1.51421i	0.0166475	+	0.999861i	$0.494701\pi$
$30$		0			0
$31$	−1.33139	−	2.30604i	−0.239125	−	0.414177i	0.721339	−	0.692583i	$-0.243527\pi$
$31$	−1.33139	−	2.30604i	−0.239125	−	0.414177i	−0.960463	+	0.278406i	$0.910194\pi$
$32$		0			0
$33$	−4.39550	−	7.80444i	−0.765159	−	1.35858i
$34$		0			0
$35$	−2.86196	+	3.05376i	−0.483760	+	0.516180i
$36$		0			0
$37$	0.880766	+	1.52553i	0.144797	+	0.250796i	0.929297	−	0.369333i	$-0.120414\pi$
$37$	0.880766	+	1.52553i	0.144797	+	0.250796i	−0.784500	+	0.620129i	$0.787080\pi$
$38$		0			0
$39$	−2.36233	−	0.0252156i	−0.378276	−	0.00403772i
$40$		0			0
$41$	−0.858924	+	1.48770i	−0.134141	+	0.232340i	−0.925269	−	0.379311i	$-0.876161\pi$
$41$	−0.858924	+	1.48770i	−0.134141	+	0.232340i	0.791128	+	0.611651i	$0.209494\pi$
$42$		0			0
$43$	5.12012	+	8.86831i	0.780811	+	1.35240i	0.931470	+	0.363819i	$0.118527\pi$
$43$	5.12012	+	8.86831i	0.780811	+	1.35240i	−0.150658	+	0.988586i	$0.548139\pi$
$44$		0			0
$45$	2.46000	−	4.05825i	0.366715	−	0.604968i
$46$		0			0
$47$	2.60417	−	4.51056i	0.379857	−	0.657932i	−0.611184	−	0.791489i	$-0.709306\pi$
$47$	2.60417	−	4.51056i	0.379857	−	0.657932i	0.991041	+	0.133556i	$0.0426397\pi$
$48$		0			0
$49$	−0.453429	−	6.98530i	−0.0647756	−	0.997900i
$50$		0			0
$51$	−7.99402	−	0.0853284i	−1.11939	−	0.0119484i
$52$		0			0
$53$	−0.479996	+	0.831377i	−0.0659325	+	0.114198i	−0.897107	−	0.441813i	$-0.854336\pi$
$53$	−0.479996	+	0.831377i	−0.0659325	+	0.114198i	0.831175	+	0.556011i	$0.187669\pi$
$54$		0			0
$55$	8.18049			1.10306
$56$		0			0
$57$	0.0567545	−	0.0959224i	0.00751732	−	0.0127052i
$58$		0			0
$59$	−4.66676	−	8.08307i	−0.607561	−	1.05233i	−0.991641	−	0.129027i	$-0.958815\pi$
$59$	−4.66676	−	8.08307i	−0.607561	−	1.05233i	0.384080	−	0.923300i	$-0.374519\pi$
$60$		0			0
$61$	−7.19512	+	12.4623i	−0.921241	+	1.59564i	−0.123742	+	0.992314i	$0.539490\pi$
$61$	−7.19512	+	12.4623i	−0.921241	+	1.59564i	−0.797498	+	0.603321i	$0.793844\pi$
$62$		0			0
$63$	2.13900	+	7.64360i	0.269489	+	0.963003i
$64$		0			0
$65$	1.07882	−	1.86856i	0.133811	−	0.231767i
$66$		0			0
$67$	−6.24903	−	10.8236i	−0.763441	−	1.32232i	−0.941067	−	0.338220i	$-0.890175\pi$
$67$	−6.24903	−	10.8236i	−0.763441	−	1.32232i	0.177626	−	0.984098i	$-0.443158\pi$
$68$		0			0
$69$	−5.73213	−	10.1777i	−0.690067	−	1.22525i
$70$		0			0
$71$	4.49160			0.533055			0.266527	−	0.963827i	$-0.414124\pi$
$71$	4.49160			0.533055			0.266527	+	0.963827i	$0.414124\pi$
$72$		0			0
$73$	−0.941655	+	1.63099i	−0.110212	+	0.190893i	−0.915856	−	0.401507i	$-0.868486\pi$
$73$	−0.941655	+	1.63099i	−0.110212	+	0.190893i	0.805643	+	0.592401i	$0.201820\pi$
$74$		0			0
$75$	−2.12293	−	3.76938i	−0.245135	−	0.435250i
$76$		0			0
$77$	−9.35619	+	9.98321i	−1.06624	+	1.13769i
$78$		0			0
$79$	3.26752	−	5.65951i	0.367625	−	0.636745i	−0.621569	−	0.783360i	$-0.713504\pi$
$79$	3.26752	−	5.65951i	0.367625	−	0.636745i	0.989194	+	0.146615i	$0.0468377\pi$
$80$		0			0
$81$	−4.16323	−	7.97919i	−0.462581	−	0.886577i
$82$		0			0
$83$	5.08661	+	8.81026i	0.558328	+	0.967052i	0.997636	+	0.0687156i	$0.0218901\pi$
$83$	5.08661	+	8.81026i	0.558328	+	0.967052i	−0.439309	+	0.898336i	$0.644777\pi$
$84$		0			0
$85$	3.65066	−	6.32314i	0.395970	−	0.685840i
$86$		0			0
$87$	−8.30455	+	14.0358i	−0.890341	+	1.50479i
$88$		0			0
$89$	−4.12369	−	7.14243i	−0.437110	−	0.757096i	0.560355	−	0.828252i	$-0.310665\pi$
$89$	−4.12369	−	7.14243i	−0.437110	−	0.757096i	−0.997465	+	0.0711559i	$0.977331\pi$
$90$		0			0
$91$	1.04647	+	3.45366i	0.109700	+	0.362042i
$92$		0			0
$93$	2.34854	−	3.96933i	0.243532	−	0.411601i
$94$		0			0
$95$	0.0508957	+	0.0881539i	0.00522178	+	0.00904440i
$96$		0			0
$97$	−7.26638	−	12.5857i	−0.737789	−	1.27789i	−0.953489	−	0.301428i	$-0.902537\pi$
$97$	−7.26638	−	12.5857i	−0.737789	−	1.27789i	0.215700	−	0.976460i	$-0.430797\pi$
$98$		0			0
$99$	8.04210	−	13.2670i	0.808262	−	1.33339i
$100$		0			0
$101$	6.24620			0.621520			0.310760	−	0.950488i	$-0.399416\pi$
$101$	6.24620			0.621520			0.310760	+	0.950488i	$0.399416\pi$
$102$		0			0
$103$	5.77762			0.569286			0.284643	−	0.958634i	$-0.408125\pi$
$103$	5.77762			0.569286			0.284643	+	0.958634i	$0.408125\pi$
$104$		0			0
$105$	−7.04118	−	1.72356i	−0.687149	−	0.168202i
$106$		0			0
$107$	0.251126	+	0.434963i	0.0242773	+	0.0420494i	0.877909	−	0.478828i	$-0.158938\pi$
$107$	0.251126	+	0.434963i	0.0242773	+	0.0420494i	−0.853632	+	0.520877i	$0.825605\pi$
$108$		0			0
$109$	−2.37218	+	4.10874i	−0.227214	+	0.393546i	−0.956981	−	0.290149i	$-0.906295\pi$
$109$	−2.37218	+	4.10874i	−0.227214	+	0.393546i	0.729767	+	0.683696i	$0.239628\pi$
$110$		0			0
$111$	−1.55365	+	2.62587i	−0.147466	+	0.249236i
$112$		0			0
$113$	−1.11328	+	1.92825i	−0.104728	+	0.181395i	−0.913627	−	0.406553i	$-0.866731\pi$
$113$	−1.11328	+	1.92825i	−0.104728	+	0.181395i	0.808899	+	0.587948i	$0.200064\pi$
$114$		0			0
$115$	10.6681			0.994804
$116$		0			0
$117$	−1.96985	−	3.58656i	−0.182112	−	0.331578i
$118$		0			0
$119$	3.54121	+	11.6870i	0.324623	+	1.07135i
$120$		0			0
$121$	15.7432			1.43120
$122$		0			0
$123$	−2.97523	−	0.0317577i	−0.268268	−	0.00286349i
$124$		0			0
$125$	11.8604			1.06082
$126$		0			0
$127$	18.6057			1.65099			0.825494	−	0.564410i	$-0.190896\pi$
$127$	18.6057			1.65099			0.825494	+	0.564410i	$0.190896\pi$
$128$		0			0
$129$	−9.03175	+	15.2648i	−0.795202	+	1.34399i
$130$		0			0
$131$	−13.5404			−1.18303			−0.591515	−	0.806294i	$-0.701470\pi$
$131$	−13.5404			−1.18303			−0.591515	+	0.806294i	$0.701470\pi$
$132$		0			0
$133$	−0.165791	−	0.0387119i	−0.0143759	−	0.00335675i
$134$		0			0
$135$	8.21545	+	0.263156i	0.707074	+	0.0226488i
$136$		0			0
$137$	13.7420			1.17406			0.587029	−	0.809566i	$-0.300298\pi$
$137$	13.7420			1.17406			0.587029	+	0.809566i	$0.300298\pi$
$138$		0			0
$139$	−6.79328	+	11.7663i	−0.576198	+	0.998005i	0.419712	+	0.907657i	$0.362131\pi$
$139$	−6.79328	+	11.7663i	−0.576198	+	0.998005i	−0.995910	+	0.0903476i	$0.971202\pi$
$140$		0			0
$141$	9.02060	+	0.0962861i	0.759671	+	0.00810875i
$142$		0			0
$143$	3.52681	−	6.10861i	0.294927	−	0.510828i
$144$		0			0
$145$	−7.44726	−	12.8990i	−0.618461	−	1.07121i
$146$		0			0
$147$	10.1565	−	6.62156i	0.837696	−	0.546137i
$148$		0			0
$149$	5.96066			0.488317			0.244158	−	0.969735i	$-0.421488\pi$
$149$	5.96066			0.488317			0.244158	+	0.969735i	$0.421488\pi$
$150$		0			0
$151$	−8.54142			−0.695091			−0.347546	−	0.937663i	$-0.612985\pi$
$151$	−8.54142			−0.695091			−0.347546	+	0.937663i	$0.612985\pi$
$152$		0			0
$153$	−6.66587	−	12.1368i	−0.538904	−	0.981200i
$154$		0			0
$155$	2.10610	+	3.64786i	0.169166	+	0.293004i
$156$		0			0
$157$	1.31996	+	2.28623i	0.105344	+	0.182461i	0.913879	−	0.405987i	$-0.133072\pi$
$157$	1.31996	+	2.28623i	0.105344	+	0.182461i	−0.808535	+	0.588449i	$0.799739\pi$
$158$		0			0
$159$	−1.66266	−	0.0177473i	−0.131857	−	0.00140745i
$160$		0			0
$161$	−12.2013	+	13.0190i	−0.961597	+	1.02604i
$162$		0			0
$163$	8.87875	+	15.3785i	0.695438	+	1.20453i	0.970033	+	0.242973i	$0.0781228\pi$
$163$	8.87875	+	15.3785i	0.695438	+	1.20453i	−0.274595	+	0.961560i	$0.588544\pi$
$164$		0			0
$165$	6.95314	+	12.3457i	0.541301	+	0.961108i
$166$		0			0
$167$	−3.98937	+	6.90979i	−0.308706	+	0.534695i	−0.978080	−	0.208231i	$-0.933229\pi$
$167$	−3.98937	+	6.90979i	−0.308706	+	0.534695i	0.669373	+	0.742926i	$0.266563\pi$
$168$		0			0
$169$	5.56979	+	9.64716i	0.428446	+	0.742090i
$170$		0			0
$171$	0.193002	+	0.00412067i	0.0147592	+	0.000315116i
$172$		0			0
$173$	−3.83170	+	6.63670i	−0.291319	+	0.504579i	−0.974122	−	0.226023i	$-0.927427\pi$
$173$	−3.83170	+	6.63670i	−0.291319	+	0.504579i	0.682803	+	0.730603i	$0.260761\pi$
$174$		0			0
$175$	−4.51884	+	4.82168i	−0.341592	+	0.364485i
$176$		0			0
$177$	8.23204	−	13.9132i	0.618758	−	1.04578i
$178$		0			0
$179$	−11.7864	+	20.4147i	−0.880958	+	1.52586i	−0.0306808	+	0.999529i	$0.509768\pi$
$179$	−11.7864	+	20.4147i	−0.880958	+	1.52586i	−0.850277	+	0.526335i	$0.823566\pi$
$180$		0			0
$181$	17.3700			1.29110			0.645551	−	0.763717i	$-0.276628\pi$
$181$	17.3700			1.29110			0.645551	+	0.763717i	$0.276628\pi$
$182$		0			0
$183$	−24.9232	−	0.266031i	−1.84238	−	0.0196656i
$184$		0			0
$185$	−1.39326	−	2.41320i	−0.102435	−	0.177422i
$186$		0			0
$187$	11.9346	−	20.6713i	0.872742	−	1.51163i
$188$		0			0
$189$	−9.71732	+	9.72490i	−0.706831	+	0.707382i
$190$		0			0
$191$	2.42330	−	4.19728i	0.175344	−	0.303704i	−0.764936	−	0.644106i	$-0.777230\pi$
$191$	2.42330	−	4.19728i	0.175344	−	0.303704i	0.940280	+	0.340402i	$0.110563\pi$
$192$		0			0
$193$	7.32091	+	12.6802i	0.526970	+	0.912739i	0.999506	+	0.0314278i	$0.0100054\pi$
$193$	7.32091	+	12.6802i	0.526970	+	0.912739i	−0.472536	+	0.881312i	$0.656661\pi$
$194$		0			0
$195$	3.73691	+	0.0398879i	0.267606	+	0.00285643i
$196$		0			0
$197$	−19.1996			−1.36791			−0.683957	−	0.729522i	$-0.739743\pi$
$197$	−19.1996			−1.36791			−0.683957	+	0.729522i	$0.739743\pi$
$198$		0			0
$199$	−6.50796	+	11.2721i	−0.461337	+	0.799060i	−0.999028	−	0.0440825i	$-0.985964\pi$
$199$	−6.50796	+	11.2721i	−0.461337	+	0.799060i	0.537691	+	0.843142i	$0.319297\pi$
$200$		0			0
$201$	11.0231	−	18.6305i	0.777511	−	1.31409i
$202$		0			0
$203$	24.2591	+	5.66448i	1.70266	+	0.397569i
$204$		0			0
$205$	1.35871	−	2.35336i	0.0948965	−	0.164366i
$206$		0			0
$207$	10.4876	−	17.3014i	0.728940	−	1.20253i
$208$		0			0
$209$	0.166385	+	0.288188i	0.0115091	+	0.0199344i
$210$		0			0
$211$	7.43389	−	12.8759i	0.511770	−	0.886412i	−0.488137	−	0.872767i	$-0.662323\pi$
$211$	7.43389	−	12.8759i	0.511770	−	0.886412i	0.999907	−	0.0136450i	$-0.00434348\pi$
$212$		0			0
$213$	3.81771	+	6.77853i	0.261585	+	0.464457i
$214$		0			0
$215$	−8.09940	−	14.0286i	−0.552374	−	0.956740i
$216$		0			0
$217$	−6.86052	−	1.60192i	−0.465722	−	0.108746i
$218$		0			0
$219$	−3.26180	−	0.0348166i	−0.220412	−	0.00235269i
$220$		0			0
$221$	−3.14778	−	5.45212i	−0.211743	−	0.366749i
$222$		0			0
$223$	−11.2085	−	19.4136i	−0.750574	−	1.30003i	−0.947545	−	0.319623i	$-0.896444\pi$
$223$	−11.2085	−	19.4136i	−0.750574	−	1.30003i	0.196971	−	0.980409i	$-0.436890\pi$
$224$		0			0
$225$	3.88417	−	6.40769i	0.258944	−	0.427179i
$226$		0			0
$227$	−3.89450			−0.258487			−0.129243	−	0.991613i	$-0.541255\pi$
$227$	−3.89450			−0.258487			−0.129243	+	0.991613i	$0.541255\pi$
$228$		0			0
$229$	−1.38717			−0.0916669			−0.0458334	−	0.998949i	$-0.514594\pi$
$229$	−1.38717			−0.0916669			−0.0458334	+	0.998949i	$0.514594\pi$
$230$		0			0
$231$	−23.0187	−	5.63458i	−1.51452	−	0.370728i
$232$		0			0
$233$	8.99057	+	15.5721i	0.588992	+	1.02016i	0.994365	+	0.106013i	$0.0338084\pi$
$233$	8.99057	+	15.5721i	0.588992	+	1.02016i	−0.405373	+	0.914151i	$0.632858\pi$
$234$		0			0
$235$	−4.11947	+	7.13514i	−0.268725	+	0.465445i
$236$		0			0
$237$	11.3184	+	0.120813i	0.735208	+	0.00784763i
$238$		0			0
$239$	2.68043	−	4.64264i	0.173382	−	0.300307i	−0.766218	−	0.642581i	$-0.777864\pi$
$239$	2.68043	−	4.64264i	0.173382	−	0.300307i	0.939600	+	0.342274i	$0.111197\pi$
$240$		0			0
$241$	0.416592			0.0268351			0.0134175	−	0.999910i	$-0.495729\pi$
$241$	0.416592			0.0268351			0.0134175	+	0.999910i	$0.495729\pi$
$242$		0			0
$243$	8.50326	−	13.0650i	0.545484	−	0.838121i
$244$		0			0
$245$	0.717269	+	11.0499i	0.0458246	+	0.705951i
$246$		0			0
$247$	0.0877694			0.00558464
$248$		0			0
$249$	−8.97263	+	15.1649i	−0.568618	+	0.961037i
$250$		0			0
$251$	−22.5606			−1.42401			−0.712006	−	0.702173i	$-0.752213\pi$
$251$	−22.5606			−1.42401			−0.712006	+	0.702173i	$0.752213\pi$
$252$		0			0
$253$	34.8756			2.19261
$254$		0			0
$255$	12.6456	+	0.134979i	0.791895	+	0.00845271i
$256$		0			0
$257$	−11.0461			−0.689039			−0.344520	−	0.938779i	$-0.611958\pi$
$257$	−11.0461			−0.689039			−0.344520	+	0.938779i	$0.611958\pi$
$258$		0			0
$259$	4.53850	+	1.05973i	0.282008	+	0.0658486i
$260$		0			0
$261$	−28.2408	−	0.602954i	−1.74806	−	0.0373219i
$262$		0			0
$263$	25.4620			1.57006			0.785028	−	0.619460i	$-0.212648\pi$
$263$	25.4620			1.57006			0.785028	+	0.619460i	$0.212648\pi$
$264$		0			0
$265$	0.759294	−	1.31514i	0.0466430	−	0.0807881i
$266$		0			0
$267$	7.27407	−	12.2941i	0.445166	−	0.752388i
$268$		0			0
$269$	2.78957	−	4.83168i	0.170083	−	0.294593i	−0.768366	−	0.640011i	$-0.778930\pi$
$269$	2.78957	−	4.83168i	0.170083	−	0.294593i	0.938449	+	0.345419i	$0.112263\pi$
$270$		0			0
$271$	1.46645	+	2.53997i	0.0890806	+	0.154292i	0.907123	−	0.420866i	$-0.138274\pi$
$271$	1.46645	+	2.53997i	0.0890806	+	0.154292i	−0.818042	+	0.575158i	$0.804940\pi$
$272$		0			0
$273$	−4.32266	+	4.51479i	−0.261619	+	0.273247i
$274$		0			0
$275$	12.9164			0.778889
$276$		0			0
$277$	22.0917			1.32736			0.663680	−	0.748016i	$-0.268993\pi$
$277$	22.0917			1.32736			0.663680	+	0.748016i	$0.268993\pi$
$278$		0			0
$279$	7.98653	+	0.170516i	0.478141	+	0.0102085i
$280$		0			0
$281$	−2.81009	−	4.86721i	−0.167636	−	0.290354i	0.769952	−	0.638101i	$-0.220280\pi$
$281$	−2.81009	−	4.86721i	−0.167636	−	0.290354i	−0.937588	+	0.347748i	$0.886947\pi$
$282$		0			0
$283$	10.6502	+	18.4466i	0.633086	+	1.09654i	0.986917	+	0.161228i	$0.0515454\pi$
$283$	10.6502	+	18.4466i	0.633086	+	1.09654i	−0.353831	+	0.935309i	$0.615121\pi$
$284$		0			0
$285$	−0.0897785	+	0.151737i	−0.00531802	+	0.00898815i
$286$		0			0
$287$	1.31798	+	4.34971i	0.0777977	+	0.256755i
$288$		0			0
$289$	−2.15195	−	3.72729i	−0.126585	−	0.219252i
$290$		0			0
$291$	12.8177	−	21.6636i	0.751387	−	1.26994i
$292$		0			0
$293$	14.1128	−	24.4440i	0.824477	−	1.42804i	−0.0778418	−	0.996966i	$-0.524803\pi$
$293$	14.1128	−	24.4440i	0.824477	−	1.42804i	0.902319	−	0.431070i	$-0.141864\pi$
$294$		0			0
$295$	7.38224	+	12.7864i	0.429811	+	0.744454i
$296$		0			0
$297$	26.8575	+	0.860295i	1.55843	+	0.0499194i
$298$		0			0
$299$	4.59927	−	7.96617i	0.265983	−	0.460696i
$300$		0			0
$301$	26.3834	+	6.16050i	1.52072	+	0.355086i
$302$		0			0
$303$	5.30906	+	9.42650i	0.304997	+	0.541538i
$304$		0			0
$305$	11.3818	−	19.7138i	0.651719	−	1.12881i
$306$		0			0
$307$	2.41329			0.137734			0.0688669	−	0.997626i	$-0.478062\pi$
$307$	2.41329			0.137734			0.0688669	+	0.997626i	$0.478062\pi$
$308$		0			0
$309$	4.91078	+	8.71935i	0.279365	+	0.496026i
$310$		0			0
$311$	4.76840	+	8.25911i	0.270391	+	0.468331i	0.968962	−	0.247210i	$-0.0795137\pi$
$311$	4.76840	+	8.25911i	0.270391	+	0.468331i	−0.698571	+	0.715541i	$0.746180\pi$
$312$		0			0
$313$	−16.3010	+	28.2341i	−0.921386	+	1.59589i	−0.124112	+	0.992268i	$0.539608\pi$
$313$	−16.3010	+	28.2341i	−0.921386	+	1.59589i	−0.797273	+	0.603619i	$0.793725\pi$
$314$		0			0
$315$	−3.38364	−	12.0912i	−0.190646	−	0.681263i
$316$		0			0
$317$	1.54977	−	2.68428i	0.0870438	−	0.150764i	−0.819216	−	0.573484i	$-0.805591\pi$
$317$	1.54977	−	2.68428i	0.0870438	−	0.150764i	0.906260	+	0.422720i	$0.138925\pi$
$318$		0			0
$319$	−24.3462	−	42.1689i	−1.36313	−	2.36100i
$320$		0			0
$321$	−0.442979	+	0.748692i	−0.0247247	+	0.0417879i
$322$		0			0
$323$	0.297008			0.0165260
$324$		0			0
$325$	1.70337	−	2.95033i	0.0944862	−	0.163655i
$326$		0			0
$327$	−8.21702	−	0.0877087i	−0.454402	−	0.00485030i
$328$		0			0
$329$	−3.99597	−	13.1879i	−0.220305	−	0.727071i
$330$		0			0
$331$	−1.83825	+	3.18394i	−0.101039	+	0.175005i	−0.912113	−	0.409939i	$-0.865550\pi$
$331$	−1.83825	+	3.18394i	−0.101039	+	0.175005i	0.811074	+	0.584944i	$0.198883\pi$
$332$		0			0
$333$	−5.28339	−	0.112803i	−0.289528	−	0.00618157i
$334$		0			0
$335$	9.88519	+	17.1216i	0.540086	+	0.935456i
$336$		0			0
$337$	6.15866	−	10.6671i	0.335483	−	0.581074i	−0.648094	−	0.761560i	$-0.724434\pi$
$337$	6.15866	−	10.6671i	0.335483	−	0.581074i	0.983578	+	0.180486i	$0.0577670\pi$
$338$		0			0
$339$	−3.85628	−	0.0411620i	−0.209444	−	0.00223562i
$340$		0			0
$341$	6.88514	+	11.9254i	0.372851	+	0.645797i
$342$		0			0
$343$	−14.3053	−	11.7626i	−0.772412	−	0.635122i
$344$		0			0
$345$	9.06751	+	16.0998i	0.488178	+	0.866786i
$346$		0			0
$347$	−8.85078	−	15.3300i	−0.475135	−	0.822958i	0.524460	−	0.851435i	$-0.324267\pi$
$347$	−8.85078	−	15.3300i	−0.475135	−	0.822958i	−0.999594	+	0.0284778i	$0.990934\pi$
$348$		0			0
$349$	0.562639	+	0.974519i	0.0301174	+	0.0521648i	0.880691	−	0.473691i	$-0.157079\pi$
$349$	0.562639	+	0.974519i	0.0301174	+	0.0521648i	−0.850574	+	0.525856i	$0.823745\pi$
$350$		0			0
$351$	3.73839	−	6.02127i	0.199540	−	0.321391i
$352$		0			0
$353$	−10.9625			−0.583475			−0.291738	−	0.956498i	$-0.594233\pi$
$353$	−10.9625			−0.583475			−0.291738	+	0.956498i	$0.594233\pi$
$354$		0			0
$355$	−7.10515			−0.377102
$356$		0			0
$357$	−14.6277	+	15.2778i	−0.774179	+	0.808589i
$358$		0			0
$359$	13.4733	+	23.3364i	0.711092	+	1.23165i	0.964448	+	0.264274i	$0.0851324\pi$
$359$	13.4733	+	23.3364i	0.711092	+	1.23165i	−0.253356	+	0.967373i	$0.581534\pi$
$360$		0			0
$361$	9.49793	−	16.4509i	0.499891	−	0.865837i
$362$		0			0
$363$	13.3812	+	23.7590i	0.702331	+	1.24703i
$364$		0			0
$365$	1.48958	−	2.58003i	0.0779682	−	0.135045i
$366$		0			0
$367$	−34.8273			−1.81797			−0.908986	−	0.416826i	$-0.863142\pi$
$367$	−34.8273			−1.81797			−0.908986	+	0.416826i	$0.863142\pi$
$368$		0			0
$369$	−2.48092	−	4.51709i	−0.129151	−	0.235150i
$370$		0			0
$371$	0.736530	+	2.43076i	0.0382387	+	0.126199i
$372$		0			0
$373$	−23.1585			−1.19910			−0.599551	−	0.800336i	$-0.704654\pi$
$373$	−23.1585			−1.19910			−0.599551	+	0.800336i	$0.704654\pi$
$374$		0			0
$375$	10.0809	+	17.8992i	0.520576	+	0.924310i
$376$		0			0
$377$	−12.8428			−0.661437
$378$		0			0
$379$	−22.7259			−1.16735			−0.583676	−	0.811987i	$-0.698386\pi$
$379$	−22.7259			−1.16735			−0.583676	+	0.811987i	$0.698386\pi$
$380$		0			0
$381$	15.8142	+	28.0789i	0.810186	+	1.43853i
$382$		0			0
$383$	−23.2041			−1.18567			−0.592837	−	0.805322i	$-0.701992\pi$
$383$	−23.2041			−1.18567			−0.592837	+	0.805322i	$0.701992\pi$
$384$		0			0
$385$	14.8003	−	15.7922i	0.754294	−	0.804844i
$386$		0			0
$387$	−30.7137	−	0.655753i	−1.56127	−	0.0333338i
$388$		0			0
$389$	−9.13474			−0.463149			−0.231575	−	0.972817i	$-0.574388\pi$
$389$	−9.13474			−0.463149			−0.231575	+	0.972817i	$0.574388\pi$
$390$		0			0
$391$	15.5637	−	26.9572i	0.787092	−	1.36328i
$392$		0			0
$393$	−11.5089	−	20.4346i	−0.580546	−	1.03079i
$394$		0			0
$395$	−5.16881	+	8.95265i	−0.260071	+	0.450456i
$396$		0			0
$397$	−19.2126	−	33.2773i	−0.964255	−	1.67014i	−0.711603	−	0.702582i	$-0.752031\pi$
$397$	−19.2126	−	33.2773i	−0.964255	−	1.67014i	−0.252652	−	0.967557i	$-0.581303\pi$
$398$		0			0
$399$	−0.0824939	−	0.283108i	−0.00412986	−	0.0141731i
$400$		0			0
$401$	2.94696			0.147164			0.0735821	−	0.997289i	$-0.476557\pi$
$401$	2.94696			0.147164			0.0735821	+	0.997289i	$0.476557\pi$
$402$		0			0
$403$	3.63196			0.180921
$404$		0			0
$405$	6.58571	+	12.6221i	0.327247	+	0.627197i
$406$		0			0
$407$	−4.55478	−	7.88912i	−0.225772	−	0.391049i
$408$		0			0
$409$	−3.30296	−	5.72089i	−0.163321	−	0.282880i	0.772737	−	0.634726i	$-0.218887\pi$
$409$	−3.30296	−	5.72089i	−0.163321	−	0.282880i	−0.936058	+	0.351847i	$0.885554\pi$
$410$		0			0
$411$	11.6802	+	20.7388i	0.576143	+	1.02297i
$412$		0			0
$413$	−24.0473	−	5.61503i	−1.18329	−	0.276297i
$414$		0			0
$415$	−8.04638	−	13.9367i	−0.394981	−	0.684127i
$416$		0			0
$417$	−23.5313	−	0.251173i	−1.15233	−	0.0123000i
$418$		0			0
$419$	0.381961	−	0.661576i	0.0186600	−	0.0323201i	−0.856545	−	0.516073i	$-0.827393\pi$
$419$	0.381961	−	0.661576i	0.0186600	−	0.0323201i	0.875205	+	0.483753i	$0.160727\pi$
$420$		0			0
$421$	−2.48798	−	4.30931i	−0.121257	−	0.210023i	0.799007	−	0.601322i	$-0.205359\pi$
$421$	−2.48798	−	4.30931i	−0.121257	−	0.210023i	−0.920264	+	0.391299i	$0.872026\pi$
$422$		0			0
$423$	7.52189	+	13.6953i	0.365727	+	0.665891i
$424$		0			0
$425$	5.76414	−	9.98378i	0.279602	−	0.484285i
$426$		0			0
$427$	11.0406	+	36.4371i	0.534290	+	1.76331i
$428$		0			0
$429$	12.2165	+	0.130399i	0.589819	+	0.00629575i
$430$		0			0
$431$	4.01856	−	6.96035i	0.193567	−	0.335268i	−0.752863	−	0.658178i	$-0.771328\pi$
$431$	4.01856	−	6.96035i	0.193567	−	0.335268i	0.946430	+	0.322909i	$0.104661\pi$
$432$		0			0
$433$	−10.8006			−0.519043			−0.259522	−	0.965737i	$-0.583565\pi$
$433$	−10.8006			−0.519043			−0.259522	+	0.965737i	$0.583565\pi$
$434$		0			0
$435$	13.1368	−	22.2028i	0.629860	−	1.06454i
$436$		0			0
$437$	0.216981	+	0.375823i	0.0103796	+	0.0179780i
$438$		0			0
$439$	−10.0597	+	17.4239i	−0.480122	+	0.831596i	−0.999740	−	0.0228028i	$-0.992741\pi$
$439$	−10.0597	+	17.4239i	−0.480122	+	0.831596i	0.519618	+	0.854399i	$0.326074\pi$
$440$		0			0
$441$	18.6257	+	9.69969i	0.886937	+	0.461890i
$442$		0			0
$443$	−4.60623	+	7.97822i	−0.218848	+	0.379057i	−0.954456	−	0.298351i	$-0.903563\pi$
$443$	−4.60623	+	7.97822i	−0.218848	+	0.379057i	0.735608	+	0.677408i	$0.236897\pi$
$444$		0			0
$445$	6.52316	+	11.2984i	0.309227	+	0.535597i
$446$		0			0
$447$	5.06636	+	8.99558i	0.239631	+	0.425476i
$448$		0			0
$449$	−22.4840			−1.06109			−0.530544	−	0.847658i	$-0.678012\pi$
$449$	−22.4840			−1.06109			−0.530544	+	0.847658i	$0.678012\pi$
$450$		0			0
$451$	4.44183	−	7.69347i	0.209158	−	0.362271i
$452$		0			0
$453$	−7.25992	−	12.8904i	−0.341101	−	0.605642i
$454$		0			0
$455$	−1.65539	−	5.46327i	−0.0776058	−	0.256122i
$456$		0			0
$457$	−9.39776	+	16.2774i	−0.439609	+	0.761425i	−0.997659	−	0.0683823i	$-0.978216\pi$
$457$	−9.39776	+	16.2774i	−0.439609	+	0.761425i	0.558050	+	0.829807i	$0.311550\pi$
$458$		0			0
$459$	12.6505	−	20.3757i	0.590477	−	0.951056i
$460$		0			0
$461$	10.3773	+	17.9739i	0.483317	+	0.837129i	0.999816	−	0.0191582i	$-0.00609862\pi$
$461$	10.3773	+	17.9739i	0.483317	+	0.837129i	−0.516500	+	0.856287i	$0.672765\pi$
$462$		0			0
$463$	−10.0414	+	17.3922i	−0.466663	+	0.808284i	−0.999275	−	0.0380753i	$-0.987877\pi$
$463$	−10.0414	+	17.3922i	−0.466663	+	0.808284i	0.532612	+	0.846360i	$0.321211\pi$
$464$		0			0
$465$	−3.71509	+	6.27899i	−0.172283	+	0.291181i
$466$		0			0
$467$	−14.6015	−	25.2905i	−0.675676	−	1.17030i	−0.976271	−	0.216553i	$-0.930519\pi$
$467$	−14.6015	−	25.2905i	−0.675676	−	1.17030i	0.300595	−	0.953752i	$-0.402815\pi$
$468$		0			0
$469$	−32.2006	−	7.51880i	−1.48689	−	0.347186i
$470$		0			0
$471$	−2.32837	+	3.93525i	−0.107286	+	0.181327i
$472$		0			0
$473$	−26.4781	−	45.8615i	−1.21747	−	2.10871i
$474$		0			0
$475$	0.0803606	+	0.139189i	0.00368720	+	0.00638642i
$476$		0			0
$477$	−1.38642	−	2.52430i	−0.0634798	−	0.115580i
$478$		0			0
$479$	40.0654			1.83064			0.915319	−	0.402731i	$-0.131939\pi$
$479$	40.0654			1.83064			0.915319	+	0.402731i	$0.131939\pi$
$480$		0			0
$481$	−2.40268			−0.109553
$482$		0			0
$483$	−30.0184	−	7.34799i	−1.36588	−	0.334345i
$484$		0			0
$485$	11.4945	+	19.9091i	0.521939	+	0.904024i
$486$		0			0
$487$	−9.32801	+	16.1566i	−0.422692	+	0.732125i	−0.996202	−	0.0870742i	$-0.972248\pi$
$487$	−9.32801	+	16.1566i	−0.422692	+	0.732125i	0.573509	+	0.819199i	$0.305582\pi$
$488$		0			0
$489$	−15.6619	+	26.4706i	−0.708254	+	1.19704i
$490$		0			0
$491$	0.285132	−	0.493864i	0.0128678	−	0.0222878i	−0.859520	−	0.511102i	$-0.829237\pi$
$491$	0.285132	−	0.493864i	0.0128678	−	0.0222878i	0.872388	+	0.488815i	$0.162571\pi$
$492$		0			0
$493$	−43.4594			−1.95731
$494$		0			0
$495$	−12.7216	+	20.9868i	−0.571794	+	0.943285i
$496$		0			0
$497$	8.12630	−	8.67090i	0.364514	−	0.388943i
$498$		0			0
$499$	0.928593			0.0415695			0.0207848	−	0.999784i	$-0.493384\pi$
$499$	0.928593			0.0415695			0.0207848	+	0.999784i	$0.493384\pi$
$500$		0			0
$501$	−13.8188	−	0.147502i	−0.617378	−	0.00658990i
$502$		0			0
$503$	3.27170			0.145878			0.0729389	−	0.997336i	$-0.476762\pi$
$503$	3.27170			0.145878			0.0729389	+	0.997336i	$0.476762\pi$
$504$		0			0
$505$	−9.88071			−0.439686
$506$		0			0
$507$	−9.82496	+	16.6055i	−0.436342	+	0.737474i
$508$		0			0
$509$	8.96781			0.397491			0.198746	−	0.980051i	$-0.436313\pi$
$509$	8.96781			0.397491			0.198746	+	0.980051i	$0.436313\pi$
$510$		0			0
$511$	1.44492	+	4.76867i	0.0639196	+	0.210953i
$512$		0			0
$513$	0.157826	+	0.294772i	0.00696819	+	0.0130145i
$514$		0			0
$515$	−9.13948			−0.402734
$516$		0			0
$517$	−13.4672	+	23.3258i	−0.592286	+	1.02587i
$518$		0			0
$519$	−13.2727	−	0.141673i	−0.582605	−	0.00621874i
$520$		0			0
$521$	−5.37649	+	9.31235i	−0.235548	+	0.407982i	−0.959432	−	0.281940i	$-0.909022\pi$
$521$	−5.37649	+	9.31235i	−0.235548	+	0.407982i	0.723884	+	0.689922i	$0.242355\pi$
$522$		0			0
$523$	16.2796	+	28.1970i	0.711856	+	1.23297i	0.964160	+	0.265322i	$0.0854784\pi$
$523$	16.2796	+	28.1970i	0.711856	+	1.23297i	−0.252304	+	0.967648i	$0.581188\pi$
$524$		0			0
$525$	−11.1175	−	2.72138i	−0.485209	−	0.118771i
$526$		0			0
$527$	12.2904			0.535377
$528$		0			0
$529$	22.4808			0.977427
$530$		0			0
$531$	27.9942	+	0.597690i	1.21484	+	0.0259375i
$532$		0			0
$533$	−1.17155	−	2.02918i	−0.0507453	−	0.0878935i
$534$		0			0
$535$	−0.397250	−	0.688057i	−0.0171746	−	0.0297473i
$536$		0			0
$537$	−40.8270	−	0.435789i	−1.76182	−	0.0188057i
$538$		0			0
$539$	2.34486	+	36.1237i	0.101000	+	1.55596i
$540$		0			0
$541$	−3.46359	−	5.99911i	−0.148911	−	0.257922i	0.781914	−	0.623386i	$-0.214244\pi$
$541$	−3.46359	−	5.99911i	−0.148911	−	0.257922i	−0.930825	+	0.365464i	$0.880910\pi$
$542$		0			0
$543$	14.7639	+	26.2141i	0.633580	+	1.12495i
$544$		0			0
$545$	3.75250	−	6.49952i	0.160739	−	0.278409i
$546$		0			0
$547$	15.8974	+	27.5351i	0.679725	+	1.17732i	0.975064	+	0.221925i	$0.0712340\pi$
$547$	15.8974	+	27.5351i	0.679725	+	1.17732i	−0.295339	+	0.955392i	$0.595433\pi$
$548$		0			0
$549$	−20.7824	−	37.8392i	−0.886971	−	1.61494i
$550$		0			0
$551$	0.302944	−	0.524715i	0.0129059	−	0.0223536i
$552$		0			0
$553$	−5.01385	−	16.5472i	−0.213211	−	0.703657i
$554$		0			0
$555$	2.45768	−	4.15379i	0.104323	−	0.176319i
$556$		0			0
$557$	14.1679	−	24.5395i	0.600314	−	1.03977i	−0.392460	−	0.919769i	$-0.628376\pi$
$557$	14.1679	−	24.5395i	0.600314	−	1.03977i	0.992773	−	0.120005i	$-0.0382909\pi$
$558$		0			0
$559$	−13.9674			−0.590758
$560$		0			0
$561$	41.3402	+	0.441266i	1.74538	+	0.0186303i
$562$		0			0
$563$	−22.3270	−	38.6715i	−0.940972	−	1.62981i	−0.763622	−	0.645664i	$-0.776581\pi$
$563$	−22.3270	−	38.6715i	−0.940972	−	1.62981i	−0.177350	−	0.984148i	$-0.556752\pi$
$564$		0			0
$565$	1.76106	−	3.05025i	0.0740885	−	0.128325i
$566$		0			0
$567$	−22.9358	−	6.39914i	−0.963213	−	0.268739i
$568$		0			0
$569$	10.6102	−	18.3775i	0.444804	−	0.770423i	−0.553235	−	0.833025i	$-0.686607\pi$
$569$	10.6102	−	18.3775i	0.444804	−	0.770423i	0.998039	+	0.0626026i	$0.0199401\pi$
$570$		0			0
$571$	5.94786	+	10.3020i	0.248910	+	0.431125i	0.963224	−	0.268701i	$-0.0865943\pi$
$571$	5.94786	+	10.3020i	0.248910	+	0.431125i	−0.714313	+	0.699826i	$0.753261\pi$
$572$		0			0
$573$	8.39407	+	0.0895985i	0.350667	+	0.00374303i
$574$		0			0
$575$	16.8442			0.702450
$576$		0			0
$577$	−19.3490	+	33.5135i	−0.805511	+	1.39519i	0.110435	+	0.993883i	$0.464776\pi$
$577$	−19.3490	+	33.5135i	−0.805511	+	1.39519i	−0.915946	+	0.401302i	$0.868558\pi$
$578$		0			0
$579$	−12.9139	+	21.8261i	−0.536682	+	0.907063i
$580$		0			0
$581$	26.2107	+	6.12018i	1.08741	+	0.253908i
$582$		0			0
$583$	2.48224	−	4.29937i	0.102804	−	0.178062i
$584$		0			0
$585$	3.11605	+	5.67350i	0.128833	+	0.234570i
$586$		0			0
$587$	−9.92138	−	17.1843i	−0.409499	−	0.709274i	0.585334	−	0.810792i	$-0.300963\pi$
$587$	−9.92138	−	17.1843i	−0.409499	−	0.709274i	−0.994834	+	0.101518i	$0.967630\pi$
$588$		0			0
$589$	−0.0856730	+	0.148390i	−0.00353010	+	0.00611431i
$590$		0			0
$591$	−16.3190	−	28.9752i	−0.671274	−	1.19188i
$592$		0			0
$593$	10.9566	+	18.9774i	0.449933	+	0.779307i	0.998381	−	0.0568775i	$-0.0181144\pi$
$593$	10.9566	+	18.9774i	0.449933	+	0.779307i	−0.548448	+	0.836185i	$0.684781\pi$
$594$		0			0
$595$	−5.60176	−	18.4875i	−0.229650	−	0.757912i
$596$		0			0
$597$	−22.5430	−	0.240624i	−0.922622	−	0.00984809i
$598$		0			0
$599$	16.5223	+	28.6174i	0.675081	+	1.16928i	0.976445	+	0.215766i	$0.0692248\pi$
$599$	16.5223	+	28.6174i	0.675081	+	1.16928i	−0.301364	+	0.953509i	$0.597442\pi$
$600$		0			0
$601$	11.4951	+	19.9100i	0.468893	+	0.812147i	0.999368	−	0.0355541i	$-0.0113196\pi$
$601$	11.4951	+	19.9100i	0.468893	+	0.812147i	−0.530475	+	0.847701i	$0.677986\pi$
$602$		0			0
$603$	37.4856	+	0.800336i	1.52653	+	0.0325922i
$604$		0			0
$605$	−24.9038			−1.01248
$606$		0			0
$607$	−27.6564			−1.12254			−0.561269	−	0.827634i	$-0.689686\pi$
$607$	−27.6564			−1.12254			−0.561269	+	0.827634i	$0.689686\pi$
$608$		0			0
$609$	12.0709	+	41.4255i	0.489136	+	1.67865i
$610$		0			0
$611$	3.55201	+	6.15226i	0.143699	+	0.248894i
$612$		0			0
$613$	−15.7684	+	27.3116i	−0.636879	+	1.10311i	0.349235	+	0.937035i	$0.386442\pi$
$613$	−15.7684	+	27.3116i	−0.636879	+	1.10311i	−0.986114	+	0.166072i	$0.946892\pi$
$614$		0			0
$615$	4.70645	+	0.0502367i	0.189782	+	0.00202574i
$616$		0			0
$617$	−10.7513	+	18.6217i	−0.432830	+	0.749683i	−0.997116	−	0.0758961i	$-0.975818\pi$
$617$	−10.7513	+	18.6217i	−0.432830	+	0.749683i	0.564286	+	0.825580i	$0.309152\pi$
$618$		0			0
$619$	−28.2522			−1.13555			−0.567776	−	0.823183i	$-0.692196\pi$
$619$	−28.2522			−1.13555			−0.567776	+	0.823183i	$0.692196\pi$
$620$		0			0
$621$	35.0246	+	1.12190i	1.40549	+	0.0450204i
$622$		0			0
$623$	−21.2489	−	4.96160i	−0.851320	−	0.198782i
$624$		0			0
$625$	−6.27330			−0.250932
$626$		0			0
$627$	−0.293499	+	0.496052i	−0.0117212	+	0.0198104i
$628$		0			0
$629$	−8.13056			−0.324187
$630$		0			0
$631$	9.12550			0.363281			0.181640	−	0.983365i	$-0.441859\pi$
$631$	9.12550			0.363281			0.181640	+	0.983365i	$0.441859\pi$
$632$		0			0
$633$	25.7503	+	0.274859i	1.02348	+	0.0109247i
$634$		0			0
$635$	−29.4319			−1.16797
$636$		0			0
$637$	8.56050	+	4.22826i	0.339179	+	0.167530i
$638$		0			0
$639$	−6.98496	+	11.5230i	−0.276321	+	0.455844i
$640$		0			0
$641$	32.8978			1.29939			0.649693	−	0.760197i	$-0.274897\pi$
$641$	32.8978			1.29939			0.649693	+	0.760197i	$0.274897\pi$
$642$		0			0
$643$	−10.1276	+	17.5415i	−0.399392	+	0.691767i	−0.993651	−	0.112506i	$-0.964112\pi$
$643$	−10.1276	+	17.5415i	−0.399392	+	0.691767i	0.594259	+	0.804274i	$0.297445\pi$
$644$		0			0
$645$	14.2871	−	24.1471i	0.562554	−	0.950790i
$646$		0			0
$647$	5.67441	−	9.82837i	0.223084	−	0.386393i	−0.732659	−	0.680596i	$-0.761721\pi$
$647$	5.67441	−	9.82837i	0.223084	−	0.386393i	0.955743	+	0.294203i	$0.0950542\pi$
$648$		0			0
$649$	24.1336	+	41.8007i	0.947328	+	1.64082i
$650$		0			0
$651$	−3.41365	−	11.7152i	−0.133792	−	0.459154i
$652$		0			0
$653$	3.58036			0.140110			0.0700552	−	0.997543i	$-0.477682\pi$
$653$	3.58036			0.140110			0.0700552	+	0.997543i	$0.477682\pi$
$654$		0			0
$655$	21.4192			0.836918
$656$		0			0
$657$	−2.71988	−	4.95217i	−0.106113	−	0.193203i
$658$		0			0
$659$	−9.13582	−	15.8237i	−0.355881	−	0.616404i	0.631387	−	0.775468i	$-0.282486\pi$
$659$	−9.13582	−	15.8237i	−0.355881	−	0.616404i	−0.987268	+	0.159064i	$0.949152\pi$
$660$		0			0
$661$	−1.11696	−	1.93462i	−0.0434446	−	0.0752482i	0.843485	−	0.537152i	$-0.180500\pi$
$661$	−1.11696	−	1.93462i	−0.0434446	−	0.0752482i	−0.886930	+	0.461904i	$0.847167\pi$
$662$		0			0
$663$	5.55260	−	9.38461i	0.215645	−	0.364468i
$664$		0			0
$665$	0.262260	+	0.0612374i	0.0101700	+	0.00237468i
$666$		0			0
$667$	−31.7496	−	54.9919i	−1.22935	−	2.12930i
$668$		0			0
$669$	19.7714	−	33.4163i	0.764407	−	1.29195i
$670$		0			0
$671$	37.2087	−	64.4474i	1.43643	−	2.48797i
$672$		0			0
$673$	−12.4804	−	21.6166i	−0.481083	−	0.833260i	0.518681	−	0.854968i	$-0.326423\pi$
$673$	−12.4804	−	21.6166i	−0.481083	−	0.833260i	−0.999764	+	0.0217074i	$0.993090\pi$
$674$		0			0
$675$	12.9716	+	0.415504i	0.499278	+	0.0159928i
$676$		0			0
$677$	9.90633	−	17.1583i	0.380731	−	0.659446i	−0.610436	−	0.792066i	$-0.709006\pi$
$677$	9.90633	−	17.1583i	0.380731	−	0.659446i	0.991167	+	0.132620i	$0.0423389\pi$
$678$		0			0
$679$	−37.4429	−	8.74287i	−1.43693	−	0.335521i
$680$		0			0
$681$	−3.31019	−	5.87741i	−0.126847	−	0.225223i
$682$		0			0
$683$	−5.72871	+	9.92242i	−0.219203	+	0.379671i	−0.954565	−	0.298004i	$-0.903679\pi$
$683$	−5.72871	+	9.92242i	−0.219203	+	0.379671i	0.735361	+	0.677675i	$0.237012\pi$
$684$		0			0
$685$	−21.7381			−0.830571
$686$		0			0
$687$	−1.17905	−	2.09346i	−0.0449835	−	0.0798705i
$688$		0			0
$689$	−0.654700	−	1.13397i	−0.0249421	−	0.0432010i
$690$		0			0
$691$	20.2552	−	35.0831i	0.770545	−	1.33462i	−0.166719	−	0.986004i	$-0.553317\pi$
$691$	20.2552	−	35.0831i	0.770545	−	1.33462i	0.937265	−	0.348619i	$-0.113349\pi$
$692$		0			0
$693$	−11.0616	−	39.5280i	−0.420196	−	1.50155i
$694$		0			0
$695$	10.7461	−	18.6128i	0.407624	−	0.706025i
$696$		0			0
$697$	−3.96446	−	6.86665i	−0.150165	−	0.260093i
$698$		0			0
$699$	−15.8591	+	26.8040i	−0.599847	+	1.01382i
$700$		0			0
$701$	−29.5416			−1.11577			−0.557885	−	0.829918i	$-0.688387\pi$
$701$	−29.5416			−1.11577			−0.557885	+	0.829918i	$0.688387\pi$
$702$		0			0
$703$	0.0566760	−	0.0981657i	0.00213758	−	0.00370239i
$704$		0			0
$705$	−14.2695	−	0.152313i	−0.537419	−	0.00573642i
$706$		0			0
$707$	11.3008	−	12.0581i	0.425009	−	0.453492i
$708$		0			0
$709$	18.7407	−	32.4599i	0.703822	−	1.21906i	−0.263293	−	0.964716i	$-0.584809\pi$
$709$	18.7407	−	32.4599i	0.703822	−	1.21906i	0.967115	−	0.254340i	$-0.0818581\pi$
$710$		0			0
$711$	9.43791	+	17.1839i	0.353949	+	0.644447i
$712$		0			0
$713$	8.97883	+	15.5518i	0.336260	+	0.582419i
$714$		0			0
$715$	−5.57897	+	9.66306i	−0.208642	+	0.361378i
$716$		0			0
$717$	9.28474	+	0.0991056i	0.346745	+	0.00370116i
$718$		0			0
$719$	−6.35418	−	11.0058i	−0.236971	−	0.410445i	0.722873	−	0.690981i	$-0.242821\pi$
$719$	−6.35418	−	11.0058i	−0.236971	−	0.410445i	−0.959844	+	0.280536i	$0.909488\pi$
$720$		0			0
$721$	10.4530	−	11.1535i	0.389290	−	0.415379i
$722$		0			0
$723$	0.354089	+	0.628703i	0.0131687	+	0.0233817i
$724$		0			0
$725$	−11.7587	−	20.3667i	−0.436707	−	0.756399i
$726$		0			0
$727$	−19.9463	−	34.5480i	−0.739768	−	1.28132i	−0.952600	−	0.304227i	$-0.901602\pi$
$727$	−19.9463	−	34.5480i	−0.739768	−	1.28132i	0.212832	−	0.977089i	$-0.431731\pi$
$728$		0			0
$729$	26.9447	+	1.72794i	0.997950	+	0.0639979i
$730$		0			0
$731$	−47.2650			−1.74816
$732$		0			0
$733$	−44.8182			−1.65540			−0.827699	−	0.561172i	$-0.810350\pi$
$733$	−44.8182			−1.65540			−0.827699	+	0.561172i	$0.810350\pi$
$734$		0			0
$735$	−16.0664	+	10.4745i	−0.592616	+	0.386357i
$736$		0			0
$737$	32.3162	+	55.9732i	1.19038	+	2.06180i
$738$		0			0
$739$	6.64954	−	11.5173i	0.244607	−	0.423672i	−0.717414	−	0.696647i	$-0.754674\pi$
$739$	6.64954	−	11.5173i	0.244607	−	0.423672i	0.962021	+	0.272975i	$0.0880076\pi$
$740$		0			0
$741$	0.0746010	+	0.132458i	0.00274054	+	0.00486596i
$742$		0			0
$743$	−2.15562	+	3.73365i	−0.0790822	+	0.136974i	−0.902854	−	0.429947i	$-0.858532\pi$
$743$	−2.15562	+	3.73365i	−0.0790822	+	0.136974i	0.823772	+	0.566921i	$0.191866\pi$
$744$		0			0
$745$	−9.42903			−0.345453
$746$		0			0
$747$	−30.5127	−	0.651460i	−1.11640	−	0.0238357i
$748$		0			0
$749$	1.29402	+	0.302153i	0.0472826	+	0.0110404i
$750$		0			0
$751$	43.5303			1.58844			0.794221	−	0.607629i	$-0.207879\pi$
$751$	43.5303			1.58844			0.794221	+	0.607629i	$0.207879\pi$
$752$		0			0
$753$	−19.1757	−	34.0475i	−0.698803	−	1.24076i
$754$		0			0
$755$	13.5115			0.491733
$756$		0			0
$757$	34.6790			1.26043			0.630215	−	0.776420i	$-0.282967\pi$
$757$	34.6790			1.26043			0.630215	+	0.776420i	$0.282967\pi$
$758$		0			0
$759$	29.6430	+	52.6327i	1.07597	+	1.91045i
$760$		0			0
$761$	−3.51946			−0.127580			−0.0637902	−	0.997963i	$-0.520319\pi$
$761$	−3.51946			−0.127580			−0.0637902	+	0.997963i	$0.520319\pi$
$762$		0			0
$763$	3.64000	+	12.0131i	0.131777	+	0.434902i
$764$		0			0
$765$	10.5446	+	19.1989i	0.381240	+	0.694136i
$766$		0			0
$767$	12.7307			0.459677
$768$		0			0
$769$	−19.5075	+	33.7879i	−0.703457	+	1.21842i	0.263788	+	0.964581i	$0.415028\pi$
$769$	−19.5075	+	33.7879i	−0.703457	+	1.21842i	−0.967245	+	0.253843i	$0.918305\pi$
$770$		0			0
$771$	−9.38884	−	16.6704i	−0.338131	−	0.600369i
$772$		0			0
$773$	23.2169	−	40.2128i	0.835054	−	1.44636i	−0.0589329	−	0.998262i	$-0.518770\pi$
$773$	23.2169	−	40.2128i	0.835054	−	1.44636i	0.893987	−	0.448094i	$-0.147897\pi$
$774$		0			0
$775$	3.32538	+	5.75972i	0.119451	+	0.206895i
$776$		0			0
$777$	2.25826	+	7.75005i	0.0810147	+	0.278031i
$778$		0			0
$779$	0.110541			0.00396054
$780$		0			0
$781$	−23.2278			−0.831156
$782$		0			0
$783$	−23.0937	−	43.1323i	−0.825303	−	1.54142i
$784$		0			0
$785$	−2.08801	−	3.61654i	−0.0745242	−	0.129080i
$786$		0			0
$787$	23.7212	+	41.0863i	0.845569	+	1.46457i	0.885126	+	0.465351i	$0.154072\pi$
$787$	23.7212	+	41.0863i	0.845569	+	1.46457i	−0.0395575	+	0.999217i	$0.512595\pi$
$788$		0			0
$789$	21.6419	+	38.4262i	0.770471	+	1.36801i
$790$		0			0
$791$	1.70827	+	5.63778i	0.0607390	+	0.200456i
$792$		0			0
$793$	−9.81393	−	16.9982i	−0.348503	−	0.603625i
$794$		0			0
$795$	2.63012	+	0.0280740i	0.0932808	+	0.000995681i
$796$		0			0
$797$	7.69773	−	13.3329i	0.272668	−	0.472274i	−0.696876	−	0.717191i	$-0.745427\pi$
$797$	7.69773	−	13.3329i	0.272668	−	0.472274i	0.969544	+	0.244917i	$0.0787607\pi$
$798$		0			0
$799$	12.0198	+	20.8190i	0.425232	+	0.736523i
$800$		0			0
$801$	24.7365	+	0.528136i	0.874020	+	0.0186608i
$802$		0			0
$803$	4.86966	−	8.43450i	0.171847	−	0.297647i
$804$		0			0
$805$	19.3009	−	20.5944i	0.680269	−	0.725858i
$806$		0			0
$807$	9.66281	+	0.103141i	0.340147	+	0.00363074i
$808$		0			0
$809$	−15.0433	+	26.0557i	−0.528893	+	0.916069i	0.470539	+	0.882379i	$0.344059\pi$
$809$	−15.0433	+	26.0557i	−0.528893	+	0.916069i	−0.999432	+	0.0336903i	$0.989274\pi$
$810$		0			0
$811$	11.2821			0.396170			0.198085	−	0.980185i	$-0.436528\pi$
$811$	11.2821			0.396170			0.198085	+	0.980185i	$0.436528\pi$
$812$		0			0
$813$	−2.58678	+	4.37200i	−0.0907224	+	0.153333i
$814$		0			0
$815$	−14.0451	−	24.3268i	−0.491978	−	0.852130i
$816$		0			0
$817$	0.329472	−	0.570662i	0.0115268	−	0.0199650i
$818$		0			0
$819$	−10.4876	−	2.68616i	−0.366468	−	0.0938620i
$820$		0			0
$821$	−1.62633	+	2.81688i	−0.0567593	+	0.0983099i	−0.893009	−	0.450039i	$-0.851410\pi$
$821$	−1.62633	+	2.81688i	−0.0567593	+	0.0983099i	0.836250	+	0.548349i	$0.184743\pi$
$822$		0			0
$823$	7.29842	+	12.6412i	0.254407	+	0.440645i	0.964734	−	0.263226i	$-0.0847865\pi$
$823$	7.29842	+	12.6412i	0.254407	+	0.440645i	−0.710327	+	0.703871i	$0.751453\pi$
$824$		0			0
$825$	10.9785	+	19.4929i	0.382223	+	0.678656i
$826$		0			0
$827$	−42.7500			−1.48656			−0.743282	−	0.668978i	$-0.766732\pi$
$827$	−42.7500			−1.48656			−0.743282	+	0.668978i	$0.766732\pi$
$828$		0			0
$829$	−17.6799	+	30.6225i	−0.614049	+	1.06356i	0.376502	+	0.926416i	$0.377127\pi$
$829$	−17.6799	+	30.6225i	−0.614049	+	1.06356i	−0.990551	+	0.137148i	$0.956207\pi$
$830$		0			0
$831$	18.7772	+	33.3398i	0.651373	+	1.15655i
$832$		0			0
$833$	28.9683	+	14.3083i	1.00369	+	0.495752i
$834$		0			0
$835$	6.31068	−	10.9304i	0.218390	−	0.378263i
$836$		0			0
$837$	6.53094	+	12.1979i	0.225742	+	0.421620i
$838$		0			0
$839$	−15.0886	−	26.1343i	−0.520917	−	0.902255i	−0.999704	−	0.0243242i	$-0.992257\pi$
$839$	−15.0886	−	26.1343i	−0.520917	−	0.902255i	0.478787	−	0.877931i	$-0.341077\pi$
$840$		0			0
$841$	−29.8280	+	51.6637i	−1.02855	+	1.78151i
$842$		0			0
$843$	4.95692	−	8.37783i	0.170725	−	0.288548i
$844$		0			0
$845$	−8.81072	−	15.2606i	−0.303098	−	0.524981i
$846$		0			0
$847$	28.4830	−	30.3918i	0.978688	−	1.04428i
$848$		0			0
$849$	−18.7866	+	31.7518i	−0.644754	+	1.08972i
$850$		0			0
$851$	−5.93984	−	10.2881i	−0.203615	−	0.352672i
$852$		0			0
$853$	−20.4789	−	35.4705i	−0.701184	−	1.21449i	−0.968051	−	0.250753i	$-0.919322\pi$
$853$	−20.4789	−	35.4705i	−0.701184	−	1.21449i	0.266867	−	0.963733i	$-0.414011\pi$
$854$		0			0
$855$	−0.305304	−	0.00651839i	−0.0104412	−	0.000222924i
$856$		0			0
$857$	30.4566			1.04038			0.520190	−	0.854051i	$-0.325861\pi$
$857$	30.4566			1.04038			0.520190	+	0.854051i	$0.325861\pi$
$858$		0			0
$859$	−3.18935			−0.108819			−0.0544096	−	0.998519i	$-0.517328\pi$
$859$	−3.18935			−0.108819			−0.0544096	+	0.998519i	$0.517328\pi$
$860$		0			0
$861$	−5.44416	+	5.68614i	−0.185537	+	0.193783i
$862$		0			0
$863$	−11.5498	−	20.0049i	−0.393161	−	0.680975i	0.599703	−	0.800222i	$-0.295285\pi$
$863$	−11.5498	−	20.0049i	−0.393161	−	0.680975i	−0.992865	+	0.119247i	$0.961952\pi$
$864$		0			0
$865$	6.06128	−	10.4984i	0.206090	−	0.356958i
$866$		0			0
$867$	3.79598	−	6.41570i	0.128918	−	0.217889i
$868$		0			0
$869$	−16.8976	+	29.2675i	−0.573212	+	0.992833i
$870$		0			0
$871$	17.0470			0.577615
$872$		0			0
$873$	43.5883	+	0.930632i	1.47524	+	0.0314971i
$874$		0			0
$875$	21.4581	−	22.8961i	0.725415	−	0.774030i
$876$		0			0
$877$	−3.28938			−0.111074			−0.0555372	−	0.998457i	$-0.517687\pi$
$877$	−3.28938			−0.111074			−0.0555372	+	0.998457i	$0.517687\pi$
$878$		0			0
$879$	48.8853	+	0.521803i	1.64886	+	0.0176000i
$880$		0			0
$881$	51.4835			1.73452			0.867262	−	0.497852i	$-0.165878\pi$
$881$	51.4835			1.73452			0.867262	+	0.497852i	$0.165878\pi$
$882$		0			0
$883$	−0.359433			−0.0120959			−0.00604794	−	0.999982i	$-0.501925\pi$
$883$	−0.359433			−0.0120959			−0.00604794	+	0.999982i	$0.501925\pi$
$884$		0			0
$885$	−13.0221	+	22.0090i	−0.437732	+	0.739824i
$886$		0			0
$887$	−11.6000			−0.389488			−0.194744	−	0.980854i	$-0.562388\pi$
$887$	−11.6000			−0.389488			−0.194744	+	0.980854i	$0.562388\pi$
$888$		0			0
$889$	33.6618	−	35.9177i	1.12898	−	1.20464i
$890$		0			0
$891$	21.5297	+	41.2635i	0.721271	+	1.38238i
$892$		0			0
$893$	−0.335149			−0.0112153
$894$		0			0
$895$	18.6446	−	32.2935i	0.623222	−	1.07945i
$896$		0			0
$897$	15.9314	+	0.170053i	0.531935	+	0.00567789i
$898$		0			0
$899$	12.5360	−	21.7130i	0.418100	−	0.724170i
$900$		0			0
$901$	−2.21548	−	3.83732i	−0.0738082	−	0.127840i
$902$		0			0
$903$	13.1279	+	45.0530i	0.436868	+	1.49927i
$904$		0			0
$905$	−27.4772			−0.913373
$906$		0			0
$907$	−24.5791			−0.816135			−0.408067	−	0.912952i	$-0.633797\pi$
$907$	−24.5791			−0.816135			−0.408067	+	0.912952i	$0.633797\pi$
$908$		0			0
$909$	−9.71356	+	16.0244i	−0.322179	+	0.531496i
$910$		0			0
$911$	20.1678	+	34.9317i	0.668190	+	1.15734i	0.978410	+	0.206675i	$0.0662642\pi$
$911$	20.1678	+	34.9317i	0.668190	+	1.15734i	−0.310219	+	0.950665i	$0.600402\pi$
$912$		0			0
$913$	−26.3048	−	45.5613i	−0.870562	−	1.50786i
$914$		0			0
$915$	39.4254	+	0.420828i	1.30336	+	0.0139121i
$916$		0			0
$917$	−24.4976	+	26.1393i	−0.808981	+	0.863197i
$918$		0			0
$919$	−10.8377	−	18.7714i	−0.357501	−	0.619210i	0.630041	−	0.776562i	$-0.283038\pi$
$919$	−10.8377	−	18.7714i	−0.357501	−	0.619210i	−0.987543	+	0.157351i	$0.949705\pi$
$920$		0			0
$921$	2.05122	+	3.64204i	0.0675898	+	0.120009i
$922$		0			0
$923$	−3.06320	+	5.30562i	−0.100827	+	0.174637i
$924$		0			0
$925$	−2.19986	−	3.81028i	−0.0723311	−	0.125281i
$926$		0			0
$927$	−8.98487	+	14.8223i	−0.295102	+	0.486828i
$928$		0			0
$929$	3.96409	−	6.86601i	0.130058	−	0.225266i	−0.793641	−	0.608386i	$-0.791817\pi$
$929$	3.96409	−	6.86601i	0.130058	−	0.225266i	0.923699	+	0.383120i	$0.125150\pi$
$930$		0			0
$931$	−0.374684	+	0.250015i	−0.0122798	+	0.00819392i
$932$		0			0
$933$	−8.41132	+	14.2162i	−0.275374	+	0.465418i
$934$		0			0
$935$	−18.8790	+	32.6994i	−0.617409	+	1.06938i
$936$		0			0
$937$	5.84549			0.190964			0.0954819	−	0.995431i	$-0.469561\pi$
$937$	5.84549			0.190964			0.0954819	+	0.995431i	$0.469561\pi$
$938$		0			0
$939$	−56.4650	−	0.602709i	−1.84267	−	0.0196687i
$940$		0			0
$941$	19.5046	+	33.7829i	0.635831	+	1.10129i	0.986339	+	0.164731i	$0.0526756\pi$
$941$	19.5046	+	33.7829i	0.635831	+	1.10129i	−0.350508	+	0.936560i	$0.613991\pi$
$942$		0			0
$943$	5.79254	−	10.0330i	0.188631	−	0.326719i
$944$		0			0
$945$	15.3716	−	15.3836i	0.500038	−	0.500428i
$946$		0			0
$947$	−3.52185	+	6.10003i	−0.114445	+	0.198224i	−0.917558	−	0.397603i	$-0.869842\pi$
$947$	−3.52185	+	6.10003i	−0.114445	+	0.198224i	0.803113	+	0.595827i	$0.203176\pi$
$948$		0			0
$949$	−1.28439	−	2.22463i	−0.0416930	−	0.0722145i
$950$		0			0
$951$	5.36826	+	0.0573009i	0.174078	+	0.00185811i
$952$		0			0
$953$	28.2379			0.914716			0.457358	−	0.889283i	$-0.348796\pi$
$953$	28.2379			0.914716			0.457358	+	0.889283i	$0.348796\pi$
$954$		0			0
$955$	−3.83336	+	6.63957i	−0.124044	+	0.214851i
$956$		0			0
$957$	42.9460	−	72.5844i	1.38825	−	2.34632i
$958$		0			0
$959$	24.8623	−	26.5285i	0.802846	−	0.856650i
$960$		0			0
$961$	11.9548	−	20.7063i	0.385639	−	0.667946i
$962$		0			0
$963$	−1.50641	−	0.0321626i	−0.0485434	−	0.00103643i
$964$		0			0
$965$	−11.5808	−	20.0585i	−0.372798	−	0.645705i
$966$		0			0
$967$	0.430925	−	0.746384i	0.0138576	−	0.0240021i	−0.859013	−	0.511953i	$-0.828922\pi$
$967$	0.430925	−	0.746384i	0.0138576	−	0.0240021i	0.872871	+	0.487951i	$0.162256\pi$
$968$		0			0
$969$	0.252447	+	0.448232i	0.00810975	+	0.0143993i
$970$		0			0
$971$	19.6403	+	34.0181i	0.630288	+	1.09169i	0.987493	+	0.157665i	$0.0503967\pi$
$971$	19.6403	+	34.0181i	0.630288	+	1.09169i	−0.357204	+	0.934026i	$0.616270\pi$
$972$		0			0
$973$	10.4239	+	34.4021i	0.334176	+	1.10288i
$974$		0			0
$975$	5.90032	+	0.0629802i	0.188962	+	0.00201698i
$976$		0			0
$977$	17.2739	+	29.9193i	0.552641	+	0.957202i	0.998083	+	0.0618913i	$0.0197132\pi$
$977$	17.2739	+	29.9193i	0.552641	+	0.957202i	−0.445442	+	0.895311i	$0.646953\pi$
$978$		0			0
$979$	21.3252	+	36.9363i	0.681555	+	1.18049i
$980$		0			0
$981$	−6.85182	−	12.4753i	−0.218762	−	0.398307i
$982$		0			0
$983$	20.0193			0.638516			0.319258	−	0.947668i	$-0.396566\pi$
$983$	20.0193			0.638516			0.319258	+	0.947668i	$0.396566\pi$
$984$		0			0
$985$	30.3714			0.967712
$986$		0			0
$987$	16.5061	−	17.2398i	0.525396	−	0.548749i
$988$		0			0
$989$	−34.5298	−	59.8074i	−1.09798	−	1.90177i
$990$		0			0
$991$	−2.27853	+	3.94653i	−0.0723799	+	0.125366i	−0.899944	−	0.436006i	$-0.856393\pi$
$991$	−2.27853	+	3.94653i	−0.0723799	+	0.125366i	0.827564	+	0.561371i	$0.189726\pi$
$992$		0			0
$993$	−6.36752	−	0.0679670i	−0.202067	−	0.00215687i
$994$		0			0
$995$	10.2948	−	17.8311i	0.326367	−	0.565284i
$996$		0			0
$997$	21.7323			0.688270			0.344135	−	0.938920i	$-0.388172\pi$
$997$	21.7323			0.688270			0.344135	+	0.938920i	$0.388172\pi$
$998$		0			0
$999$	−4.32047	−	8.06936i	−0.136694	−	0.255303i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1008.2.t.k.193.8		22
3.2	odd	2		3024.2.t.l.1873.7		22
4.3	odd	2		504.2.t.d.193.4	yes	22
7.2	even	3		1008.2.q.k.625.1		22
9.2	odd	6		3024.2.q.k.2881.5		22
9.7	even	3		1008.2.q.k.529.1		22
12.11	even	2		1512.2.t.d.361.7		22
21.2	odd	6		3024.2.q.k.2305.5		22
28.23	odd	6		504.2.q.d.121.11	yes	22
36.7	odd	6		504.2.q.d.25.11	✓	22
36.11	even	6		1512.2.q.c.1369.5		22
63.2	odd	6		3024.2.t.l.289.7		22
63.16	even	3	inner	1008.2.t.k.961.8		22
84.23	even	6		1512.2.q.c.793.5		22
252.79	odd	6		504.2.t.d.457.4	yes	22
252.191	even	6		1512.2.t.d.289.7		22

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
504.2.q.d.25.11	✓	22	36.7	odd	6
504.2.q.d.121.11	yes	22	28.23	odd	6
504.2.t.d.193.4	yes	22	4.3	odd	2
504.2.t.d.457.4	yes	22	252.79	odd	6
1008.2.q.k.529.1		22	9.7	even	3
1008.2.q.k.625.1		22	7.2	even	3
1008.2.t.k.193.8		22	1.1	even	1	trivial
1008.2.t.k.961.8		22	63.16	even	3	inner
1512.2.q.c.793.5		22	84.23	even	6
1512.2.q.c.1369.5		22	36.11	even	6
1512.2.t.d.289.7		22	252.191	even	6
1512.2.t.d.361.7		22	12.11	even	2
3024.2.q.k.2305.5		22	21.2	odd	6
3024.2.q.k.2881.5		22	9.2	odd	6
3024.2.t.l.289.7		22	63.2	odd	6
3024.2.t.l.1873.7		22	3.2	odd	2

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:	\( N \)	\(=\)	\( 1008 = 2^{4} \cdot 3^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1008.t (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.849966 + 1.50916i) q^{3} -1.58188 q^{5} +(1.80922 - 1.93047i) q^{7} +(-1.55512 + 2.56547i) q^{9} +O(q^{10})\)	\(q+(0.849966 + 1.50916i) q^{3} -1.58188 q^{5} +(1.80922 - 1.93047i) q^{7} +(-1.55512 + 2.56547i) q^{9} -5.17139 q^{11} +(-0.681985 + 1.18123i) q^{13} +(-1.34454 - 2.38730i) q^{15} +(-2.30781 + 3.99724i) q^{17} +(-0.0321742 - 0.0557274i) q^{19} +(4.45116 + 1.08957i) q^{21} -6.74395 q^{23} -2.49767 q^{25} +(-5.19349 - 0.166357i) q^{27} +(4.70787 + 8.15427i) q^{29} +(-1.33139 - 2.30604i) q^{31} +(-4.39550 - 7.80444i) q^{33} +(-2.86196 + 3.05376i) q^{35} +(0.880766 + 1.52553i) q^{37} +(-2.36233 - 0.0252156i) q^{39} +(-0.858924 + 1.48770i) q^{41} +(5.12012 + 8.86831i) q^{43} +(2.46000 - 4.05825i) q^{45} +(2.60417 - 4.51056i) q^{47} +(-0.453429 - 6.98530i) q^{49} +(-7.99402 - 0.0853284i) q^{51} +(-0.479996 + 0.831377i) q^{53} +8.18049 q^{55} +(0.0567545 - 0.0959224i) q^{57} +(-4.66676 - 8.08307i) q^{59} +(-7.19512 + 12.4623i) q^{61} +(2.13900 + 7.64360i) q^{63} +(1.07882 - 1.86856i) q^{65} +(-6.24903 - 10.8236i) q^{67} +(-5.73213 - 10.1777i) q^{69} +4.49160 q^{71} +(-0.941655 + 1.63099i) q^{73} +(-2.12293 - 3.76938i) q^{75} +(-9.35619 + 9.98321i) q^{77} +(3.26752 - 5.65951i) q^{79} +(-4.16323 - 7.97919i) q^{81} +(5.08661 + 8.81026i) q^{83} +(3.65066 - 6.32314i) q^{85} +(-8.30455 + 14.0358i) q^{87} +(-4.12369 - 7.14243i) q^{89} +(1.04647 + 3.45366i) q^{91} +(2.34854 - 3.96933i) q^{93} +(0.0508957 + 0.0881539i) q^{95} +(-7.26638 - 12.5857i) q^{97} +(8.04210 - 13.2670i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 22 q - 2 q^{3} - 6 q^{5} - 7 q^{7} - 8 q^{9}+O(q^{10}) \) 22 * q - 2 * q^3 - 6 * q^5 - 7 * q^7 - 8 * q^9	\( 22 q - 2 q^{3} - 6 q^{5} - 7 q^{7} - 8 q^{9} - 6 q^{11} - 3 q^{13} + q^{15} + 7 q^{17} + q^{19} - 15 q^{21} + 4 q^{23} + 20 q^{25} + 4 q^{27} + 9 q^{29} + 4 q^{31} - 31 q^{33} - 14 q^{35} + 2 q^{37} - 8 q^{39} + 16 q^{41} + 22 q^{45} - 5 q^{47} - 15 q^{49} - 7 q^{51} + 11 q^{53} - 22 q^{55} + 7 q^{57} + 19 q^{59} - 13 q^{61} - 21 q^{63} + 13 q^{65} - 26 q^{67} - 4 q^{69} + 48 q^{71} - 35 q^{73} + 8 q^{75} - 4 q^{77} - 10 q^{79} - 8 q^{81} + 28 q^{83} - 20 q^{85} - 9 q^{87} + 6 q^{89} + 37 q^{91} - 32 q^{93} - 12 q^{95} - 29 q^{97} + 56 q^{99}+O(q^{100}) \) 22 * q - 2 * q^3 - 6 * q^5 - 7 * q^7 - 8 * q^9 - 6 * q^11 - 3 * q^13 + q^15 + 7 * q^17 + q^19 - 15 * q^21 + 4 * q^23 + 20 * q^25 + 4 * q^27 + 9 * q^29 + 4 * q^31 - 31 * q^33 - 14 * q^35 + 2 * q^37 - 8 * q^39 + 16 * q^41 + 22 * q^45 - 5 * q^47 - 15 * q^49 - 7 * q^51 + 11 * q^53 - 22 * q^55 + 7 * q^57 + 19 * q^59 - 13 * q^61 - 21 * q^63 + 13 * q^65 - 26 * q^67 - 4 * q^69 + 48 * q^71 - 35 * q^73 + 8 * q^75 - 4 * q^77 - 10 * q^79 - 8 * q^81 + 28 * q^83 - 20 * q^85 - 9 * q^87 + 6 * q^89 + 37 * q^91 - 32 * q^93 - 12 * q^95 - 29 * q^97 + 56 * q^99

Introduction

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