LMFDB - Embedded newform 1008.2.bh.c.95.15

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1008,2,Mod(95,1008)]

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([3, 0, 5, 4]))

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

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

chi := DirichletCharacter("1008.95");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1008 = 2^{4} \cdot 3^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1008.bh (of order $6$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$8.04892052375$
Analytic rank:	$0$
Dimension:	$30$
Relative dimension:	$15$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			95.15
Character	$\chi$	$=$	1008.95
Dual form			1008.2.bh.c.191.15

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.72102 + 0.195155i) q^{3} -2.71056i q^{5} +(-1.81297 + 1.92695i) q^{7} +(2.92383 + 0.671730i) q^{9} +O(q^{10})$	\(q+(1.72102 + 0.195155i) q^{3} -2.71056i q^{5} +(-1.81297 + 1.92695i) q^{7} +(2.92383 + 0.671730i) q^{9} -1.42297 q^{11} +(2.56378 - 4.44059i) q^{13} +(0.528979 - 4.66494i) q^{15} +(1.04103 + 0.601041i) q^{17} +(6.15547 - 3.55386i) q^{19} +(-3.49622 + 2.96251i) q^{21} -7.49622 q^{23} -2.34715 q^{25} +(4.90088 + 1.72666i) q^{27} +(6.90901 - 3.98892i) q^{29} +(6.36392 - 3.67421i) q^{31} +(-2.44895 - 0.277698i) q^{33} +(5.22311 + 4.91418i) q^{35} +(-0.194581 - 0.337025i) q^{37} +(5.27892 - 7.14203i) q^{39} +(-1.52819 - 0.882303i) q^{41} +(0.214184 - 0.123659i) q^{43} +(1.82077 - 7.92522i) q^{45} +(-3.40171 + 5.89194i) q^{47} +(-0.426244 - 6.98701i) q^{49} +(1.67435 + 1.23757i) q^{51} +(-10.7865 - 6.22758i) q^{53} +3.85704i q^{55} +(11.2873 - 4.91501i) q^{57} +(2.37824 + 4.11923i) q^{59} +(0.102313 - 0.177212i) q^{61} +(-6.59522 + 4.41623i) q^{63} +(-12.0365 - 6.94928i) q^{65} +(-4.62294 + 2.66906i) q^{67} +(-12.9012 - 1.46292i) q^{69} -2.22420 q^{71} +(-7.54731 + 13.0723i) q^{73} +(-4.03949 - 0.458057i) q^{75} +(2.57980 - 2.74198i) q^{77} +(8.33242 + 4.81072i) q^{79} +(8.09756 + 3.92805i) q^{81} +(-2.59188 - 4.48927i) q^{83} +(1.62916 - 2.82179i) q^{85} +(12.6690 - 5.51669i) q^{87} +(4.17410 - 2.40992i) q^{89} +(3.90872 + 12.9910i) q^{91} +(11.6695 - 5.08145i) q^{93} +(-9.63297 - 16.6848i) q^{95} +(2.40373 + 4.16339i) q^{97} +(-4.16051 - 0.955849i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 30 q - 3 q^{3} - 2 q^{7} - q^{9}+O(q^{10}) $ 30 * q - 3 * q^3 - 2 * q^7 - q^9	$ 30 q - 3 q^{3} - 2 q^{7} - q^{9} + 6 q^{11} + 12 q^{17} + 9 q^{19} + 14 q^{21} - 24 q^{23} - 36 q^{25} + 27 q^{27} + 27 q^{29} + 6 q^{31} - 20 q^{33} - 6 q^{35} + 6 q^{37} - 15 q^{39} + 9 q^{41} - 21 q^{43} - 8 q^{45} + 12 q^{49} - 15 q^{51} - 3 q^{53} + 20 q^{57} + 3 q^{59} - 3 q^{61} + 24 q^{63} - 39 q^{67} + 10 q^{69} + 18 q^{71} + 21 q^{73} + 21 q^{75} + 36 q^{77} - 33 q^{79} - 17 q^{81} - 15 q^{83} - 3 q^{85} + 78 q^{87} + 6 q^{89} - 26 q^{91} - 3 q^{93} - 27 q^{95} - 6 q^{97} - 48 q^{99}+O(q^{100}) $ 30 * q - 3 * q^3 - 2 * q^7 - q^9 + 6 * q^11 + 12 * q^17 + 9 * q^19 + 14 * q^21 - 24 * q^23 - 36 * q^25 + 27 * q^27 + 27 * q^29 + 6 * q^31 - 20 * q^33 - 6 * q^35 + 6 * q^37 - 15 * q^39 + 9 * q^41 - 21 * q^43 - 8 * q^45 + 12 * q^49 - 15 * q^51 - 3 * q^53 + 20 * q^57 + 3 * q^59 - 3 * q^61 + 24 * q^63 - 39 * q^67 + 10 * q^69 + 18 * q^71 + 21 * q^73 + 21 * q^75 + 36 * q^77 - 33 * q^79 - 17 * q^81 - 15 * q^83 - 3 * q^85 + 78 * q^87 + 6 * q^89 - 26 * q^91 - 3 * q^93 - 27 * q^95 - 6 * q^97 - 48 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$127$	$577$	$757$	$785$
$\chi(n)$	$-1$	$e\left(\frac{2}{3}\right)$	$1$	$e\left(\frac{5}{6}\right)$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	1.72102	+	0.195155i	0.993632	+	0.112673i
$3$	1.72102	+	0.195155i	0.993632	+	0.112673i
$4$		0			0
$5$		−	2.71056i		−	1.21220i	−0.795388	−	0.606100i	$-0.792733\pi$
$5$		−	2.71056i		−	1.21220i	0.795388	−	0.606100i	$-0.207267\pi$
$6$		0			0
$7$	−1.81297	+	1.92695i	−0.685240	+	0.728317i
$7$	−1.81297	+	1.92695i	−0.685240	+	0.728317i
$8$		0			0
$9$	2.92383	+	0.671730i	0.974610	+	0.223910i
$10$		0			0
$11$	−1.42297			−0.429040			−0.214520	−	0.976720i	$-0.568819\pi$
$11$	−1.42297			−0.429040			−0.214520	+	0.976720i	$0.568819\pi$
$12$		0			0
$13$	2.56378	−	4.44059i	0.711064	−	1.23160i	−0.253394	−	0.967363i	$-0.581547\pi$
$13$	2.56378	−	4.44059i	0.711064	−	1.23160i	0.964458	−	0.264236i	$-0.0851198\pi$
$14$		0			0
$15$	0.528979	−	4.66494i	0.136582	−	1.20448i
$16$		0			0
$17$	1.04103	+	0.601041i	0.252488	+	0.145774i	0.620903	−	0.783887i	$-0.286766\pi$
$17$	1.04103	+	0.601041i	0.252488	+	0.145774i	−0.368415	+	0.929661i	$0.620099\pi$
$18$		0			0
$19$	6.15547	−	3.55386i	1.41216	−	0.815312i	0.416570	−	0.909104i	$-0.363232\pi$
$19$	6.15547	−	3.55386i	1.41216	−	0.815312i	0.995592	+	0.0937915i	$0.0298987\pi$
$20$		0			0
$21$	−3.49622	+	2.96251i	−0.762938	+	0.646472i
$22$		0			0
$23$	−7.49622			−1.56307			−0.781535	−	0.623861i	$-0.785563\pi$
$23$	−7.49622			−1.56307			−0.781535	+	0.623861i	$0.785563\pi$
$24$		0			0
$25$	−2.34715			−0.469430
$26$		0			0
$27$	4.90088	+	1.72666i	0.943175	+	0.332296i
$28$		0			0
$29$	6.90901	−	3.98892i	1.28297	−	0.740724i	0.305581	−	0.952166i	$-0.401149\pi$
$29$	6.90901	−	3.98892i	1.28297	−	0.740724i	0.977390	+	0.211443i	$0.0678161\pi$
$30$		0			0
$31$	6.36392	−	3.67421i	1.14299	−	0.659908i	0.195824	−	0.980639i	$-0.437262\pi$
$31$	6.36392	−	3.67421i	1.14299	−	0.659908i	0.947170	+	0.320731i	$0.103929\pi$
$32$		0			0
$33$	−2.44895	−	0.277698i	−0.426308	−	0.0483411i
$34$		0			0
$35$	5.22311	+	4.91418i	0.882866	+	0.830648i
$36$		0			0
$37$	−0.194581	−	0.337025i	−0.0319890	−	0.0554065i	0.849588	−	0.527447i	$-0.176851\pi$
$37$	−0.194581	−	0.337025i	−0.0319890	−	0.0554065i	−0.881577	+	0.472041i	$0.843517\pi$
$38$		0			0
$39$	5.27892	−	7.14203i	0.845304	−	1.14364i
$40$		0			0
$41$	−1.52819	−	0.882303i	−0.238664	−	0.137793i	0.375899	−	0.926661i	$-0.377334\pi$
$41$	−1.52819	−	0.882303i	−0.238664	−	0.137793i	−0.614562	+	0.788868i	$0.710667\pi$
$42$		0			0
$43$	0.214184	−	0.123659i	0.0326628	−	0.0188579i	−0.483580	−	0.875300i	$-0.660664\pi$
$43$	0.214184	−	0.123659i	0.0326628	−	0.0188579i	0.516242	+	0.856442i	$0.327330\pi$
$44$		0			0
$45$	1.82077	−	7.92522i	0.271424	−	1.18142i
$46$		0			0
$47$	−3.40171	+	5.89194i	−0.496191	+	0.859428i	−0.999990	−	0.00439269i	$-0.998602\pi$
$47$	−3.40171	+	5.89194i	−0.496191	+	0.859428i	0.503799	+	0.863821i	$0.331935\pi$
$48$		0			0
$49$	−0.426244	−	6.98701i	−0.0608920	−	0.998144i
$50$		0			0
$51$	1.67435	+	1.23757i	0.234455	+	0.173294i
$52$		0			0
$53$	−10.7865	−	6.22758i	−1.48164	−	0.855423i	−0.481853	−	0.876252i	$-0.660036\pi$
$53$	−10.7865	−	6.22758i	−1.48164	−	0.855423i	−0.999783	+	0.0208286i	$0.993370\pi$
$54$		0			0
$55$			3.85704i			0.520083i
$56$		0			0
$57$	11.2873	−	4.91501i	1.49503	−	0.651008i
$58$		0			0
$59$	2.37824	+	4.11923i	0.309620	+	0.536278i	0.978279	−	0.207291i	$-0.0664648\pi$
$59$	2.37824	+	4.11923i	0.309620	+	0.536278i	−0.668659	+	0.743569i	$0.733131\pi$
$60$		0			0
$61$	0.102313	−	0.177212i	0.0130999	−	0.0226897i	−0.859401	−	0.511302i	$-0.829163\pi$
$61$	0.102313	−	0.177212i	0.0130999	−	0.0226897i	0.872501	+	0.488612i	$0.162497\pi$
$62$		0			0
$63$	−6.59522	+	4.41623i	−0.830919	+	0.556393i
$64$		0			0
$65$	−12.0365	−	6.94928i	−1.49295	−	0.861952i
$66$		0			0
$67$	−4.62294	+	2.66906i	−0.564783	+	0.326077i	−0.755063	−	0.655652i	$-0.772394\pi$
$67$	−4.62294	+	2.66906i	−0.564783	+	0.326077i	0.190280	+	0.981730i	$0.439060\pi$
$68$		0			0
$69$	−12.9012	−	1.46292i	−1.55312	−	0.176115i
$70$		0			0
$71$	−2.22420			−0.263964			−0.131982	−	0.991252i	$-0.542134\pi$
$71$	−2.22420			−0.263964			−0.131982	+	0.991252i	$0.542134\pi$
$72$		0			0
$73$	−7.54731	+	13.0723i	−0.883345	+	1.53000i	−0.0357471	+	0.999361i	$0.511381\pi$
$73$	−7.54731	+	13.0723i	−0.883345	+	1.53000i	−0.847598	+	0.530638i	$0.821952\pi$
$74$		0			0
$75$	−4.03949	−	0.458057i	−0.466440	−	0.0528918i
$76$		0			0
$77$	2.57980	−	2.74198i	0.293996	−	0.312477i
$78$		0			0
$79$	8.33242	+	4.81072i	0.937470	+	0.541249i	0.889166	−	0.457584i	$-0.151285\pi$
$79$	8.33242	+	4.81072i	0.937470	+	0.541249i	0.0483037	+	0.998833i	$0.484618\pi$
$80$		0			0
$81$	8.09756	+	3.92805i	0.899728	+	0.436450i
$82$		0			0
$83$	−2.59188	−	4.48927i	−0.284496	−	0.492761i	0.687991	−	0.725719i	$-0.258493\pi$
$83$	−2.59188	−	4.48927i	−0.284496	−	0.492761i	−0.972487	+	0.232958i	$0.925159\pi$
$84$		0			0
$85$	1.62916	−	2.82179i	0.176707	−	0.306066i
$86$		0			0
$87$	12.6690	−	5.51669i	1.35826	−	0.591451i
$88$		0			0
$89$	4.17410	−	2.40992i	0.442454	−	0.255451i	−0.262184	−	0.965018i	$-0.584443\pi$
$89$	4.17410	−	2.40992i	0.442454	−	0.255451i	0.704638	+	0.709567i	$0.251109\pi$
$90$		0			0
$91$	3.90872	+	12.9910i	0.409745	+	1.36182i
$92$		0			0
$93$	11.6695	−	5.08145i	1.21007	−	0.526922i
$94$		0			0
$95$	−9.63297	−	16.6848i	−0.988322	−	1.71182i
$96$		0			0
$97$	2.40373	+	4.16339i	0.244062	+	0.422728i	0.961868	−	0.273516i	$-0.0881865\pi$
$97$	2.40373	+	4.16339i	0.244062	+	0.422728i	−0.717805	+	0.696244i	$0.754853\pi$
$98$		0			0
$99$	−4.16051	−	0.955849i	−0.418147	−	0.0960665i
$100$		0			0
$101$		−	3.88565i		−	0.386636i	−0.981136	−	0.193318i	$-0.938075\pi$
$101$		−	3.88565i		−	0.386636i	0.981136	−	0.193318i	$-0.0619250\pi$
$102$		0			0
$103$			12.7719i			1.25845i	0.777222	+	0.629226i	$0.216628\pi$
$103$			12.7719i			1.25845i	−0.777222	+	0.629226i	$0.783372\pi$
$104$		0			0
$105$	8.03006	+	9.47672i	0.783653	+	0.924834i
$106$		0			0
$107$	6.20389	+	10.7455i	0.599753	+	1.03880i	0.992857	+	0.119309i	$0.0380679\pi$
$107$	6.20389	+	10.7455i	0.599753	+	1.03880i	−0.393104	+	0.919494i	$0.628599\pi$
$108$		0			0
$109$	−6.14048	+	10.6356i	−0.588152	+	1.01871i	0.406323	+	0.913730i	$0.366811\pi$
$109$	−6.14048	+	10.6356i	−0.588152	+	1.01871i	−0.994474	+	0.104979i	$0.966523\pi$
$110$		0			0
$111$	−0.269107	−	0.618000i	−0.0255425	−	0.0586579i
$112$		0			0
$113$	13.2555	+	7.65305i	1.24697	+	0.719938i	0.970504	−	0.241086i	$-0.0775035\pi$
$113$	13.2555	+	7.65305i	1.24697	+	0.719938i	0.276465	+	0.961024i	$0.410837\pi$
$114$		0			0
$115$			20.3190i			1.89475i
$116$		0			0
$117$	10.4789	−	11.2614i	0.968778	−	1.04111i
$118$		0			0
$119$	−3.04554	+	0.916344i	−0.279185	+	0.0840011i
$120$		0			0
$121$	−8.97517			−0.815924
$122$		0			0
$123$	−2.45787	−	1.81670i	−0.221619	−	0.163806i
$124$		0			0
$125$		−	7.19072i		−	0.643158i
$126$		0			0
$127$		−	15.1494i		−	1.34429i	−0.740418	−	0.672147i	$-0.765372\pi$
$127$		−	15.1494i		−	1.34429i	0.740418	−	0.672147i	$-0.234628\pi$
$128$		0			0
$129$	0.392749	−	0.171021i	0.0345796	−	0.0150576i
$130$		0			0
$131$	−9.24044			−0.807341			−0.403671	−	0.914904i	$-0.632266\pi$
$131$	−9.24044			−0.807341			−0.403671	+	0.914904i	$0.632266\pi$
$132$		0			0
$133$	−4.31161	+	18.3043i	−0.373864	+	1.58719i
$134$		0			0
$135$	4.68022	−	13.2841i	0.402809	−	1.14332i
$136$		0			0
$137$			4.12231i			0.352193i	0.984373	+	0.176096i	$0.0563470\pi$
$137$			4.12231i			0.352193i	−0.984373	+	0.176096i	$0.943653\pi$
$138$		0			0
$139$	3.87372	+	2.23649i	0.328564	+	0.189697i	0.655204	−	0.755452i	$-0.272583\pi$
$139$	3.87372	+	2.23649i	0.328564	+	0.189697i	−0.326639	+	0.945149i	$0.605916\pi$
$140$		0			0
$141$	−7.00426	+	9.47630i	−0.589865	+	0.798048i
$142$		0			0
$143$	−3.64817	+	6.31881i	−0.305075	+	0.528406i
$144$		0			0
$145$	−10.8122	−	18.7273i	−0.897905	−	1.55522i
$146$		0			0
$147$	0.629972	−	12.1080i	0.0519592	−	0.998649i
$148$		0			0
$149$			20.2640i			1.66009i	0.557696	+	0.830045i	$0.311686\pi$
$149$			20.2640i			1.66009i	−0.557696	+	0.830045i	$0.688314\pi$
$150$		0			0
$151$			7.44219i			0.605637i	0.953048	+	0.302818i	$0.0979275\pi$
$151$			7.44219i			0.605637i	−0.953048	+	0.302818i	$0.902072\pi$
$152$		0			0
$153$	2.64007	+	2.45664i	0.213437	+	0.198607i
$154$		0			0
$155$	−9.95918	−	17.2498i	−0.799940	−	1.38554i
$156$		0			0
$157$	7.47069	+	12.9396i	0.596226	+	1.03269i	0.993373	+	0.114939i	$0.0366672\pi$
$157$	7.47069	+	12.9396i	0.596226	+	1.03269i	−0.397146	+	0.917755i	$0.629999\pi$
$158$		0			0
$159$	−17.3484	−	12.8228i	−1.37582	−	1.01692i
$160$		0			0
$161$	13.5905	−	14.4448i	1.07108	−	1.13841i
$162$		0			0
$163$	10.3855	−	5.99605i	0.813453	−	0.469647i	−0.0347008	−	0.999398i	$-0.511048\pi$
$163$	10.3855	−	5.99605i	0.813453	−	0.469647i	0.848153	+	0.529751i	$0.177714\pi$
$164$		0			0
$165$	−0.752718	+	6.63804i	−0.0585991	+	0.516771i
$166$		0			0
$167$	8.91245	−	15.4368i	0.689666	−	1.19454i	−0.282280	−	0.959332i	$-0.591091\pi$
$167$	8.91245	−	15.4368i	0.689666	−	1.19454i	0.971946	−	0.235205i	$-0.0755760\pi$
$168$		0			0
$169$	−6.64592	−	11.5111i	−0.511225	−	0.885467i
$170$		0			0
$171$	20.3848	−	6.25607i	1.55886	−	0.478414i
$172$		0			0
$173$	−21.8668	−	12.6248i	−1.66250	−	0.959847i	−0.971514	−	0.236981i	$-0.923842\pi$
$173$	−21.8668	−	12.6248i	−1.66250	−	0.959847i	−0.690989	−	0.722866i	$-0.742825\pi$
$174$		0			0
$175$	4.25532	−	4.52283i	0.321672	−	0.341894i
$176$		0			0
$177$	3.28911	+	7.55340i	0.247225	+	0.567748i
$178$		0			0
$179$	−4.16327	+	7.21099i	−0.311177	+	0.538975i	−0.978617	−	0.205689i	$-0.934057\pi$
$179$	−4.16327	+	7.21099i	−0.311177	+	0.538975i	0.667440	+	0.744663i	$0.267390\pi$
$180$		0			0
$181$	15.6017			1.15967			0.579833	−	0.814735i	$-0.303118\pi$
$181$	15.6017			1.15967			0.579833	+	0.814735i	$0.303118\pi$
$182$		0			0
$183$	0.210667	−	0.285018i	0.0155730	−	0.0210692i
$184$		0			0
$185$	−0.913526	+	0.527424i	−0.0671638	+	0.0387770i
$186$		0			0
$187$	−1.48136	−	0.855261i	−0.108327	−	0.0625429i
$188$		0			0
$189$	−12.2124	+	6.31334i	−0.888318	+	0.459228i
$190$		0			0
$191$	5.42827	−	9.40204i	0.392776	−	0.680308i	−0.600039	−	0.799971i	$-0.704848\pi$
$191$	5.42827	−	9.40204i	0.392776	−	0.680308i	0.992815	+	0.119663i	$0.0381815\pi$
$192$		0			0
$193$	−2.60478	−	4.51161i	−0.187496	−	0.324753i	0.756919	−	0.653509i	$-0.226704\pi$
$193$	−2.60478	−	4.51161i	−0.187496	−	0.324753i	−0.944415	+	0.328756i	$0.893371\pi$
$194$		0			0
$195$	−19.3589	−	14.3088i	−1.38632	−	1.02468i
$196$		0			0
$197$			20.7479i			1.47823i	0.673582	+	0.739113i	$0.264755\pi$
$197$			20.7479i			1.47823i	−0.673582	+	0.739113i	$0.735245\pi$
$198$		0			0
$199$	1.76108	+	1.01676i	0.124839	+	0.0720760i	0.561119	−	0.827735i	$-0.310371\pi$
$199$	1.76108	+	1.01676i	0.124839	+	0.0720760i	−0.436280	+	0.899811i	$0.643704\pi$
$200$		0			0
$201$	−8.47707	+	3.69132i	−0.597926	+	0.260365i
$202$		0			0
$203$	−4.83943	+	20.5451i	−0.339661	+	1.44198i
$204$		0			0
$205$	−2.39154	+	4.14226i	−0.167032	+	0.289308i
$206$		0			0
$207$	−21.9177	−	5.03544i	−1.52338	−	0.349987i
$208$		0			0
$209$	−8.75902	+	5.05702i	−0.605874	+	0.349802i
$210$		0			0
$211$	0.705274	+	0.407190i	0.0485531	+	0.0280321i	0.524080	−	0.851669i	$-0.324409\pi$
$211$	0.705274	+	0.407190i	0.0485531	+	0.0280321i	−0.475527	+	0.879701i	$0.657743\pi$
$212$		0			0
$213$	−3.82789	−	0.434063i	−0.262283	−	0.0297415i
$214$		0			0
$215$	−0.335187	−	0.580560i	−0.0228595	−	0.0395939i
$216$		0			0
$217$	−4.45762	+	18.9242i	−0.302603	+	1.28466i
$218$		0			0
$219$	−15.5402	+	21.0248i	−1.05011	+	1.42073i
$220$		0			0
$221$	5.33796	−	3.08187i	0.359070	−	0.207309i
$222$		0			0
$223$	−9.40736	+	5.43134i	−0.629963	+	0.363709i	−0.780738	−	0.624859i	$-0.785157\pi$
$223$	−9.40736	+	5.43134i	−0.629963	+	0.363709i	0.150775	+	0.988568i	$0.451823\pi$
$224$		0			0
$225$	−6.86266	−	1.57665i	−0.457511	−	0.105110i
$226$		0			0
$227$	−20.2988			−1.34728			−0.673638	−	0.739062i	$-0.735269\pi$
$227$	−20.2988			−1.34728			−0.673638	+	0.739062i	$0.735269\pi$
$228$		0			0
$229$	5.02282			0.331917			0.165959	−	0.986133i	$-0.446928\pi$
$229$	5.02282			0.331917			0.165959	+	0.986133i	$0.446928\pi$
$230$		0			0
$231$	4.97500	−	4.21554i	0.327331	−	0.277362i
$232$		0			0
$233$	12.4121	−	7.16616i	0.813147	−	0.469470i	−0.0349007	−	0.999391i	$-0.511111\pi$
$233$	12.4121	−	7.16616i	0.813147	−	0.469470i	0.848047	+	0.529920i	$0.177778\pi$
$234$		0			0
$235$	15.9705	+	9.22056i	1.04180	+	0.601483i
$236$		0			0
$237$	13.4014	+	9.90547i	0.870517	+	0.643429i
$238$		0			0
$239$	−9.71239	+	16.8224i	−0.628242	+	1.08815i	0.359662	+	0.933083i	$0.382892\pi$
$239$	−9.71239	+	16.8224i	−0.628242	+	1.08815i	−0.987904	+	0.155065i	$0.950441\pi$
$240$		0			0
$241$	−6.11762			−0.394070			−0.197035	−	0.980396i	$-0.563131\pi$
$241$	−6.11762			−0.394070			−0.197035	+	0.980396i	$0.563131\pi$
$242$		0			0
$243$	13.1695	+	8.34053i	0.844823	+	0.535046i
$244$		0			0
$245$	−18.9387	+	1.15536i	−1.20995	+	0.0738133i
$246$		0			0
$247$		−	36.4453i		−	2.31896i
$248$		0			0
$249$	−3.58458	−	8.23194i	−0.227163	−	0.521678i
$250$		0			0
$251$	−2.54044			−0.160351			−0.0801757	−	0.996781i	$-0.525548\pi$
$251$	−2.54044			−0.160351			−0.0801757	+	0.996781i	$0.525548\pi$
$252$		0			0
$253$	10.6669			0.670620
$254$		0			0
$255$	3.35450	−	4.53842i	0.210067	−	0.284207i
$256$		0			0
$257$			18.5285i			1.15577i	0.816117	+	0.577886i	$0.196122\pi$
$257$			18.5285i			1.15577i	−0.816117	+	0.577886i	$0.803878\pi$
$258$		0			0
$259$	1.00220	+	0.236069i	0.0622736	+	0.0146686i
$260$		0			0
$261$	22.8802	−	7.02193i	1.41625	−	0.434646i
$262$		0			0
$263$	−12.4370			−0.766901			−0.383451	−	0.923561i	$-0.625264\pi$
$263$	−12.4370			−0.766901			−0.383451	+	0.923561i	$0.625264\pi$
$264$		0			0
$265$	−16.8802	+	29.2374i	−1.03694	+	1.79604i
$266$		0			0
$267$	7.65402	−	3.33292i	0.468418	−	0.203972i
$268$		0			0
$269$	21.0139	+	12.1324i	1.28124	+	0.739723i	0.977075	−	0.212897i	$-0.0682899\pi$
$269$	21.0139	+	12.1324i	1.28124	+	0.739723i	0.304163	+	0.952620i	$0.401623\pi$
$270$		0			0
$271$	−17.6964	+	10.2170i	−1.07498	+	0.620638i	−0.929537	−	0.368729i	$-0.879793\pi$
$271$	−17.6964	+	10.2170i	−1.07498	+	0.620638i	−0.145440	+	0.989367i	$0.546460\pi$
$272$		0			0
$273$	4.19175	+	23.1205i	0.253696	+	1.39932i
$274$		0			0
$275$	3.33991			0.201404
$276$		0			0
$277$	13.2708			0.797366			0.398683	−	0.917089i	$-0.369467\pi$
$277$	13.2708			0.797366			0.398683	+	0.917089i	$0.369467\pi$
$278$		0			0
$279$	21.0751	−	6.46793i	1.26173	−	0.387225i
$280$		0			0
$281$	1.56448	−	0.903251i	0.0933289	−	0.0538835i	−0.452609	−	0.891709i	$-0.649507\pi$
$281$	1.56448	−	0.903251i	0.0933289	−	0.0538835i	0.545938	+	0.837826i	$0.316173\pi$
$282$		0			0
$283$	−24.4119	+	14.0942i	−1.45114	+	0.837816i	−0.998546	−	0.0539018i	$-0.982834\pi$
$283$	−24.4119	+	14.0942i	−1.45114	+	0.837816i	−0.452593	+	0.891717i	$0.649501\pi$
$284$		0			0
$285$	−13.3224	−	30.5948i	−0.789153	−	1.81228i
$286$		0			0
$287$	4.47073	−	1.34515i	0.263899	−	0.0794019i
$288$		0			0
$289$	−7.77750	−	13.4710i	−0.457500	−	0.792413i
$290$		0			0
$291$	3.32437	+	7.63438i	0.194878	+	0.447535i
$292$		0			0
$293$	−8.28005	−	4.78049i	−0.483726	−	0.279279i	0.238242	−	0.971206i	$-0.423429\pi$
$293$	−8.28005	−	4.78049i	−0.483726	−	0.279279i	−0.721968	+	0.691927i	$0.756762\pi$
$294$		0			0
$295$	11.1654	−	6.44636i	0.650076	−	0.375322i
$296$		0			0
$297$	−6.97379	−	2.45698i	−0.404660	−	0.142568i
$298$		0			0
$299$	−19.2187	+	33.2877i	−1.11144	+	1.92508i
$300$		0			0
$301$	−0.150026	+	0.636913i	−0.00864735	+	0.0367111i
$302$		0			0
$303$	0.758302	−	6.68728i	0.0435633	−	0.384174i
$304$		0			0
$305$	−0.480344	−	0.277327i	−0.0275044	−	0.0158797i
$306$		0			0
$307$		−	19.8578i		−	1.13334i	−0.823944	−	0.566671i	$-0.808231\pi$
$307$		−	19.8578i		−	1.13334i	0.823944	−	0.566671i	$-0.191769\pi$
$308$		0			0
$309$	−2.49249	+	21.9807i	−0.141793	+	1.25044i
$310$		0			0
$311$	−0.378886	−	0.656249i	−0.0214846	−	0.0372125i	0.855083	−	0.518491i	$-0.173506\pi$
$311$	−0.378886	−	0.656249i	−0.0214846	−	0.0372125i	−0.876568	+	0.481278i	$0.840173\pi$
$312$		0			0
$313$	3.97641	−	6.88735i	0.224760	−	0.389296i	−0.731487	−	0.681855i	$-0.761174\pi$
$313$	3.97641	−	6.88735i	0.224760	−	0.389296i	0.956247	+	0.292559i	$0.0945068\pi$
$314$		0			0
$315$	11.9705	+	17.8767i	0.674460	+	1.00724i
$316$		0			0
$317$	−12.2839	−	7.09213i	−0.689934	−	0.398334i	0.113653	−	0.993520i	$-0.463745\pi$
$317$	−12.2839	−	7.09213i	−0.689934	−	0.398334i	−0.803587	+	0.595187i	$0.797078\pi$
$318$		0			0
$319$	−9.83128	+	5.67609i	−0.550446	+	0.317800i
$320$		0			0
$321$	8.58001	+	19.7039i	0.478889	+	1.09976i
$322$		0			0
$323$	8.54408			0.475405
$324$		0			0
$325$	−6.01757	+	10.4227i	−0.333795	+	0.578149i
$326$		0			0
$327$	−12.6435	+	17.1058i	−0.699187	+	0.945953i
$328$		0			0
$329$	−5.18623	−	17.2369i	−0.285926	−	0.950299i
$330$		0			0
$331$	7.30828	+	4.21944i	0.401700	+	0.231921i	0.687217	−	0.726452i	$-0.258832\pi$
$331$	7.30828	+	4.21944i	0.401700	+	0.231921i	−0.285518	+	0.958373i	$0.592165\pi$
$332$		0			0
$333$	−0.342533	−	1.11611i	−0.0187707	−	0.0611624i
$334$		0			0
$335$	7.23465	+	12.5308i	0.395271	+	0.684630i
$336$		0			0
$337$	6.41921	−	11.1184i	0.349677	−	0.605658i	−0.636515	−	0.771264i	$-0.719625\pi$
$337$	6.41921	−	11.1184i	0.349677	−	0.605658i	0.986192	+	0.165606i	$0.0529582\pi$
$338$		0			0
$339$	21.3194	+	15.7579i	1.15791	+	0.855853i
$340$		0			0
$341$	−9.05564	+	5.22828i	−0.490390	+	0.283127i
$342$		0			0
$343$	14.2364	+	11.8459i	0.768691	+	0.639620i
$344$		0			0
$345$	−3.96534	+	34.9694i	−0.213487	+	1.88269i
$346$		0			0
$347$	−5.27698	−	9.14000i	−0.283283	−	0.490661i	0.688908	−	0.724849i	$-0.258090\pi$
$347$	−5.27698	−	9.14000i	−0.283283	−	0.490661i	−0.972191	+	0.234188i	$0.924757\pi$
$348$		0			0
$349$	−7.84572	−	13.5892i	−0.419972	−	0.727412i	0.575964	−	0.817475i	$-0.304627\pi$
$349$	−7.84572	−	13.5892i	−0.419972	−	0.727412i	−0.995936	+	0.0900624i	$0.971293\pi$
$350$		0			0
$351$	20.2322	−	17.3361i	1.07991	−	0.925330i
$352$		0			0
$353$		−	0.0215722i		−	0.00114817i	−1.00000		0.000574087i	$-0.999817\pi$
$353$		−	0.0215722i		−	0.00114817i	1.00000		0.000574087i	$-0.000182738\pi$
$354$		0			0
$355$			6.02883i			0.319977i
$356$		0			0
$357$	−5.42027	+	0.982696i	−0.286871	+	0.0520098i
$358$		0			0
$359$	−3.41437	−	5.91386i	−0.180203	−	0.312121i	0.761746	−	0.647875i	$-0.224342\pi$
$359$	−3.41437	−	5.91386i	−0.180203	−	0.312121i	−0.941950	+	0.335754i	$0.891009\pi$
$360$		0			0
$361$	15.7599	−	27.2969i	0.829468	−	1.43668i
$362$		0			0
$363$	−15.4465	−	1.75155i	−0.810729	−	0.0919323i
$364$		0			0
$365$	35.4333	+	20.4574i	1.85467	+	1.07079i
$366$		0			0
$367$		−	3.46331i		−	0.180783i	−0.995906	−	0.0903916i	$-0.971188\pi$
$367$		−	3.46331i		−	0.180783i	0.995906	−	0.0903916i	$-0.0288119\pi$
$368$		0			0
$369$	−3.87551	−	3.60624i	−0.201751	−	0.187733i
$370$		0			0
$371$	31.5558	−	9.49452i	1.63830	−	0.492931i
$372$		0			0
$373$	8.53539			0.441946			0.220973	−	0.975280i	$-0.429077\pi$
$373$	8.53539			0.441946			0.220973	+	0.975280i	$0.429077\pi$
$374$		0			0
$375$	1.40330	−	12.3754i	0.0724662	−	0.639062i
$376$		0			0
$377$		−	40.9068i		−	2.10681i
$378$		0			0
$379$			6.38671i			0.328063i	0.986455	+	0.164032i	$0.0524499\pi$
$379$			6.38671i			0.328063i	−0.986455	+	0.164032i	$0.947550\pi$
$380$		0			0
$381$	2.95648	−	26.0725i	0.151465	−	1.33573i
$382$		0			0
$383$	−26.5208			−1.35515			−0.677575	−	0.735454i	$-0.736969\pi$
$383$	−26.5208			−1.35515			−0.677575	+	0.735454i	$0.736969\pi$
$384$		0			0
$385$	−7.43230	−	6.99271i	−0.378785	−	0.356382i
$386$		0			0
$387$	0.709305	−	0.217685i	0.0360560	−	0.0110655i
$388$		0			0
$389$		−	0.286122i		−	0.0145069i	−0.999974	−	0.00725347i	$-0.997691\pi$
$389$		−	0.286122i		−	0.0145069i	0.999974	−	0.00725347i	$-0.00230887\pi$
$390$		0			0
$391$	−7.80382	−	4.50554i	−0.394656	−	0.227855i
$392$		0			0
$393$	−15.9030	−	1.80331i	−0.802200	−	0.0909652i
$394$		0			0
$395$	13.0398	−	22.5855i	0.656102	−	1.13640i
$396$		0			0
$397$	15.6448	+	27.0975i	0.785188	+	1.35998i	0.928887	+	0.370363i	$0.120767\pi$
$397$	15.6448	+	27.0975i	0.785188	+	1.35998i	−0.143699	+	0.989621i	$0.545900\pi$
$398$		0			0
$399$	−10.9925	+	30.6607i	−0.550316	+	1.53496i
$400$		0			0
$401$		−	14.5305i		−	0.725621i	−0.931863	−	0.362810i	$-0.881817\pi$
$401$		−	14.5305i		−	0.725621i	0.931863	−	0.362810i	$-0.118183\pi$
$402$		0			0
$403$		−	37.6794i		−	1.87695i
$404$		0			0
$405$	10.6472	−	21.9489i	0.529065	−	1.09065i
$406$		0			0
$407$	0.276882	+	0.479574i	0.0137245	+	0.0237716i
$408$		0			0
$409$	9.34916	+	16.1932i	0.462286	+	0.800704i	0.999074	−	0.0430136i	$-0.0136959\pi$
$409$	9.34916	+	16.1932i	0.462286	+	0.800704i	−0.536788	+	0.843717i	$0.680363\pi$
$410$		0			0
$411$	−0.804487	+	7.09458i	−0.0396824	+	0.349950i
$412$		0			0
$413$	−12.2492	−	2.88532i	−0.602744	−	0.141977i
$414$		0			0
$415$	−12.1684	+	7.02545i	−0.597325	+	0.344866i
$416$		0			0
$417$	6.23029	+	4.60502i	0.305098	+	0.225509i
$418$		0			0
$419$	0.0728005	−	0.126094i	0.00355653	−	0.00616010i	−0.864242	−	0.503077i	$-0.832201\pi$
$419$	0.0728005	−	0.126094i	0.00355653	−	0.00616010i	0.867798	+	0.496917i	$0.165535\pi$
$420$		0			0
$421$	−10.4460	−	18.0930i	−0.509107	−	0.881799i	−0.999944	−	0.0105480i	$-0.996642\pi$
$421$	−10.4460	−	18.0930i	−0.509107	−	0.881799i	0.490837	−	0.871251i	$-0.336691\pi$
$422$		0			0
$423$	−13.9038	+	14.9420i	−0.676027	+	0.726505i
$424$		0			0
$425$	−2.44346	−	1.41073i	−0.118525	−	0.0684306i
$426$		0			0
$427$	0.155986	+	0.518433i	0.00754870	+	0.0250887i
$428$		0			0
$429$	−7.51172	+	10.1629i	−0.362669	+	0.490667i
$430$		0			0
$431$	−10.5495	+	18.2723i	−0.508151	+	0.880144i	0.491804	+	0.870706i	$0.336338\pi$
$431$	−10.5495	+	18.2723i	−0.508151	+	0.880144i	−0.999955	+	0.00943786i	$0.996996\pi$
$432$		0			0
$433$	9.19616			0.441939			0.220970	−	0.975281i	$-0.429078\pi$
$433$	9.19616			0.441939			0.220970	+	0.975281i	$0.429078\pi$
$434$		0			0
$435$	−14.9533	−	34.3401i	−0.716957	−	1.64648i
$436$		0			0
$437$	−46.1428	+	26.6405i	−2.20731	+	1.27439i
$438$		0			0
$439$	−9.80671	−	5.66190i	−0.468049	−	0.270228i	0.247374	−	0.968920i	$-0.420432\pi$
$439$	−9.80671	−	5.66190i	−0.468049	−	0.270228i	−0.715422	+	0.698692i	$0.753766\pi$
$440$		0			0
$441$	3.44712	−	20.7151i	0.164149	−	0.986436i
$442$		0			0
$443$	17.4472	−	30.2194i	0.828940	−	1.43577i	−0.0699313	−	0.997552i	$-0.522278\pi$
$443$	17.4472	−	30.2194i	0.828940	−	1.43577i	0.898871	−	0.438214i	$-0.144389\pi$
$444$		0			0
$445$	−6.53223	−	11.3142i	−0.309657	−	0.536342i
$446$		0			0
$447$	−3.95461	+	34.8748i	−0.187047	+	1.64952i
$448$		0			0
$449$		−	24.4981i		−	1.15614i	−0.815988	−	0.578069i	$-0.803806\pi$
$449$		−	24.4981i		−	1.15614i	0.815988	−	0.578069i	$-0.196194\pi$
$450$		0			0
$451$	2.17457	+	1.25549i	0.102396	+	0.0591186i
$452$		0			0
$453$	−1.45238	+	12.8082i	−0.0682386	+	0.601780i
$454$		0			0
$455$	35.2128	−	10.5948i	1.65080	−	0.496693i
$456$		0			0
$457$	−16.9258	+	29.3164i	−0.791756	+	1.37136i	0.133123	+	0.991100i	$0.457499\pi$
$457$	−16.9258	+	29.3164i	−0.791756	+	1.37136i	−0.924879	+	0.380262i	$0.875834\pi$
$458$		0			0
$459$	4.06419	+	4.74315i	0.189700	+	0.221391i
$460$		0			0
$461$	0.526552	−	0.304005i	0.0245240	−	0.0141589i	−0.487688	−	0.873018i	$-0.662160\pi$
$461$	0.526552	−	0.304005i	0.0245240	−	0.0141589i	0.512212	+	0.858859i	$0.328826\pi$
$462$		0			0
$463$	13.6357	+	7.87260i	0.633707	+	0.365871i	0.782186	−	0.623045i	$-0.214105\pi$
$463$	13.6357	+	7.87260i	0.633707	+	0.365871i	−0.148479	+	0.988915i	$0.547438\pi$
$464$		0			0
$465$	−13.7736	−	31.6309i	−0.638734	−	1.46685i
$466$		0			0
$467$	−3.73247	−	6.46483i	−0.172718	−	0.299156i	0.766651	−	0.642064i	$-0.221922\pi$
$467$	−3.73247	−	6.46483i	−0.172718	−	0.299156i	−0.939369	+	0.342907i	$0.888588\pi$
$468$		0			0
$469$	3.23815	−	13.7471i	0.149524	−	0.634782i
$470$		0			0
$471$	10.3320	+	23.7273i	0.476073	+	1.09330i
$472$		0			0
$473$	−0.304777	+	0.175963i	−0.0140137	+	0.00809079i
$474$		0			0
$475$	−14.4478	+	8.34144i	−0.662910	+	0.382732i
$476$		0			0
$477$	−27.3546	−	25.4540i	−1.25248	−	1.16546i
$478$		0			0
$479$	28.0935			1.28363			0.641813	−	0.766862i	$-0.278183\pi$
$479$	28.0935			1.28363			0.641813	+	0.766862i	$0.278183\pi$
$480$		0			0
$481$	−1.99545			−0.0909848
$482$		0			0
$483$	26.2085	−	22.2076i	1.19253	−	1.01048i
$484$		0			0
$485$	11.2851	−	6.51547i	0.512431	−	0.295852i
$486$		0			0
$487$	−23.2895	−	13.4462i	−1.05535	−	0.609305i	−0.131205	−	0.991355i	$-0.541885\pi$
$487$	−23.2895	−	13.4462i	−1.05535	−	0.609305i	−0.924141	+	0.382051i	$0.875218\pi$
$488$		0			0
$489$	19.0438	−	8.29256i	0.861189	−	0.375003i
$490$		0			0
$491$	−0.958840	+	1.66076i	−0.0432719	+	0.0749491i	−0.886850	−	0.462057i	$-0.847111\pi$
$491$	−0.958840	+	1.66076i	−0.0432719	+	0.0749491i	0.843578	+	0.537006i	$0.180445\pi$
$492$		0			0
$493$	9.59002			0.431913
$494$		0			0
$495$	−2.59089	+	11.2773i	−0.116452	+	0.506878i
$496$		0			0
$497$	4.03242	−	4.28591i	0.180879	−	0.192249i
$498$		0			0
$499$		−	5.87095i		−	0.262820i	−0.991328	−	0.131410i	$-0.958050\pi$
$499$		−	5.87095i		−	0.262820i	0.991328	−	0.131410i	$-0.0419504\pi$
$500$		0			0
$501$	18.3511	−	24.8278i	0.819866	−	1.10922i
$502$		0			0
$503$	10.9558			0.488495			0.244248	−	0.969713i	$-0.421459\pi$
$503$	10.9558			0.488495			0.244248	+	0.969713i	$0.421459\pi$
$504$		0			0
$505$	−10.5323			−0.468681
$506$		0			0
$507$	−9.19133	−	21.1078i	−0.408201	−	0.937430i
$508$		0			0
$509$			38.5507i			1.70873i	0.519675	+	0.854364i	$0.326053\pi$
$509$			38.5507i			1.70873i	−0.519675	+	0.854364i	$0.673947\pi$
$510$		0			0
$511$	−11.5066	−	38.2430i	−0.509021	−	1.69177i
$512$		0			0
$513$	36.3036	−	6.78865i	1.60284	−	0.299726i
$514$		0			0
$515$	34.6190			1.52550
$516$		0			0
$517$	4.84052	−	8.38403i	0.212886	−	0.368729i
$518$		0			0
$519$	−35.1695	−	25.9950i	−1.54377	−	1.14105i
$520$		0			0
$521$	−16.6259	−	9.59898i	−0.728395	−	0.420539i	0.0894400	−	0.995992i	$-0.471492\pi$
$521$	−16.6259	−	9.59898i	−0.728395	−	0.420539i	−0.817835	+	0.575453i	$0.804826\pi$
$522$		0			0
$523$	−12.6079	+	7.27919i	−0.551306	+	0.318297i	−0.749649	−	0.661836i	$-0.769778\pi$
$523$	−12.6079	+	7.27919i	−0.551306	+	0.318297i	0.198343	+	0.980133i	$0.436444\pi$
$524$		0			0
$525$	8.20615	−	6.95344i	0.358146	−	0.303473i
$526$		0			0
$527$	8.83341			0.384789
$528$		0			0
$529$	33.1934			1.44319
$530$		0			0
$531$	4.18655	+	13.6415i	0.181681	+	0.591989i
$532$		0			0
$533$	−7.83590	+	4.52406i	−0.339410	+	0.195959i
$534$		0			0
$535$	29.1262	−	16.8160i	1.25924	−	0.727021i
$536$		0			0
$537$	−8.57233	+	11.5978i	−0.369923	+	0.500481i
$538$		0			0
$539$	0.606531	+	9.94228i	0.0261251	+	0.428244i
$540$		0			0
$541$	−2.33531	−	4.04487i	−0.100403	−	0.173903i	0.811448	−	0.584425i	$-0.198680\pi$
$541$	−2.33531	−	4.04487i	−0.100403	−	0.173903i	−0.911851	+	0.410522i	$0.865346\pi$
$542$		0			0
$543$	26.8509	+	3.04475i	1.15228	+	0.130663i
$544$		0			0
$545$	28.8285	+	16.6442i	1.23488	+	0.712957i
$546$		0			0
$547$	30.6708	−	17.7078i	1.31139	−	0.757130i	0.329062	−	0.944308i	$-0.393267\pi$
$547$	30.6708	−	17.7078i	1.31139	−	0.757130i	0.982326	+	0.187178i	$0.0599341\pi$
$548$		0			0
$549$	0.418185	−	0.449410i	0.0178477	−	0.0191804i
$550$		0			0
$551$	28.3521	−	49.1073i	1.20784	−	2.09204i
$552$		0			0
$553$	−24.3765	+	7.33440i	−1.03659	+	0.311890i
$554$		0			0
$555$	−1.67513	+	0.729430i	−0.0711052	+	0.0309626i
$556$		0			0
$557$	19.7408	+	11.3974i	0.836446	+	0.482922i	0.856054	−	0.516886i	$-0.172909\pi$
$557$	19.7408	+	11.3974i	0.836446	+	0.482922i	−0.0196089	+	0.999808i	$0.506242\pi$
$558$		0			0
$559$		−	1.26814i		−	0.0536367i
$560$		0			0
$561$	−2.38254	−	1.76102i	−0.100591	−	0.0743502i
$562$		0			0
$563$	15.3460	+	26.5800i	0.646756	+	1.12021i	0.983893	+	0.178759i	$0.0572082\pi$
$563$	15.3460	+	26.5800i	0.646756	+	1.12021i	−0.337137	+	0.941456i	$0.609458\pi$
$564$		0			0
$565$	20.7441	−	35.9298i	0.872709	−	1.51158i
$566$		0			0
$567$	−22.2498	+	8.48210i	−0.934404	+	0.356215i
$568$		0			0
$569$	33.9766	+	19.6164i	1.42437	+	0.822362i	0.996669	−	0.0815573i	$-0.0259894\pi$
$569$	33.9766	+	19.6164i	1.42437	+	0.822362i	0.427704	+	0.903919i	$0.359323\pi$
$570$		0			0
$571$	−1.61803	+	0.934171i	−0.0677125	+	0.0390938i	−0.533474	−	0.845816i	$-0.679114\pi$
$571$	−1.61803	+	0.934171i	−0.0677125	+	0.0390938i	0.465762	+	0.884910i	$0.345780\pi$
$572$		0			0
$573$	11.1770	−	15.1218i	0.466927	−	0.631721i
$574$		0			0
$575$	17.5947			0.733751
$576$		0			0
$577$	20.6560	−	35.7773i	0.859921	−	1.48943i	−0.0120819	−	0.999927i	$-0.503846\pi$
$577$	20.6560	−	35.7773i	0.859921	−	1.48943i	0.872003	−	0.489500i	$-0.162821\pi$
$578$		0			0
$579$	−3.60242	−	8.27291i	−0.149711	−	0.343811i
$580$		0			0
$581$	13.3496	+	3.14452i	0.553834	+	0.130456i
$582$		0			0
$583$	15.3488	+	8.86163i	0.635682	+	0.367011i
$584$		0			0
$585$	−30.5247	−	28.4038i	−1.26204	−	1.17435i
$586$		0			0
$587$	−7.03460	−	12.1843i	−0.290349	−	0.502899i	0.683543	−	0.729910i	$-0.260438\pi$
$587$	−7.03460	−	12.1843i	−0.290349	−	0.502899i	−0.973892	+	0.227011i	$0.927105\pi$
$588$		0			0
$589$	26.1153	−	45.2330i	1.07606	−	1.86379i
$590$		0			0
$591$	−4.04904	+	35.7075i	−0.166555	+	1.46881i
$592$		0			0
$593$	36.5014	−	21.0741i	1.49893	−	0.865410i	0.498935	−	0.866639i	$-0.333725\pi$
$593$	36.5014	−	21.0741i	1.49893	−	0.865410i	0.999999	+	0.00122942i	$0.000391338\pi$
$594$		0			0
$595$	2.48381	+	8.25514i	0.101826	+	0.338428i
$596$		0			0
$597$	2.83242	+	2.09354i	0.115923	+	0.0856830i
$598$		0			0
$599$	8.18506	+	14.1769i	0.334432	+	0.579254i	0.983376	−	0.181583i	$-0.0581221\pi$
$599$	8.18506	+	14.1769i	0.334432	+	0.579254i	−0.648943	+	0.760837i	$0.724789\pi$
$600$		0			0
$601$	3.42868	+	5.93864i	0.139859	+	0.242242i	0.927443	−	0.373965i	$-0.122002\pi$
$601$	3.42868	+	5.93864i	0.139859	+	0.242242i	−0.787584	+	0.616207i	$0.788669\pi$
$602$		0			0
$603$	−15.3096	+	4.69850i	−0.623455	+	0.191338i
$604$		0			0
$605$			24.3278i			0.989064i
$606$		0			0
$607$			42.2279i			1.71398i	0.515334	+	0.856989i	$0.327668\pi$
$607$			42.2279i			1.71398i	−0.515334	+	0.856989i	$0.672332\pi$
$608$		0			0
$609$	−12.3382	+	34.4141i	−0.499970	+	1.39453i
$610$		0			0
$611$	17.4425	+	30.2113i	0.705647	+	1.22222i
$612$		0			0
$613$	3.14051	−	5.43953i	0.126844	−	0.219700i	−0.795608	−	0.605812i	$-0.792849\pi$
$613$	3.14051	−	5.43953i	0.126844	−	0.219700i	0.922452	+	0.386111i	$0.126182\pi$
$614$		0			0
$615$	−4.92427	+	6.66220i	−0.198566	+	0.268646i
$616$		0			0
$617$	22.8749	+	13.2068i	0.920910	+	0.531688i	0.883925	−	0.467628i	$-0.154891\pi$
$617$	22.8749	+	13.2068i	0.920910	+	0.531688i	0.0369847	+	0.999316i	$0.488225\pi$
$618$		0			0
$619$		−	7.98926i		−	0.321116i	−0.987026	−	0.160558i	$-0.948671\pi$
$619$		−	7.98926i		−	0.321116i	0.987026	−	0.160558i	$-0.0513293\pi$
$620$		0			0
$621$	−36.7381	−	12.9434i	−1.47425	−	0.519402i
$622$		0			0
$623$	−2.92376	+	12.4124i	−0.117138	+	0.497292i
$624$		0			0
$625$	−31.2266			−1.24907
$626$		0			0
$627$	−16.0614	+	6.99388i	−0.641429	+	0.279309i
$628$		0			0
$629$		−	0.467805i		−	0.0186526i
$630$		0			0
$631$		−	28.8074i		−	1.14681i	−0.819274	−	0.573403i	$-0.805623\pi$
$631$		−	28.8074i		−	1.14681i	0.819274	−	0.573403i	$-0.194377\pi$
$632$		0			0
$633$	1.13433	+	0.838420i	0.0450854	+	0.0333242i
$634$		0			0
$635$	−41.0635			−1.62955
$636$		0			0
$637$	−32.1193	−	16.0204i	−1.27261	−	0.634750i
$638$		0			0
$639$	−6.50318	−	1.49406i	−0.257262	−	0.0591042i
$640$		0			0
$641$		−	30.1334i		−	1.19020i	−0.803653	−	0.595099i	$-0.797113\pi$
$641$		−	30.1334i		−	1.19020i	0.803653	−	0.595099i	$-0.202887\pi$
$642$		0			0
$643$	13.6075	+	7.85629i	0.536627	+	0.309822i	0.743711	−	0.668501i	$-0.233064\pi$
$643$	13.6075	+	7.85629i	0.536627	+	0.309822i	−0.207084	+	0.978323i	$0.566397\pi$
$644$		0			0
$645$	−0.463564	−	1.06457i	−0.0182528	−	0.0419174i
$646$		0			0
$647$	11.3703	−	19.6939i	0.447012	−	0.774248i	−0.551177	−	0.834388i	$-0.685821\pi$
$647$	11.3703	−	19.6939i	0.447012	−	0.774248i	0.998190	+	0.0601397i	$0.0191546\pi$
$648$		0			0
$649$	−3.38415	−	5.86152i	−0.132839	−	0.230085i
$650$		0			0
$651$	−11.3648	+	31.6990i	−0.445422	+	1.24238i
$652$		0			0
$653$		−	40.7387i		−	1.59423i	−0.603829	−	0.797114i	$-0.706359\pi$
$653$		−	40.7387i		−	1.59423i	0.603829	−	0.797114i	$-0.293641\pi$
$654$		0			0
$655$			25.0468i			0.978659i
$656$		0			0
$657$	−30.8481	+	33.1515i	−1.20350	+	1.29336i
$658$		0			0
$659$	−15.8968	−	27.5340i	−0.619251	−	1.07257i	−0.989623	−	0.143690i	$-0.954103\pi$
$659$	−15.8968	−	27.5340i	−0.619251	−	1.07257i	0.370372	−	0.928884i	$-0.379230\pi$
$660$		0			0
$661$	19.7459	+	34.2009i	0.768026	+	1.33026i	0.938632	+	0.344921i	$0.112094\pi$
$661$	19.7459	+	34.2009i	0.768026	+	1.33026i	−0.170606	+	0.985339i	$0.554572\pi$
$662$		0			0
$663$	9.78819	−	4.26224i	0.380142	−	0.165532i
$664$		0			0
$665$	49.6150	+	11.6869i	1.92399	+	0.453198i
$666$		0			0
$667$	−51.7915	+	29.9018i	−2.00537	+	1.15780i
$668$		0			0
$669$	−17.2502	+	7.51156i	−0.666932	+	0.290414i
$670$		0			0
$671$	−0.145588	+	0.252166i	−0.00562038	+	0.00973478i
$672$		0			0
$673$	−6.03747	−	10.4572i	−0.232727	−	0.403095i	0.725883	−	0.687819i	$-0.241432\pi$
$673$	−6.03747	−	10.4572i	−0.232727	−	0.403095i	−0.958610	+	0.284723i	$0.908098\pi$
$674$		0			0
$675$	−11.5031	−	4.05273i	−0.442754	−	0.155990i
$676$		0			0
$677$	8.17385	+	4.71917i	0.314146	+	0.181373i	0.648780	−	0.760976i	$-0.275279\pi$
$677$	8.17385	+	4.71917i	0.314146	+	0.181373i	−0.334634	+	0.942348i	$0.608613\pi$
$678$		0			0
$679$	−12.3805	−	2.91625i	−0.475121	−	0.111916i
$680$		0			0
$681$	−34.9346	−	3.96139i	−1.33870	−	0.151801i
$682$		0			0
$683$	18.4219	−	31.9076i	0.704893	−	1.22091i	−0.261837	−	0.965112i	$-0.584328\pi$
$683$	18.4219	−	31.9076i	0.704893	−	1.22091i	0.966730	−	0.255799i	$-0.0823384\pi$
$684$		0			0
$685$	11.1738			0.426928
$686$		0			0
$687$	8.64437	+	0.980226i	0.329803	+	0.0373979i
$688$		0			0
$689$	−55.3083	+	31.9322i	−2.10708	+	1.21652i
$690$		0			0
$691$	−14.2544	−	8.22979i	−0.542263	−	0.313076i	0.203732	−	0.979027i	$-0.434693\pi$
$691$	−14.2544	−	8.22979i	−0.542263	−	0.313076i	−0.745996	+	0.665951i	$0.768026\pi$
$692$		0			0
$693$	9.38477	−	6.28415i	0.356498	−	0.238715i
$694$		0			0
$695$	6.06215	−	10.4999i	0.229950	−	0.398286i
$696$		0			0
$697$	−1.06060	−	1.83702i	−0.0401731	−	0.0695819i
$698$		0			0
$699$	22.7601	−	9.91082i	0.860865	−	0.374862i
$700$		0			0
$701$			23.7098i			0.895506i	0.894157	+	0.447753i	$0.147776\pi$
$701$			23.7098i			0.895506i	−0.894157	+	0.447753i	$0.852224\pi$
$702$		0			0
$703$	−2.39548	−	1.38303i	−0.0903472	−	0.0521620i
$704$		0			0
$705$	25.6861	+	18.9855i	0.967394	+	0.715035i
$706$		0			0
$707$	7.48743	+	7.04458i	0.281594	+	0.264939i
$708$		0			0
$709$	−18.7824	+	32.5320i	−0.705387	+	1.22177i	0.261164	+	0.965294i	$0.415894\pi$
$709$	−18.7824	+	32.5320i	−0.705387	+	1.22177i	−0.966552	+	0.256472i	$0.917440\pi$
$710$		0			0
$711$	21.1311	+	19.6629i	0.792476	+	0.737415i
$712$		0			0
$713$	−47.7054	+	27.5427i	−1.78658	+	1.03148i
$714$		0			0
$715$	17.1275	+	9.88859i	0.640534	+	0.369812i
$716$		0			0
$717$	−19.9982	+	27.0562i	−0.746846	+	1.01043i
$718$		0			0
$719$	13.5085	+	23.3975i	0.503783	+	0.872578i	0.999990	+	0.00437396i	$0.00139228\pi$
$719$	13.5085	+	23.3975i	0.503783	+	0.872578i	−0.496207	+	0.868204i	$0.665274\pi$
$720$		0			0
$721$	−24.6108	−	23.1551i	−0.916553	−	0.862342i
$722$		0			0
$723$	−10.5286	−	1.19388i	−0.391561	−	0.0444009i
$724$		0			0
$725$	−16.2165	+	9.36258i	−0.602264	+	0.347718i
$726$		0			0
$727$	−6.96075	+	4.01879i	−0.258160	+	0.149049i	−0.623495	−	0.781827i	$-0.714288\pi$
$727$	−6.96075	+	4.01879i	−0.258160	+	0.149049i	0.365335	+	0.930876i	$0.380954\pi$
$728$		0			0
$729$	21.0373	+	16.9243i	0.779159	+	0.626827i
$730$		0			0
$731$	0.297298			0.0109960
$732$		0			0
$733$	−9.75948			−0.360475			−0.180237	−	0.983623i	$-0.557687\pi$
$733$	−9.75948			−0.360475			−0.180237	+	0.983623i	$0.557687\pi$
$734$		0			0
$735$	−32.8194	−	1.70758i	−1.21056	−	0.0629850i
$736$		0			0
$737$	6.57829	−	3.79798i	0.242314	−	0.139900i
$738$		0			0
$739$	−8.20806	−	4.73893i	−0.301938	−	0.174324i	0.341375	−	0.939927i	$-0.389107\pi$
$739$	−8.20806	−	4.73893i	−0.301938	−	0.174324i	−0.643313	+	0.765603i	$0.722441\pi$
$740$		0			0
$741$	7.11246	−	62.7231i	0.261283	−	2.30419i
$742$		0			0
$743$	−23.9246	+	41.4386i	−0.877709	+	1.52024i	−0.0238602	+	0.999715i	$0.507596\pi$
$743$	−23.9246	+	41.4386i	−0.877709	+	1.52024i	−0.853849	+	0.520521i	$0.825738\pi$
$744$		0			0
$745$	54.9268			2.01236
$746$		0			0
$747$	−4.56264	−	14.8669i	−0.166938	−	0.543951i
$748$		0			0
$749$	−31.9534	−	7.52668i	−1.16755	−	0.275019i
$750$		0			0
$751$		−	21.7520i		−	0.793740i	−0.917875	−	0.396870i	$-0.870096\pi$
$751$		−	21.7520i		−	0.793740i	0.917875	−	0.396870i	$-0.129904\pi$
$752$		0			0
$753$	−4.37216	−	0.495779i	−0.159330	−	0.0180672i
$754$		0			0
$755$	20.1725			0.734153
$756$		0			0
$757$	18.2247			0.662390			0.331195	−	0.943562i	$-0.392548\pi$
$757$	18.2247			0.662390			0.331195	+	0.943562i	$0.392548\pi$
$758$		0			0
$759$	18.3579	+	2.08169i	0.666350	+	0.0755605i
$760$		0			0
$761$		−	7.47676i		−	0.271032i	−0.990775	−	0.135516i	$-0.956731\pi$
$761$		−	7.47676i		−	0.271032i	0.990775	−	0.135516i	$-0.0432693\pi$
$762$		0			0
$763$	−9.36174	−	31.1145i	−0.338918	−	1.12642i
$764$		0			0
$765$	6.65887	−	7.15607i	0.240752	−	0.258728i
$766$		0			0
$767$	24.3891			0.880639
$768$		0			0
$769$	−11.1663	+	19.3406i	−0.402666	+	0.697439i	−0.994047	−	0.108954i	$-0.965250\pi$
$769$	−11.1663	+	19.3406i	−0.402666	+	0.697439i	0.591380	+	0.806393i	$0.298583\pi$
$770$		0			0
$771$	−3.61591	+	31.8879i	−0.130224	+	1.14841i
$772$		0			0
$773$	−41.7168	−	24.0852i	−1.50045	−	0.866285i	−1.00000		0.000519449i	$-0.999835\pi$
$773$	−41.7168	−	24.0852i	−1.50045	−	0.866285i	−0.500450	−	0.865766i	$-0.666832\pi$
$774$		0			0
$775$	−14.9371	+	8.62391i	−0.536555	+	0.309780i
$776$		0			0
$777$	1.67874	+	0.601864i	0.0602243	+	0.0215918i
$778$		0			0
$779$	−12.5423			−0.449376
$780$		0			0
$781$	3.16496			0.113251
$782$		0			0
$783$	40.7478	−	7.61970i	1.45621	−	0.272306i
$784$		0			0
$785$	35.0737	−	20.2498i	1.25183	−	0.722746i
$786$		0			0
$787$	−3.62124	+	2.09072i	−0.129083	+	0.0745263i	−0.563151	−	0.826354i	$-0.690411\pi$
$787$	−3.62124	+	2.09072i	−0.129083	+	0.0745263i	0.434068	+	0.900880i	$0.357078\pi$
$788$		0			0
$789$	−21.4044	−	2.42715i	−0.762018	−	0.0864087i
$790$		0			0
$791$	−38.7788	+	11.6678i	−1.37882	+	0.414859i
$792$		0			0
$793$	−0.524617	−	0.908664i	−0.0186297	−	0.0322676i
$794$		0			0
$795$	−34.7571	+	47.0240i	−1.23271	+	1.66777i
$796$		0			0
$797$	28.4260	+	16.4118i	1.00690	+	0.581335i	0.910283	−	0.413986i	$-0.135864\pi$
$797$	28.4260	+	16.4118i	1.00690	+	0.581335i	0.0966189	+	0.995321i	$0.469197\pi$
$798$		0			0
$799$	−7.08260	+	4.08914i	−0.250564	+	0.144663i
$800$		0			0
$801$	13.8232	−	4.24232i	0.488418	−	0.149895i
$802$		0			0
$803$	10.7396	−	18.6015i	0.378991	−	0.656431i
$804$		0			0
$805$	−39.1536	−	36.8378i	−1.37998	−	1.29836i
$806$		0			0
$807$	33.7976	+	24.9810i	1.18973	+	0.879373i
$808$		0			0
$809$	−3.93633	−	2.27264i	−0.138394	−	0.0799018i	0.429204	−	0.903207i	$-0.358794\pi$
$809$	−3.93633	−	2.27264i	−0.138394	−	0.0799018i	−0.567598	+	0.823306i	$0.692127\pi$
$810$		0			0
$811$		−	31.5008i		−	1.10614i	−0.833133	−	0.553072i	$-0.813455\pi$
$811$		−	31.5008i		−	1.10614i	0.833133	−	0.553072i	$-0.186545\pi$
$812$		0			0
$813$	−32.4497	+	14.1301i	−1.13806	+	0.495566i
$814$		0			0
$815$	−16.2527	−	28.1505i	−0.569306	−	0.986068i
$816$		0			0
$817$	0.878937	−	1.52236i	0.0307501	−	0.0532608i
$818$		0			0
$819$	2.70202	+	40.6089i	0.0944161	+	1.41899i
$820$		0			0
$821$	−24.4725	−	14.1292i	−0.854095	−	0.493112i	0.00793570	−	0.999969i	$-0.497474\pi$
$821$	−24.4725	−	14.1292i	−0.854095	−	0.493112i	−0.862030	+	0.506857i	$0.830807\pi$
$822$		0			0
$823$	−12.9961	+	7.50328i	−0.453014	+	0.261548i	−0.709102	−	0.705106i	$-0.750900\pi$
$823$	−12.9961	+	7.50328i	−0.453014	+	0.261548i	0.256088	+	0.966653i	$0.417566\pi$
$824$		0			0
$825$	5.74806	+	0.651799i	0.200122	+	0.0226927i
$826$		0			0
$827$	−24.7519			−0.860709			−0.430354	−	0.902660i	$-0.641611\pi$
$827$	−24.7519			−0.860709			−0.430354	+	0.902660i	$0.641611\pi$
$828$		0			0
$829$	−1.67861	+	2.90744i	−0.0583005	+	0.100979i	−0.893703	−	0.448660i	$-0.851901\pi$
$829$	−1.67861	+	2.90744i	−0.0583005	+	0.100979i	0.835402	+	0.549639i	$0.185235\pi$
$830$		0			0
$831$	22.8394	+	2.58986i	0.792288	+	0.0898413i
$832$		0			0
$833$	3.75575	−	7.52991i	0.130129	−	0.260896i
$834$		0			0
$835$	−41.8425	−	24.1578i	−1.44802	−	0.836013i
$836$		0			0
$837$	37.5329	−	7.01854i	1.29733	−	0.242596i
$838$		0			0
$839$	2.54338	+	4.40526i	0.0878073	+	0.152087i	0.906584	−	0.422025i	$-0.138681\pi$
$839$	2.54338	+	4.40526i	0.0878073	+	0.152087i	−0.818777	+	0.574112i	$0.805347\pi$
$840$		0			0
$841$	17.3229	−	30.0042i	0.597343	−	1.03463i
$842$		0			0
$843$	2.86877	−	1.24920i	0.0988058	−	0.0430247i
$844$		0			0
$845$	−31.2015	+	18.0142i	−1.07336	+	0.619707i
$846$		0			0
$847$	16.2718	−	17.2947i	0.559104	−	0.594252i
$848$		0			0
$849$	−44.7640	+	19.4924i	−1.53630	+	0.668977i
$850$		0			0
$851$	1.45862	+	2.52641i	0.0500010	+	0.0866042i
$852$		0			0
$853$	20.5066	+	35.5185i	0.702134	+	1.21613i	0.967716	+	0.252043i	$0.0811024\pi$
$853$	20.5066	+	35.5185i	0.702134	+	1.21613i	−0.265582	+	0.964088i	$0.585564\pi$
$854$		0			0
$855$	−16.9575	−	55.2542i	−0.579933	−	1.88965i
$856$		0			0
$857$			31.3869i			1.07216i	0.844168	+	0.536078i	$0.180095\pi$
$857$			31.3869i			1.07216i	−0.844168	+	0.536078i	$0.819905\pi$
$858$		0			0
$859$		−	55.3235i		−	1.88761i	−0.330496	−	0.943807i	$-0.607216\pi$
$859$		−	55.3235i		−	1.88761i	0.330496	−	0.943807i	$-0.392784\pi$
$860$		0			0
$861$	7.95673	−	1.44256i	0.271165	−	0.0491622i
$862$		0			0
$863$	7.18055	+	12.4371i	0.244429	+	0.423363i	0.961971	−	0.273152i	$-0.0880662\pi$
$863$	7.18055	+	12.4371i	0.244429	+	0.423363i	−0.717542	+	0.696515i	$0.754733\pi$
$864$		0			0
$865$	−34.2203	+	59.2714i	−1.16353	+	2.01529i
$866$		0			0
$867$	−10.7563	−	24.7017i	−0.365303	−	0.838915i
$868$		0			0
$869$	−11.8567	−	6.84549i	−0.402212	−	0.232217i
$870$		0			0
$871$			27.3715i			0.927448i
$872$		0			0
$873$	4.23143	+	13.7877i	0.143212	+	0.466643i
$874$		0			0
$875$	13.8561	+	13.0366i	0.468423	+	0.440717i
$876$		0			0
$877$	51.0736			1.72463			0.862316	−	0.506370i	$-0.169013\pi$
$877$	51.0736			1.72463			0.862316	+	0.506370i	$0.169013\pi$
$878$		0			0
$879$	−13.3172	−	9.84321i	−0.449178	−	0.332003i
$880$		0			0
$881$			38.4851i			1.29660i	0.761387	+	0.648298i	$0.224519\pi$
$881$			38.4851i			1.29660i	−0.761387	+	0.648298i	$0.775481\pi$
$882$		0			0
$883$		−	16.7854i		−	0.564872i	−0.959286	−	0.282436i	$-0.908857\pi$
$883$		−	16.7854i		−	0.564872i	0.959286	−	0.282436i	$-0.0911425\pi$
$884$		0			0
$885$	20.4740	−	8.91534i	0.688225	−	0.299686i
$886$		0			0
$887$	34.3127			1.15211			0.576054	−	0.817412i	$-0.304592\pi$
$887$	34.3127			1.15211			0.576054	+	0.817412i	$0.304592\pi$
$888$		0			0
$889$	29.1921	+	27.4655i	0.979073	+	0.921164i
$890$		0			0
$891$	−11.5225	−	5.58948i	−0.386020	−	0.187255i
$892$		0			0
$893$			48.3569i			1.61820i
$894$		0			0
$895$	19.5458	+	11.2848i	0.653345	+	0.377209i
$896$		0			0
$897$	−39.5720	+	53.5382i	−1.32127	+	1.78759i
$898$		0			0
$899$	29.3123	−	50.7703i	0.977618	−	1.69328i
$900$		0			0
$901$	−7.48606	−	12.9662i	−0.249397	−	0.431968i
$902$		0			0
$903$	−0.382494	+	1.06686i	−0.0127286	+	0.0355030i
$904$		0			0
$905$		−	42.2894i		−	1.40575i
$906$		0			0
$907$		−	30.2567i		−	1.00466i	−0.864677	−	0.502328i	$-0.832477\pi$
$907$		−	30.2567i		−	1.00466i	0.864677	−	0.502328i	$-0.167523\pi$
$908$		0			0
$909$	2.61011	−	11.3610i	0.0865718	−	0.376820i
$910$		0			0
$911$	22.9890	+	39.8181i	0.761660	+	1.31923i	0.941995	+	0.335628i	$0.108948\pi$
$911$	22.9890	+	39.8181i	0.761660	+	1.31923i	−0.180335	+	0.983605i	$0.557718\pi$
$912$		0			0
$913$	3.68816	+	6.38807i	0.122060	+	0.211414i
$914$		0			0
$915$	−0.772560	−	0.571026i	−0.0255401	−	0.0188775i
$916$		0			0
$917$	16.7527	−	17.8058i	0.553223	−	0.588001i
$918$		0			0
$919$	−6.58006	+	3.79900i	−0.217056	+	0.125317i	−0.604586	−	0.796540i	$-0.706662\pi$
$919$	−6.58006	+	3.79900i	−0.217056	+	0.125317i	0.387530	+	0.921857i	$0.373328\pi$
$920$		0			0
$921$	3.87533	−	34.1756i	0.127697	−	1.12613i
$922$		0			0
$923$	−5.70235	+	9.87677i	−0.187695	+	0.325098i
$924$		0			0
$925$	0.456711	+	0.791046i	0.0150166	+	0.0260094i
$926$		0			0
$927$	−8.57927	+	37.3428i	−0.281780	+	1.22650i
$928$		0			0
$929$	32.9192	+	19.0059i	1.08004	+	0.623564i	0.930908	−	0.365253i	$-0.119018\pi$
$929$	32.9192	+	19.0059i	1.08004	+	0.623564i	0.149136	+	0.988817i	$0.452351\pi$
$930$		0			0
$931$	−27.4546	−	41.4935i	−0.899789	−	1.35990i
$932$		0			0
$933$	−0.524000	−	1.20336i	−0.0171550	−	0.0393963i
$934$		0			0
$935$	−2.31824	+	4.01531i	−0.0758145	+	0.131315i
$936$		0			0
$937$	−53.0882			−1.73431			−0.867157	−	0.498034i	$-0.834055\pi$
$937$	−53.0882			−1.73431			−0.867157	+	0.498034i	$0.834055\pi$
$938$		0			0
$939$	8.18759	−	11.0773i	0.267192	−	0.361493i
$940$		0			0
$941$	8.25032	−	4.76333i	0.268953	−	0.155280i	−0.359459	−	0.933161i	$-0.617039\pi$
$941$	8.25032	−	4.76333i	0.268953	−	0.155280i	0.628412	+	0.777881i	$0.283705\pi$
$942$		0			0
$943$	11.4557	+	6.61394i	0.373048	+	0.215379i
$944$		0			0
$945$	17.1127	+	33.1024i	0.556676	+	1.07682i
$946$		0			0
$947$	3.80505	−	6.59053i	0.123647	−	0.214164i	−0.797556	−	0.603245i	$-0.793874\pi$
$947$	3.80505	−	6.59053i	0.123647	−	0.214164i	0.921203	+	0.389081i	$0.127207\pi$
$948$		0			0
$949$	38.6992	+	67.0291i	1.25623	+	2.17586i
$950$		0			0
$951$	−19.7568	−	14.6030i	−0.640659	−	0.473534i
$952$		0			0
$953$			8.51742i			0.275906i	0.990439	+	0.137953i	$0.0440524\pi$
$953$			8.51742i			0.275906i	−0.990439	+	0.137953i	$0.955948\pi$
$954$		0			0
$955$	−25.4848	−	14.7137i	−0.824669	−	0.476123i
$956$		0			0
$957$	−18.0276	+	7.85006i	−0.582748	+	0.253756i
$958$		0			0
$959$	−7.94347	−	7.47364i	−0.256508	−	0.241336i
$960$		0			0
$961$	11.4996	−	19.9180i	0.370956	−	0.642515i
$962$		0			0
$963$	10.9211	+	35.5852i	0.351927	+	1.14672i
$964$		0			0
$965$	−12.2290	+	7.06042i	−0.393666	+	0.227283i
$966$		0			0
$967$	−13.0326	−	7.52437i	−0.419100	−	0.241967i	0.275592	−	0.961275i	$-0.411126\pi$
$967$	−13.0326	−	7.52437i	−0.419100	−	0.241967i	−0.694692	+	0.719307i	$0.744459\pi$
$968$		0			0
$969$	14.7045	+	1.66742i	0.472378	+	0.0535651i
$970$		0			0
$971$	13.1706	+	22.8121i	0.422664	+	0.732076i	0.996199	−	0.0871050i	$-0.0277616\pi$
$971$	13.1706	+	22.8121i	0.422664	+	0.732076i	−0.573535	+	0.819181i	$0.694428\pi$
$972$		0			0
$973$	−11.3325	+	3.40974i	−0.363305	+	0.109311i
$974$		0			0
$975$	−12.3904	+	16.7634i	−0.396811	+	0.536858i
$976$		0			0
$977$	−23.5996	+	13.6252i	−0.755017	+	0.435909i	−0.827504	−	0.561460i	$-0.810240\pi$
$977$	−23.5996	+	13.6252i	−0.755017	+	0.435909i	0.0724869	+	0.997369i	$0.476906\pi$
$978$		0			0
$979$	−5.93960	+	3.42923i	−0.189830	+	0.109599i
$980$		0			0
$981$	−25.0980	+	26.9720i	−0.801317	+	0.861150i
$982$		0			0
$983$	−40.3581			−1.28722			−0.643612	−	0.765352i	$-0.722565\pi$
$983$	−40.3581			−1.28722			−0.643612	+	0.765352i	$0.722565\pi$
$984$		0			0
$985$	56.2384			1.79191
$986$		0			0
$987$	−5.56177	−	30.6771i	−0.177033	−	0.976464i
$988$		0			0
$989$	−1.60557	+	0.926979i	−0.0510543	+	0.0294762i
$990$		0			0
$991$	24.0823	+	13.9039i	0.765000	+	0.441673i	0.831088	−	0.556141i	$-0.187718\pi$
$991$	24.0823	+	13.9039i	0.765000	+	0.441673i	−0.0660879	+	0.997814i	$0.521052\pi$
$992$		0			0
$993$	11.7543	+	8.68799i	0.373010	+	0.275705i
$994$		0			0
$995$	2.75598	−	4.77350i	0.0873706	−	0.151330i
$996$		0			0
$997$	46.2357			1.46430			0.732149	−	0.681144i	$-0.238517\pi$
$997$	46.2357			1.46430			0.732149	+	0.681144i	$0.238517\pi$
$998$		0			0
$999$	−0.371692	−	1.98769i	−0.0117598	−	0.0628878i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1008.2.bh.c.95.15	✓	30
3.2	odd	2		3024.2.bh.c.2447.13		30
4.3	odd	2		1008.2.bh.d.95.1	yes	30
7.2	even	3		1008.2.cj.c.527.5	yes	30
9.2	odd	6		1008.2.cj.d.767.11	yes	30
9.7	even	3		3024.2.cj.d.1439.13		30
12.11	even	2		3024.2.bh.d.2447.13		30
21.2	odd	6		3024.2.cj.c.2879.13		30
28.23	odd	6		1008.2.cj.d.527.11	yes	30
36.7	odd	6		3024.2.cj.c.1439.13		30
36.11	even	6		1008.2.cj.c.767.5	yes	30
63.2	odd	6		1008.2.bh.d.191.1	yes	30
63.16	even	3		3024.2.bh.d.1871.3		30
84.23	even	6		3024.2.cj.d.2879.13		30
252.79	odd	6		3024.2.bh.c.1871.3		30
252.191	even	6	inner	1008.2.bh.c.191.15	yes	30

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1008.2.bh.c.95.15	✓	30	1.1	even	1	trivial
1008.2.bh.c.191.15	yes	30	252.191	even	6	inner
1008.2.bh.d.95.1	yes	30	4.3	odd	2
1008.2.bh.d.191.1	yes	30	63.2	odd	6
1008.2.cj.c.527.5	yes	30	7.2	even	3
1008.2.cj.c.767.5	yes	30	36.11	even	6
1008.2.cj.d.527.11	yes	30	28.23	odd	6
1008.2.cj.d.767.11	yes	30	9.2	odd	6
3024.2.bh.c.1871.3		30	252.79	odd	6
3024.2.bh.c.2447.13		30	3.2	odd	2
3024.2.bh.d.1871.3		30	63.16	even	3
3024.2.bh.d.2447.13		30	12.11	even	2
3024.2.cj.c.1439.13		30	36.7	odd	6
3024.2.cj.c.2879.13		30	21.2	odd	6
3024.2.cj.d.1439.13		30	9.7	even	3
3024.2.cj.d.2879.13		30	84.23	even	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 1008 = 2^{4} \cdot 3^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1008.bh (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(1.72102 + 0.195155i) q^{3} -2.71056i q^{5} +(-1.81297 + 1.92695i) q^{7} +(2.92383 + 0.671730i) q^{9} +O(q^{10})\)	\(q+(1.72102 + 0.195155i) q^{3} -2.71056i q^{5} +(-1.81297 + 1.92695i) q^{7} +(2.92383 + 0.671730i) q^{9} -1.42297 q^{11} +(2.56378 - 4.44059i) q^{13} +(0.528979 - 4.66494i) q^{15} +(1.04103 + 0.601041i) q^{17} +(6.15547 - 3.55386i) q^{19} +(-3.49622 + 2.96251i) q^{21} -7.49622 q^{23} -2.34715 q^{25} +(4.90088 + 1.72666i) q^{27} +(6.90901 - 3.98892i) q^{29} +(6.36392 - 3.67421i) q^{31} +(-2.44895 - 0.277698i) q^{33} +(5.22311 + 4.91418i) q^{35} +(-0.194581 - 0.337025i) q^{37} +(5.27892 - 7.14203i) q^{39} +(-1.52819 - 0.882303i) q^{41} +(0.214184 - 0.123659i) q^{43} +(1.82077 - 7.92522i) q^{45} +(-3.40171 + 5.89194i) q^{47} +(-0.426244 - 6.98701i) q^{49} +(1.67435 + 1.23757i) q^{51} +(-10.7865 - 6.22758i) q^{53} +3.85704i q^{55} +(11.2873 - 4.91501i) q^{57} +(2.37824 + 4.11923i) q^{59} +(0.102313 - 0.177212i) q^{61} +(-6.59522 + 4.41623i) q^{63} +(-12.0365 - 6.94928i) q^{65} +(-4.62294 + 2.66906i) q^{67} +(-12.9012 - 1.46292i) q^{69} -2.22420 q^{71} +(-7.54731 + 13.0723i) q^{73} +(-4.03949 - 0.458057i) q^{75} +(2.57980 - 2.74198i) q^{77} +(8.33242 + 4.81072i) q^{79} +(8.09756 + 3.92805i) q^{81} +(-2.59188 - 4.48927i) q^{83} +(1.62916 - 2.82179i) q^{85} +(12.6690 - 5.51669i) q^{87} +(4.17410 - 2.40992i) q^{89} +(3.90872 + 12.9910i) q^{91} +(11.6695 - 5.08145i) q^{93} +(-9.63297 - 16.6848i) q^{95} +(2.40373 + 4.16339i) q^{97} +(-4.16051 - 0.955849i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 30 q - 3 q^{3} - 2 q^{7} - q^{9}+O(q^{10}) \) 30 * q - 3 * q^3 - 2 * q^7 - q^9	\( 30 q - 3 q^{3} - 2 q^{7} - q^{9} + 6 q^{11} + 12 q^{17} + 9 q^{19} + 14 q^{21} - 24 q^{23} - 36 q^{25} + 27 q^{27} + 27 q^{29} + 6 q^{31} - 20 q^{33} - 6 q^{35} + 6 q^{37} - 15 q^{39} + 9 q^{41} - 21 q^{43} - 8 q^{45} + 12 q^{49} - 15 q^{51} - 3 q^{53} + 20 q^{57} + 3 q^{59} - 3 q^{61} + 24 q^{63} - 39 q^{67} + 10 q^{69} + 18 q^{71} + 21 q^{73} + 21 q^{75} + 36 q^{77} - 33 q^{79} - 17 q^{81} - 15 q^{83} - 3 q^{85} + 78 q^{87} + 6 q^{89} - 26 q^{91} - 3 q^{93} - 27 q^{95} - 6 q^{97} - 48 q^{99}+O(q^{100}) \) 30 * q - 3 * q^3 - 2 * q^7 - q^9 + 6 * q^11 + 12 * q^17 + 9 * q^19 + 14 * q^21 - 24 * q^23 - 36 * q^25 + 27 * q^27 + 27 * q^29 + 6 * q^31 - 20 * q^33 - 6 * q^35 + 6 * q^37 - 15 * q^39 + 9 * q^41 - 21 * q^43 - 8 * q^45 + 12 * q^49 - 15 * q^51 - 3 * q^53 + 20 * q^57 + 3 * q^59 - 3 * q^61 + 24 * q^63 - 39 * q^67 + 10 * q^69 + 18 * q^71 + 21 * q^73 + 21 * q^75 + 36 * q^77 - 33 * q^79 - 17 * q^81 - 15 * q^83 - 3 * q^85 + 78 * q^87 + 6 * q^89 - 26 * q^91 - 3 * q^93 - 27 * q^95 - 6 * q^97 - 48 * q^99

Introduction

L-functions

Modular forms

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Database

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