LMFDB - Embedded newform 1008.2.df.e.689.18

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1008,2,Mod(689,1008)]

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, 5, 1]))

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

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

chi := DirichletCharacter("1008.689");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1008 = 2^{4} \cdot 3^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1008.df (of order $6$, degree $2$, not minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$8.04892052375$
Analytic rank:	$0$
Dimension:	$48$
Relative dimension:	$24$ over $\Q(\zeta_{6})$
Twist minimal:	no (minimal twist has level 504)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			689.18
Character	$\chi$	$=$	1008.689
Dual form			1008.2.df.e.929.18

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.11231 + 1.32769i) q^{3} +3.53401 q^{5} +(-1.30083 - 2.30388i) q^{7} +(-0.525517 + 2.95361i) q^{9} +O(q^{10})$	\(q+(1.11231 + 1.32769i) q^{3} +3.53401 q^{5} +(-1.30083 - 2.30388i) q^{7} +(-0.525517 + 2.95361i) q^{9} -1.81827i q^{11} +(2.78280 + 1.60665i) q^{13} +(3.93093 + 4.69207i) q^{15} +(-2.93434 + 5.08242i) q^{17} +(2.09143 - 1.20749i) q^{19} +(1.61190 - 4.28973i) q^{21} +3.84871i q^{23} +7.48923 q^{25} +(-4.50602 + 2.58762i) q^{27} +(5.79110 - 3.34349i) q^{29} +(4.21959 - 2.43618i) q^{31} +(2.41410 - 2.02249i) q^{33} +(-4.59714 - 8.14192i) q^{35} +(-0.905385 - 1.56817i) q^{37} +(0.962213 + 5.48178i) q^{39} +(5.03152 - 8.71485i) q^{41} +(2.36232 + 4.09166i) q^{43} +(-1.85718 + 10.4381i) q^{45} +(-3.96076 + 6.86023i) q^{47} +(-3.61569 + 5.99390i) q^{49} +(-10.0118 + 1.75736i) q^{51} +(2.26517 + 1.30780i) q^{53} -6.42580i q^{55} +(3.92950 + 1.43366i) q^{57} +(-4.40604 - 7.63149i) q^{59} +(-8.98447 - 5.18718i) q^{61} +(7.48837 - 2.63142i) q^{63} +(9.83443 + 5.67791i) q^{65} +(-3.92384 - 6.79630i) q^{67} +(-5.10990 + 4.28098i) q^{69} +7.62952i q^{71} +(-11.7672 - 6.79382i) q^{73} +(8.33037 + 9.94337i) q^{75} +(-4.18907 + 2.36526i) q^{77} +(-0.921268 + 1.59568i) q^{79} +(-8.44766 - 3.10435i) q^{81} +(5.61748 + 9.72975i) q^{83} +(-10.3700 + 17.9613i) q^{85} +(10.8806 + 3.96977i) q^{87} +(-6.89792 - 11.9475i) q^{89} +(0.0815748 - 8.50119i) q^{91} +(7.92800 + 2.89251i) q^{93} +(7.39114 - 4.26728i) q^{95} +(-13.7982 + 7.96638i) q^{97} +(5.37048 + 0.955533i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q + 2 q^{9}+O(q^{10}) $ 48 * q + 2 * q^9	$ 48 q + 2 q^{9} - 8 q^{15} - 10 q^{21} + 48 q^{25} - 18 q^{27} + 18 q^{29} - 18 q^{31} + 12 q^{33} + 4 q^{39} - 6 q^{41} + 6 q^{43} - 18 q^{45} - 18 q^{47} - 12 q^{49} - 6 q^{51} - 12 q^{53} + 4 q^{57} + 18 q^{61} + 32 q^{63} - 36 q^{65} - 12 q^{77} - 6 q^{79} + 6 q^{81} + 54 q^{87} - 18 q^{89} - 6 q^{91} + 4 q^{93} + 54 q^{95} + 64 q^{99}+O(q^{100}) $ 48 * q + 2 * q^9 - 8 * q^15 - 10 * q^21 + 48 * q^25 - 18 * q^27 + 18 * q^29 - 18 * q^31 + 12 * q^33 + 4 * q^39 - 6 * q^41 + 6 * q^43 - 18 * q^45 - 18 * q^47 - 12 * q^49 - 6 * q^51 - 12 * q^53 + 4 * q^57 + 18 * q^61 + 32 * q^63 - 36 * q^65 - 12 * q^77 - 6 * q^79 + 6 * q^81 + 54 * q^87 - 18 * q^89 - 6 * q^91 + 4 * q^93 + 54 * q^95 + 64 * q^99

Display 100 coefficients 10 coefficients

Character values

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

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

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
$3$	1.11231	+	1.32769i	0.642195	+	0.766542i
$3$	1.11231	+	1.32769i	0.642195	+	0.766542i
$4$		0			0
$5$	3.53401			1.58046			0.790229	−	0.612812i	$-0.209962\pi$
$5$	3.53401			1.58046			0.790229	+	0.612812i	$0.209962\pi$
$6$		0			0
$7$	−1.30083	−	2.30388i	−0.491667	−	0.870783i
$7$	−1.30083	−	2.30388i	−0.491667	−	0.870783i
$8$		0			0
$9$	−0.525517	+	2.95361i	−0.175172	+	0.984538i
$10$		0			0
$11$		−	1.81827i		−	0.548230i	−0.961697	−	0.274115i	$-0.911615\pi$
$11$		−	1.81827i		−	0.548230i	0.961697	−	0.274115i	$-0.0883849\pi$
$12$		0			0
$13$	2.78280	+	1.60665i	0.771809	+	0.445604i	0.833519	−	0.552490i	$-0.186322\pi$
$13$	2.78280	+	1.60665i	0.771809	+	0.445604i	−0.0617107	+	0.998094i	$0.519656\pi$
$14$		0			0
$15$	3.93093	+	4.69207i	1.01496	+	1.21149i
$16$		0			0
$17$	−2.93434	+	5.08242i	−0.711682	+	1.23267i	0.252544	+	0.967585i	$0.418733\pi$
$17$	−2.93434	+	5.08242i	−0.711682	+	1.23267i	−0.964225	+	0.265083i	$0.914600\pi$
$18$		0			0
$19$	2.09143	−	1.20749i	0.479807	−	0.277017i	−0.240529	−	0.970642i	$-0.577321\pi$
$19$	2.09143	−	1.20749i	0.479807	−	0.277017i	0.720336	+	0.693625i	$0.243988\pi$
$20$		0			0
$21$	1.61190	−	4.28973i	0.351746	−	0.936096i
$22$		0			0
$23$			3.84871i			0.802512i	0.915966	+	0.401256i	$0.131426\pi$
$23$			3.84871i			0.802512i	−0.915966	+	0.401256i	$0.868574\pi$
$24$		0			0
$25$	7.48923			1.49785
$26$		0			0
$27$	−4.50602	+	2.58762i	−0.867184	+	0.497988i
$28$		0			0
$29$	5.79110	−	3.34349i	1.07538	−	0.620871i	0.145734	−	0.989324i	$-0.453446\pi$
$29$	5.79110	−	3.34349i	1.07538	−	0.620871i	0.929647	+	0.368452i	$0.120112\pi$
$30$		0			0
$31$	4.21959	−	2.43618i	0.757861	−	0.437551i	−0.0706663	−	0.997500i	$-0.522513\pi$
$31$	4.21959	−	2.43618i	0.757861	−	0.437551i	0.828527	+	0.559949i	$0.189179\pi$
$32$		0			0
$33$	2.41410	−	2.02249i	0.420241	−	0.352070i
$34$		0			0
$35$	−4.59714	−	8.14192i	−0.777059	−	1.37624i
$36$		0			0
$37$	−0.905385	−	1.56817i	−0.148844	−	0.257806i	0.781956	−	0.623333i	$-0.214222\pi$
$37$	−0.905385	−	1.56817i	−0.148844	−	0.257806i	−0.930801	+	0.365527i	$0.880889\pi$
$38$		0			0
$39$	0.962213	+	5.48178i	0.154077	+	0.877788i
$40$		0			0
$41$	5.03152	−	8.71485i	0.785792	−	1.36103i	−0.142733	−	0.989761i	$-0.545589\pi$
$41$	5.03152	−	8.71485i	0.785792	−	1.36103i	0.928525	−	0.371270i	$-0.121078\pi$
$42$		0			0
$43$	2.36232	+	4.09166i	0.360251	+	0.623973i	0.988002	−	0.154441i	$-0.0493577\pi$
$43$	2.36232	+	4.09166i	0.360251	+	0.623973i	−0.627751	+	0.778414i	$0.716024\pi$
$44$		0			0
$45$	−1.85718	+	10.4381i	−0.276852	+	1.55602i
$46$		0			0
$47$	−3.96076	+	6.86023i	−0.577736	+	1.00067i	0.418003	+	0.908446i	$0.362730\pi$
$47$	−3.96076	+	6.86023i	−0.577736	+	1.00067i	−0.995738	+	0.0922218i	$0.970603\pi$
$48$		0			0
$49$	−3.61569	+	5.99390i	−0.516527	+	0.856271i
$50$		0			0
$51$	−10.0118	+	1.75736i	−1.40193	+	0.246080i
$52$		0			0
$53$	2.26517	+	1.30780i	0.311146	+	0.179640i	0.647439	−	0.762117i	$-0.275840\pi$
$53$	2.26517	+	1.30780i	0.311146	+	0.179640i	−0.336293	+	0.941757i	$0.609173\pi$
$54$		0			0
$55$		−	6.42580i		−	0.866454i
$56$		0			0
$57$	3.92950	+	1.43366i	0.520474	+	0.189893i
$58$		0			0
$59$	−4.40604	−	7.63149i	−0.573618	−	0.993535i	−0.996190	−	0.0872059i	$-0.972206\pi$
$59$	−4.40604	−	7.63149i	−0.573618	−	0.993535i	0.422573	−	0.906329i	$-0.361127\pi$
$60$		0			0
$61$	−8.98447	−	5.18718i	−1.15034	−	0.664151i	−0.201372	−	0.979515i	$-0.564540\pi$
$61$	−8.98447	−	5.18718i	−1.15034	−	0.664151i	−0.948971	+	0.315364i	$0.897873\pi$
$62$		0			0
$63$	7.48837	−	2.63142i	0.943445	−	0.331528i
$64$		0			0
$65$	9.83443	+	5.67791i	1.21981	+	0.704258i
$66$		0			0
$67$	−3.92384	−	6.79630i	−0.479374	−	0.830300i	0.520346	−	0.853955i	$-0.325803\pi$
$67$	−3.92384	−	6.79630i	−0.479374	−	0.830300i	−0.999720	+	0.0236554i	$0.992470\pi$
$68$		0			0
$69$	−5.10990	+	4.28098i	−0.615159	+	0.515369i
$70$		0			0
$71$			7.62952i			0.905458i	0.891648	+	0.452729i	$0.149549\pi$
$71$			7.62952i			0.905458i	−0.891648	+	0.452729i	$0.850451\pi$
$72$		0			0
$73$	−11.7672	−	6.79382i	−1.37725	−	0.795156i	−0.385423	−	0.922740i	$-0.625945\pi$
$73$	−11.7672	−	6.79382i	−1.37725	−	0.795156i	−0.991828	+	0.127584i	$0.959278\pi$
$74$		0			0
$75$	8.33037	+	9.94337i	0.961909	+	1.14816i
$76$		0			0
$77$	−4.18907	+	2.36526i	−0.477389	+	0.269547i
$78$		0			0
$79$	−0.921268	+	1.59568i	−0.103651	+	0.179528i	−0.913186	−	0.407543i	$-0.866386\pi$
$79$	−0.921268	+	1.59568i	−0.103651	+	0.179528i	0.809535	+	0.587071i	$0.199719\pi$
$80$		0			0
$81$	−8.44766	−	3.10435i	−0.938629	−	0.344927i
$82$		0			0
$83$	5.61748	+	9.72975i	0.616598	+	1.06798i	0.990102	+	0.140351i	$0.0448230\pi$
$83$	5.61748	+	9.72975i	0.616598	+	1.06798i	−0.373504	+	0.927629i	$0.621844\pi$
$84$		0			0
$85$	−10.3700	+	17.9613i	−1.12478	+	1.94818i
$86$		0			0
$87$	10.8806	+	3.96977i	1.16653	+	0.425604i
$88$		0			0
$89$	−6.89792	−	11.9475i	−0.731178	−	1.26644i	−0.956380	−	0.292125i	$-0.905638\pi$
$89$	−6.89792	−	11.9475i	−0.731178	−	1.26644i	0.225202	−	0.974312i	$-0.427696\pi$
$90$		0			0
$91$	0.0815748	−	8.50119i	0.00855137	−	0.891167i
$92$		0			0
$93$	7.92800	+	2.89251i	0.822095	+	0.299939i
$94$		0			0
$95$	7.39114	−	4.26728i	0.758315	−	0.437813i
$96$		0			0
$97$	−13.7982	+	7.96638i	−1.40099	+	0.808863i	−0.994494	−	0.104789i	$-0.966583\pi$
$97$	−13.7982	+	7.96638i	−1.40099	+	0.808863i	−0.406497	+	0.913652i	$0.633250\pi$
$98$		0			0
$99$	5.37048	+	0.955533i	0.539753	+	0.0960346i
$100$		0			0
$101$	11.1250			1.10698			0.553489	−	0.832856i	$-0.313296\pi$
$101$	11.1250			1.10698			0.553489	+	0.832856i	$0.313296\pi$
$102$		0			0
$103$			0.603028i			0.0594181i	0.999559	+	0.0297091i	$0.00945808\pi$
$103$			0.603028i			0.0594181i	−0.999559	+	0.0297091i	$0.990542\pi$
$104$		0			0
$105$	5.69647	−	15.1599i	0.555919	−	1.47946i
$106$		0			0
$107$	11.3342	−	6.54381i	1.09572	−	0.632614i	0.160627	−	0.987015i	$-0.448649\pi$
$107$	11.3342	−	6.54381i	1.09572	−	0.632614i	0.935094	+	0.354401i	$0.115315\pi$
$108$		0			0
$109$	−1.37061	+	2.37396i	−0.131280	+	0.227384i	−0.924170	−	0.381981i	$-0.875242\pi$
$109$	−1.37061	+	2.37396i	−0.131280	+	0.227384i	0.792890	+	0.609365i	$0.208575\pi$
$110$		0			0
$111$	1.07497	−	2.94637i	0.102032	−	0.279657i
$112$		0			0
$113$	6.65125	+	3.84010i	0.625697	+	0.361246i	0.779084	−	0.626920i	$-0.215685\pi$
$113$	6.65125	+	3.84010i	0.625697	+	0.361246i	−0.153387	+	0.988166i	$0.549018\pi$
$114$		0			0
$115$			13.6014i			1.26834i
$116$		0			0
$117$	−6.20782	+	7.37498i	−0.573913	+	0.681817i
$118$		0			0
$119$	15.5263	+	0.148986i	1.42330	+	0.0136575i
$120$		0			0
$121$	7.69388			0.699444
$122$		0			0
$123$	17.1672	−	3.01335i	1.54792	−	0.271705i
$124$		0			0
$125$	8.79697			0.786825
$126$		0			0
$127$	−17.9246			−1.59055			−0.795277	−	0.606246i	$-0.792675\pi$
$127$	−17.9246			−1.59055			−0.795277	+	0.606246i	$0.792675\pi$
$128$		0			0
$129$	−2.80481	+	7.68765i	−0.246950	+	0.676859i
$130$		0			0
$131$	−16.9707			−1.48273			−0.741367	−	0.671100i	$-0.765822\pi$
$131$	−16.9707			−1.48273			−0.741367	+	0.671100i	$0.765822\pi$
$132$		0			0
$133$	−5.50250	−	3.24766i	−0.477127	−	0.281608i
$134$		0			0
$135$	−15.9243	+	9.14468i	−1.37055	+	0.787049i
$136$		0			0
$137$		−	5.56139i		−	0.475142i	−0.971370	−	0.237571i	$-0.923649\pi$
$137$		−	5.56139i		−	0.475142i	0.971370	−	0.237571i	$-0.0763512\pi$
$138$		0			0
$139$	12.4503	+	7.18817i	1.05602	+	0.609693i	0.924328	−	0.381598i	$-0.124626\pi$
$139$	12.4503	+	7.18817i	1.05602	+	0.609693i	0.131690	+	0.991291i	$0.457960\pi$
$140$		0			0
$141$	−13.5139	+	2.37208i	−1.13807	+	0.199765i
$142$		0			0
$143$	2.92132	−	5.05988i	0.244293	−	0.423129i
$144$		0			0
$145$	20.4658	−	11.8159i	1.69959	−	0.981261i
$146$		0			0
$147$	−11.9798	+	1.86659i	−0.988078	+	0.153954i
$148$		0			0
$149$		−	6.42112i		−	0.526039i	−0.964791	−	0.263019i	$-0.915282\pi$
$149$		−	6.42112i		−	0.526039i	0.964791	−	0.263019i	$-0.0847184\pi$
$150$		0			0
$151$	−15.9925			−1.30145			−0.650727	−	0.759312i	$-0.725536\pi$
$151$	−15.9925			−1.30145			−0.650727	+	0.759312i	$0.725536\pi$
$152$		0			0
$153$	−13.4695	−	11.3378i	−1.08894	−	0.916607i
$154$		0			0
$155$	14.9121	−	8.60949i	1.19777	−	0.691531i
$156$		0			0
$157$	−12.0612	+	6.96356i	−0.962592	+	0.555753i	−0.896970	−	0.442092i	$-0.854236\pi$
$157$	−12.0612	+	6.96356i	−0.962592	+	0.555753i	−0.0656219	+	0.997845i	$0.520903\pi$
$158$		0			0
$159$	0.783234	+	4.46213i	0.0621145	+	0.353870i
$160$		0			0
$161$	8.86696	−	5.00652i	0.698814	−	0.394569i
$162$		0			0
$163$	−7.79498	−	13.5013i	−0.610550	−	1.05750i	−0.991148	−	0.132762i	$-0.957615\pi$
$163$	−7.79498	−	13.5013i	−0.610550	−	1.05750i	0.380598	−	0.924740i	$-0.375718\pi$
$164$		0			0
$165$	8.53146	−	7.14750i	0.664173	−	0.556432i
$166$		0			0
$167$	6.58728	−	11.4095i	0.509739	−	0.882893i	−0.490198	−	0.871611i	$-0.663075\pi$
$167$	6.58728	−	11.4095i	0.509739	−	0.882893i	0.999936	−	0.0112821i	$-0.00359127\pi$
$168$		0			0
$169$	−1.33736	−	2.31638i	−0.102874	−	0.178183i
$170$		0			0
$171$	2.46737	+	6.81183i	0.188685	+	0.520914i
$172$		0			0
$173$	−5.60402	+	9.70645i	−0.426066	+	0.737968i	−0.996519	−	0.0833623i	$-0.973434\pi$
$173$	−5.60402	+	9.70645i	−0.426066	+	0.737968i	0.570453	+	0.821330i	$0.306767\pi$
$174$		0			0
$175$	−9.74221	−	17.2543i	−0.736442	−	1.30430i
$176$		0			0
$177$	5.23134	−	14.3385i	0.393212	−	1.07774i
$178$		0			0
$179$	−9.22783	−	5.32769i	−0.689721	−	0.398210i	0.113787	−	0.993505i	$-0.463702\pi$
$179$	−9.22783	−	5.32769i	−0.689721	−	0.398210i	−0.803507	+	0.595295i	$0.797035\pi$
$180$		0			0
$181$			11.8897i			0.883754i	0.897076	+	0.441877i	$0.145687\pi$
$181$			11.8897i			0.883754i	−0.897076	+	0.441877i	$0.854313\pi$
$182$		0			0
$183$	−3.10658	−	17.6984i	−0.229645	−	1.30830i
$184$		0			0
$185$	−3.19964	−	5.54194i	−0.235242	−	0.407451i
$186$		0			0
$187$	9.24123	+	5.33543i	0.675786	+	0.390165i
$188$		0			0
$189$	11.8231	+	7.01525i	0.860006	+	0.510285i
$190$		0			0
$191$	−0.193961	−	0.111983i	−0.0140345	−	0.00810283i	0.492966	−	0.870048i	$-0.335913\pi$
$191$	−0.193961	−	0.111983i	−0.0140345	−	0.00810283i	−0.507001	+	0.861946i	$0.669246\pi$
$192$		0			0
$193$	−13.0373	−	22.5812i	−0.938442	−	1.62543i	−0.768378	−	0.639996i	$-0.778936\pi$
$193$	−13.0373	−	22.5812i	−0.938442	−	1.62543i	−0.170064	−	0.985433i	$-0.554398\pi$
$194$		0			0
$195$	3.40047	+	19.3727i	0.243513	+	1.38731i
$196$		0			0
$197$			1.56289i			0.111352i	0.998449	+	0.0556758i	$0.0177313\pi$
$197$			1.56289i			0.111352i	−0.998449	+	0.0556758i	$0.982269\pi$
$198$		0			0
$199$	−13.4725	−	7.77832i	−0.955037	−	0.551391i	−0.0603949	−	0.998175i	$-0.519236\pi$
$199$	−13.4725	−	7.77832i	−0.955037	−	0.551391i	−0.894642	+	0.446784i	$0.852569\pi$
$200$		0			0
$201$	4.65883	−	12.7693i	0.328608	−	0.900674i
$202$		0			0
$203$	−15.2362	−	8.99266i	−1.06937	−	0.631161i
$204$		0			0
$205$	17.7815	−	30.7984i	1.24191	−	2.15105i
$206$		0			0
$207$	−11.3676	−	2.02256i	−0.790104	−	0.140578i
$208$		0			0
$209$	−2.19554	−	3.80279i	−0.151869	−	0.263045i
$210$		0			0
$211$	−6.98216	+	12.0935i	−0.480672	+	0.832548i	−0.999754	−	0.0221763i	$-0.992941\pi$
$211$	−6.98216	+	12.0935i	−0.480672	+	0.832548i	0.519082	+	0.854724i	$0.326274\pi$
$212$		0			0
$213$	−10.1296	+	8.48642i	−0.694071	+	0.581480i
$214$		0			0
$215$	8.34848	+	14.4600i	0.569361	+	0.986163i
$216$		0			0
$217$	−11.1016	−	6.55236i	−0.753628	−	0.444803i
$218$		0			0
$219$	−4.06878	−	23.1801i	−0.274943	−	1.56637i
$220$		0			0
$221$	−16.3313	+	9.42890i	−1.09856	+	0.634256i
$222$		0			0
$223$	21.4242	−	12.3693i	1.43467	−	0.828307i	0.437198	−	0.899366i	$-0.355971\pi$
$223$	21.4242	−	12.3693i	1.43467	−	0.828307i	0.997472	+	0.0710586i	$0.0226377\pi$
$224$		0			0
$225$	−3.93571	+	22.1203i	−0.262381	+	1.47469i
$226$		0			0
$227$	6.24153			0.414265			0.207132	−	0.978313i	$-0.433587\pi$
$227$	6.24153			0.414265			0.207132	+	0.978313i	$0.433587\pi$
$228$		0			0
$229$			15.8574i			1.04789i	0.851753	+	0.523943i	$0.175540\pi$
$229$			15.8574i			1.04789i	−0.851753	+	0.523943i	$0.824460\pi$
$230$		0			0
$231$	−7.79990	−	2.93087i	−0.513196	−	0.192837i
$232$		0			0
$233$	2.94574	−	1.70072i	0.192982	−	0.111418i	−0.400396	−	0.916342i	$-0.631127\pi$
$233$	2.94574	−	1.70072i	0.192982	−	0.111418i	0.593378	+	0.804924i	$0.297794\pi$
$234$		0			0
$235$	−13.9974	+	24.2441i	−0.913087	+	1.58151i
$236$		0			0
$237$	−3.14331	+	0.551742i	−0.204180	+	0.0358395i
$238$		0			0
$239$	16.3482	+	9.43864i	1.05748	+	0.610535i	0.924733	−	0.380615i	$-0.124288\pi$
$239$	16.3482	+	9.43864i	1.05748	+	0.610535i	0.132744	+	0.991150i	$0.457621\pi$
$240$		0			0
$241$		−	11.1845i		−	0.720460i	−0.932864	−	0.360230i	$-0.882698\pi$
$241$		−	11.1845i		−	0.720460i	0.932864	−	0.360230i	$-0.117302\pi$
$242$		0			0
$243$	−5.27485	−	14.6689i	−0.338382	−	0.941009i
$244$		0			0
$245$	−12.7779	+	21.1825i	−0.816348	+	1.35330i
$246$		0			0
$247$	7.76003			0.493759
$248$		0			0
$249$	−6.66969	+	18.2808i	−0.422675	+	1.15850i
$250$		0			0
$251$	−15.4537			−0.975431			−0.487716	−	0.873003i	$-0.662170\pi$
$251$	−15.4537			−0.975431			−0.487716	+	0.873003i	$0.662170\pi$
$252$		0			0
$253$	6.99801			0.439961
$254$		0			0
$255$	−35.3818	+	6.21053i	−2.21569	+	0.388918i
$256$		0			0
$257$	−10.6448			−0.664002			−0.332001	−	0.943279i	$-0.607724\pi$
$257$	−10.6448			−0.664002			−0.332001	+	0.943279i	$0.607724\pi$
$258$		0			0
$259$	−2.43512	+	4.12582i	−0.151311	+	0.256366i
$260$		0			0
$261$	6.83207	+	18.8617i	0.422895	+	1.16751i
$262$		0			0
$263$			11.0875i			0.683685i	0.939757	+	0.341842i	$0.111051\pi$
$263$			11.0875i			0.683685i	−0.939757	+	0.341842i	$0.888949\pi$
$264$		0			0
$265$	8.00515	+	4.62178i	0.491753	+	0.283913i
$266$		0			0
$267$	8.18998	−	22.4477i	0.501218	−	1.37378i
$268$		0			0
$269$	−3.14147	+	5.44119i	−0.191539	+	0.331755i	−0.945760	−	0.324865i	$-0.894681\pi$
$269$	−3.14147	+	5.44119i	−0.191539	+	0.331755i	0.754221	+	0.656620i	$0.228014\pi$
$270$		0			0
$271$	−0.954533	+	0.551100i	−0.0579838	+	0.0334769i	−0.528712	−	0.848802i	$-0.677325\pi$
$271$	−0.954533	+	0.551100i	−0.0579838	+	0.0334769i	0.470728	+	0.882278i	$0.343991\pi$
$272$		0			0
$273$	11.3777	−	9.34768i	0.688608	−	0.565748i
$274$		0			0
$275$		−	13.6175i		−	0.821164i
$276$		0			0
$277$	−15.3616			−0.922990			−0.461495	−	0.887143i	$-0.652687\pi$
$277$	−15.3616			−0.922990			−0.461495	+	0.887143i	$0.652687\pi$
$278$		0			0
$279$	4.97807	+	13.7433i	0.298030	+	0.822790i
$280$		0			0
$281$	18.9133	−	10.9196i	1.12827	−	0.651407i	0.184771	−	0.982782i	$-0.440846\pi$
$281$	18.9133	−	10.9196i	1.12827	−	0.651407i	0.943499	+	0.331374i	$0.107512\pi$
$282$		0			0
$283$	9.59426	−	5.53925i	0.570320	−	0.329274i	−0.186957	−	0.982368i	$-0.559863\pi$
$283$	9.59426	−	5.53925i	0.570320	−	0.329274i	0.757277	+	0.653094i	$0.226529\pi$
$284$		0			0
$285$	13.8869	+	5.06658i	0.822588	+	0.300119i
$286$		0			0
$287$	−26.6231	−	0.255467i	−1.57151	−	0.0150797i
$288$		0			0
$289$	−8.72069	−	15.1047i	−0.512982	−	0.888511i
$290$		0			0
$291$	−25.9248	−	9.45857i	−1.51974	−	0.554471i
$292$		0			0
$293$	12.6330	−	21.8810i	0.738027	−	1.27830i	−0.215355	−	0.976536i	$-0.569091\pi$
$293$	12.6330	−	21.8810i	0.738027	−	1.27830i	0.953382	−	0.301765i	$-0.0975757\pi$
$294$		0			0
$295$	−15.5710	−	26.9698i	−0.906578	−	1.57024i
$296$		0			0
$297$	4.70500	+	8.19317i	0.273012	+	0.475416i
$298$		0			0
$299$	−6.18353	+	10.7102i	−0.357603	+	0.619386i
$300$		0			0
$301$	6.35371	−	10.7651i	0.366222	−	0.620488i
$302$		0			0
$303$	12.3745	+	14.7705i	0.710896	+	0.848545i
$304$		0			0
$305$	−31.7512	−	18.3316i	−1.81807	−	1.04966i
$306$		0			0
$307$			12.2163i			0.697219i	0.937268	+	0.348610i	$0.113346\pi$
$307$			12.2163i			0.697219i	−0.937268	+	0.348610i	$0.886654\pi$
$308$		0			0
$309$	−0.800634	+	0.670756i	−0.0455465	+	0.0381580i
$310$		0			0
$311$	4.74484	+	8.21830i	0.269055	+	0.466017i	0.968618	−	0.248554i	$-0.0799553\pi$
$311$	4.74484	+	8.21830i	0.269055	+	0.466017i	−0.699563	+	0.714571i	$0.746622\pi$
$312$		0			0
$313$	11.7358	+	6.77564i	0.663344	+	0.382982i	0.793550	−	0.608505i	$-0.208231\pi$
$313$	11.7358	+	6.77564i	0.663344	+	0.382982i	−0.130206	+	0.991487i	$0.541564\pi$
$314$		0			0
$315$	26.4640	−	9.29947i	1.49108	−	0.523966i
$316$		0			0
$317$	13.7559	+	7.94197i	0.772608	+	0.446065i	0.833804	−	0.552060i	$-0.186158\pi$
$317$	13.7559	+	7.94197i	0.772608	+	0.446065i	−0.0611961	+	0.998126i	$0.519492\pi$
$318$		0			0
$319$	−6.07939	−	10.5298i	−0.340380	−	0.589556i
$320$		0			0
$321$	21.2954	+	7.76954i	1.18859	+	0.433654i
$322$		0			0
$323$			14.1727i			0.788591i
$324$		0			0
$325$	20.8410	+	12.0326i	1.15605	+	0.667446i
$326$		0			0
$327$	−4.67642	+	0.820849i	−0.258607	+	0.0453930i
$328$		0			0
$329$	20.9574	+	0.201101i	1.15542	+	0.0110870i
$330$		0			0
$331$	5.48697	−	9.50372i	0.301591	−	0.522371i	−0.674905	−	0.737904i	$-0.735816\pi$
$331$	5.48697	−	9.50372i	0.301591	−	0.522371i	0.976497	+	0.215533i	$0.0691489\pi$
$332$		0			0
$333$	5.10757	−	1.85006i	0.279893	−	0.101382i
$334$		0			0
$335$	−13.8669	−	24.0182i	−0.757630	−	1.31225i
$336$		0			0
$337$	2.80751	−	4.86275i	0.152935	−	0.264891i	−0.779370	−	0.626564i	$-0.784461\pi$
$337$	2.80751	−	4.86275i	0.152935	−	0.264891i	0.932305	+	0.361673i	$0.117794\pi$
$338$		0			0
$339$	2.29982	+	13.1022i	0.124909	+	0.711613i
$340$		0			0
$341$	−4.42964	−	7.67237i	−0.239879	−	0.415482i
$342$		0			0
$343$	18.5126	+	0.533054i	0.999586	+	0.0287822i
$344$		0			0
$345$	−18.0584	+	15.1290i	−0.972233	+	0.814519i
$346$		0			0
$347$	4.18003	−	2.41334i	0.224396	−	0.129555i	−0.383588	−	0.923504i	$-0.625312\pi$
$347$	4.18003	−	2.41334i	0.224396	−	0.129555i	0.607984	+	0.793949i	$0.291978\pi$
$348$		0			0
$349$	22.7167	−	13.1155i	1.21600	−	0.702056i	0.251937	−	0.967744i	$-0.418932\pi$
$349$	22.7167	−	13.1155i	1.21600	−	0.702056i	0.964059	+	0.265688i	$0.0855991\pi$
$350$		0			0
$351$	−16.6967	−	0.0387633i	−0.891206	−	0.00206903i
$352$		0			0
$353$	−34.9914			−1.86240			−0.931201	−	0.364505i	$-0.881238\pi$
$353$	−34.9914			−1.86240			−0.931201	+	0.364505i	$0.881238\pi$
$354$		0			0
$355$			26.9628i			1.43104i
$356$		0			0
$357$	17.0724	+	20.7799i	0.903565	+	1.09979i
$358$		0			0
$359$	21.6396	−	12.4936i	1.14209	−	0.659388i	0.195146	−	0.980774i	$-0.437482\pi$
$359$	21.6396	−	12.4936i	1.14209	−	0.659388i	0.946948	+	0.321386i	$0.104149\pi$
$360$		0			0
$361$	−6.58394	+	11.4037i	−0.346523	+	0.600196i
$362$		0			0
$363$	8.55801	+	10.2151i	0.449179	+	0.536153i
$364$		0			0
$365$	−41.5855	−	24.0094i	−2.17669	−	1.25671i
$366$		0			0
$367$			24.6067i			1.28446i	0.766512	+	0.642230i	$0.221991\pi$
$367$			24.6067i			1.28446i	−0.766512	+	0.642230i	$0.778009\pi$
$368$		0			0
$369$	23.0962	+	19.4410i	1.20234	+	1.01206i
$370$		0			0
$371$	0.0664013	−	6.91990i	0.00344738	−	0.359264i
$372$		0			0
$373$	−10.4374			−0.540428			−0.270214	−	0.962800i	$-0.587094\pi$
$373$	−10.4374			−0.540428			−0.270214	+	0.962800i	$0.587094\pi$
$374$		0			0
$375$	9.78499	+	11.6796i	0.505295	+	0.603134i
$376$		0			0
$377$	21.4873			1.10665
$378$		0			0
$379$	−31.8728			−1.63719			−0.818597	−	0.574368i	$-0.805248\pi$
$379$	−31.8728			−1.63719			−0.818597	+	0.574368i	$0.805248\pi$
$380$		0			0
$381$	−19.9378	−	23.7983i	−1.02145	−	1.21923i
$382$		0			0
$383$	24.7719			1.26579			0.632893	−	0.774239i	$-0.281867\pi$
$383$	24.7719			1.26579			0.632893	+	0.774239i	$0.281867\pi$
$384$		0			0
$385$	−14.8042	+	8.35886i	−0.754494	+	0.426007i
$386$		0			0
$387$	−13.3266	+	4.82715i	−0.677431	+	0.245378i
$388$		0			0
$389$		−	23.0227i		−	1.16729i	−0.812007	−	0.583647i	$-0.801625\pi$
$389$		−	23.0227i		−	1.16729i	0.812007	−	0.583647i	$-0.198375\pi$
$390$		0			0
$391$	−19.5608	−	11.2934i	−0.989232	−	0.571133i
$392$		0			0
$393$	−18.8767	−	22.5318i	−0.952204	−	1.13658i
$394$		0			0
$395$	−3.25577	+	5.63916i	−0.163816	+	0.283737i
$396$		0			0
$397$	23.9247	−	13.8129i	1.20075	−	0.693251i	0.240025	−	0.970767i	$-0.422844\pi$
$397$	23.9247	−	13.8129i	1.20075	−	0.693251i	0.960721	+	0.277515i	$0.0895109\pi$
$398$		0			0
$399$	−1.80862	−	10.9180i	−0.0905442	−	0.546585i
$400$		0			0
$401$			5.32384i			0.265860i	0.991125	+	0.132930i	$0.0424385\pi$
$401$			5.32384i			0.265860i	−0.991125	+	0.132930i	$0.957561\pi$
$402$		0			0
$403$	15.6563			0.779898
$404$		0			0
$405$	−29.8541	−	10.9708i	−1.48346	−	0.545143i
$406$		0			0
$407$	−2.85137	+	1.64624i	−0.141337	+	0.0816009i
$408$		0			0
$409$	6.11912	−	3.53288i	0.302571	−	0.174690i	−0.341026	−	0.940054i	$-0.610774\pi$
$409$	6.11912	−	3.53288i	0.302571	−	0.174690i	0.643597	+	0.765364i	$0.277441\pi$
$410$		0			0
$411$	7.38380	−	6.18602i	0.364216	−	0.305134i
$412$		0			0
$413$	−11.8505	+	20.0782i	−0.583124	+	0.987985i
$414$		0			0
$415$	19.8522	+	34.3851i	0.974507	+	1.68790i
$416$		0			0
$417$	4.30496	+	24.5256i	0.210815	+	1.20102i
$418$		0			0
$419$	1.94504	−	3.36891i	0.0950215	−	0.164582i	−0.814596	−	0.580029i	$-0.803041\pi$
$419$	1.94504	−	3.36891i	0.0950215	−	0.164582i	0.909618	+	0.415447i	$0.136375\pi$
$420$		0			0
$421$	−2.18533	−	3.78510i	−0.106506	−	0.184475i	0.807846	−	0.589393i	$-0.200633\pi$
$421$	−2.18533	−	3.78510i	−0.106506	−	0.184475i	−0.914353	+	0.404919i	$0.867300\pi$
$422$		0			0
$423$	−18.1810	−	15.3037i	−0.883992	−	0.744092i
$424$		0			0
$425$	−21.9759	+	38.0634i	−1.06599	+	1.84635i
$426$		0			0
$427$	−0.263371	+	27.4467i	−0.0127454	+	1.32824i
$428$		0			0
$429$	9.96738	−	1.74957i	0.481230	−	0.0844698i
$430$		0			0
$431$	−10.7505	−	6.20681i	−0.517834	−	0.298971i	0.218214	−	0.975901i	$-0.429977\pi$
$431$	−10.7505	−	6.20681i	−0.517834	−	0.298971i	−0.736048	+	0.676929i	$0.763310\pi$
$432$		0			0
$433$			25.2979i			1.21574i	0.794036	+	0.607870i	$0.207976\pi$
$433$			25.2979i			1.21574i	−0.794036	+	0.607870i	$0.792024\pi$
$434$		0			0
$435$	38.4523	+	14.0292i	1.84365	+	0.672649i
$436$		0			0
$437$	4.64728	+	8.04932i	0.222309	+	0.385051i
$438$		0			0
$439$	23.2408	+	13.4181i	1.10922	+	0.640410i	0.938628	−	0.344931i	$-0.112098\pi$
$439$	23.2408	+	13.4181i	1.10922	+	0.640410i	0.170595	+	0.985341i	$0.445431\pi$
$440$		0			0
$441$	−15.8036	−	13.8292i	−0.752550	−	0.658535i
$442$		0			0
$443$	11.3051	+	6.52699i	0.537120	+	0.310107i	0.743911	−	0.668279i	$-0.232969\pi$
$443$	11.3051	+	6.52699i	0.537120	+	0.310107i	−0.206791	+	0.978385i	$0.566302\pi$
$444$		0			0
$445$	−24.3773	−	42.2227i	−1.15560	−	2.00155i
$446$		0			0
$447$	8.52526	−	7.14230i	0.403231	−	0.337819i
$448$		0			0
$449$		−	0.468645i		−	0.0221167i	−0.999939	−	0.0110584i	$-0.996480\pi$
$449$		−	0.468645i		−	0.0221167i	0.999939	−	0.0110584i	$-0.00352006\pi$
$450$		0			0
$451$	−15.8460	−	9.14868i	−0.746158	−	0.430795i
$452$		0			0
$453$	−17.7887	−	21.2331i	−0.835787	−	0.997618i
$454$		0			0
$455$	0.288286	−	30.0433i	0.0135151	−	1.40845i
$456$		0			0
$457$	2.06486	−	3.57644i	0.0965901	−	0.167299i	−0.813681	−	0.581312i	$-0.802540\pi$
$457$	2.06486	−	3.57644i	0.0965901	−	0.167299i	0.910271	+	0.414013i	$0.135873\pi$
$458$		0			0
$459$	0.0707962	−	30.4945i	0.00330448	−	1.42336i
$460$		0			0
$461$	12.9115	+	22.3633i	0.601347	+	1.04156i	0.992617	+	0.121288i	$0.0387023\pi$
$461$	12.9115	+	22.3633i	0.601347	+	1.04156i	−0.391271	+	0.920276i	$0.627964\pi$
$462$		0			0
$463$	2.56402	−	4.44101i	0.119160	−	0.206391i	−0.800275	−	0.599633i	$-0.795313\pi$
$463$	2.56402	−	4.44101i	0.119160	−	0.206391i	0.919435	+	0.393242i	$0.128647\pi$
$464$		0			0
$465$	28.0176	+	10.2221i	1.29929	+	0.474041i
$466$		0			0
$467$	1.26091	+	2.18396i	0.0583480	+	0.101062i	0.893724	−	0.448617i	$-0.148083\pi$
$467$	1.26091	+	2.18396i	0.0583480	+	0.101062i	−0.835376	+	0.549679i	$0.814750\pi$
$468$		0			0
$469$	−10.5536	+	17.8809i	−0.487319	+	0.825662i
$470$		0			0
$471$	−22.6613	−	8.26791i	−1.04418	−	0.380965i
$472$		0			0
$473$	7.43976	−	4.29535i	0.342081	−	0.197500i
$474$		0			0
$475$	15.6632	−	9.04316i	0.718677	−	0.414929i
$476$		0			0
$477$	−5.05312	+	6.00318i	−0.231366	+	0.274867i
$478$		0			0
$479$	11.4924			0.525103			0.262552	−	0.964918i	$-0.415436\pi$
$479$	11.4924			0.525103			0.262552	+	0.964918i	$0.415436\pi$
$480$		0			0
$481$		−	5.81854i		−	0.265303i
$482$		0			0
$483$	16.5099	+	6.20374i	0.751228	+	0.282280i
$484$		0			0
$485$	−48.7629	+	28.1533i	−2.21421	+	1.27837i
$486$		0			0
$487$	10.8463	−	18.7864i	0.491493	−	0.851292i	−0.508459	−	0.861086i	$-0.669785\pi$
$487$	10.8463	−	18.7864i	0.491493	−	0.851292i	0.999952	+	0.00979483i	$0.00311784\pi$
$488$		0			0
$489$	9.25506	−	25.3670i	0.418528	−	1.14713i
$490$		0			0
$491$	19.3592	+	11.1771i	0.873669	+	0.504413i	0.868566	−	0.495574i	$-0.165042\pi$
$491$	19.3592	+	11.1771i	0.873669	+	0.504413i	0.00510349	+	0.999987i	$0.498376\pi$
$492$		0			0
$493$			39.2438i			1.76745i
$494$		0			0
$495$	18.9793	+	3.37686i	0.853057	+	0.151779i
$496$		0			0
$497$	17.5775	−	9.92470i	0.788457	−	0.445184i
$498$		0			0
$499$	−17.5246			−0.784510			−0.392255	−	0.919857i	$-0.628305\pi$
$499$	−17.5246			−0.784510			−0.392255	+	0.919857i	$0.628305\pi$
$500$		0			0
$501$	22.4754	−	3.94508i	1.00413	−	0.176253i
$502$		0			0
$503$	7.60926			0.339280			0.169640	−	0.985506i	$-0.445739\pi$
$503$	7.60926			0.339280			0.169640	+	0.985506i	$0.445739\pi$
$504$		0			0
$505$	39.3159			1.74953
$506$		0			0
$507$	1.58787	−	4.35215i	0.0705197	−	0.193286i
$508$		0			0
$509$	−6.78746			−0.300849			−0.150424	−	0.988622i	$-0.548064\pi$
$509$	−6.78746			−0.300849			−0.150424	+	0.988622i	$0.548064\pi$
$510$		0			0
$511$	−0.344945	+	35.9479i	−0.0152595	+	1.59024i
$512$		0			0
$513$	−6.29951	+	10.8528i	−0.278130	+	0.479163i
$514$		0			0
$515$			2.13111i			0.0939078i
$516$		0			0
$517$	12.4738	+	7.20174i	0.548596	+	0.316732i
$518$		0			0
$519$	−19.1206	+	3.35622i	−0.839300	+	0.147322i
$520$		0			0
$521$	−13.8435	+	23.9777i	−0.606497	+	1.05048i	0.385316	+	0.922785i	$0.374092\pi$
$521$	−13.8435	+	23.9777i	−0.606497	+	1.05048i	−0.991813	+	0.127698i	$0.959241\pi$
$522$		0			0
$523$	0.834923	−	0.482043i	0.0365086	−	0.0210783i	−0.481635	−	0.876372i	$-0.659957\pi$
$523$	0.834923	−	0.482043i	0.0365086	−	0.0210783i	0.518143	+	0.855294i	$0.326623\pi$
$524$		0			0
$525$	12.0719	−	32.1268i	0.526861	−	1.40213i
$526$		0			0
$527$			28.5943i			1.24559i
$528$		0			0
$529$	8.18740			0.355974
$530$		0			0
$531$	24.8559	−	9.00327i	1.07865	−	0.390709i
$532$		0			0
$533$	28.0034	−	16.1678i	1.21296	−	0.700304i
$534$		0			0
$535$	40.0552	−	23.1259i	1.73174	−	0.999820i
$536$		0			0
$537$	−3.19073	−	18.1778i	−0.137690	−	0.784428i
$538$		0			0
$539$	10.8985	+	6.57430i	0.469433	+	0.283175i
$540$		0			0
$541$	2.36867	+	4.10266i	0.101837	+	0.176387i	0.912442	−	0.409207i	$-0.134195\pi$
$541$	2.36867	+	4.10266i	0.101837	+	0.176387i	−0.810604	+	0.585594i	$0.800861\pi$
$542$		0			0
$543$	−15.7858	+	13.2251i	−0.677435	+	0.567542i
$544$		0			0
$545$	−4.84374	+	8.38960i	−0.207483	+	0.359371i
$546$		0			0
$547$	0.840875	+	1.45644i	0.0359532	+	0.0622728i	0.883442	−	0.468540i	$-0.155220\pi$
$547$	0.840875	+	1.45644i	0.0359532	+	0.0622728i	−0.847489	+	0.530813i	$0.821887\pi$
$548$		0			0
$549$	20.0424	−	23.8107i	0.855390	−	1.01622i
$550$		0			0
$551$	8.07446	−	13.9854i	0.343984	−	0.595797i
$552$		0			0
$553$	4.87467	+	0.0467758i	0.207292	+	0.00198911i
$554$		0			0
$555$	3.79897	−	10.4125i	0.161257	−	0.441986i
$556$		0			0
$557$	8.14983	+	4.70530i	0.345319	+	0.199370i	0.662622	−	0.748954i	$-0.269444\pi$
$557$	8.14983	+	4.70530i	0.345319	+	0.199370i	−0.317303	+	0.948324i	$0.602777\pi$
$558$		0			0
$559$			15.1817i			0.642117i
$560$		0			0
$561$	3.19536	+	18.2042i	0.134908	+	0.768580i
$562$		0			0
$563$	15.5319	+	26.9020i	0.654591	+	1.13378i	0.981996	+	0.188901i	$0.0604924\pi$
$563$	15.5319	+	26.9020i	0.654591	+	1.13378i	−0.327405	+	0.944884i	$0.606174\pi$
$564$		0			0
$565$	23.5056	+	13.5710i	0.988888	+	0.570935i
$566$		0			0
$567$	3.83694	+	23.5006i	0.161136	+	0.986932i
$568$		0			0
$569$	17.4099	+	10.0516i	0.729859	+	0.421384i	0.818371	−	0.574691i	$-0.194878\pi$
$569$	17.4099	+	10.0516i	0.729859	+	0.421384i	−0.0885114	+	0.996075i	$0.528211\pi$
$570$		0			0
$571$	−3.93707	−	6.81920i	−0.164761	−	0.285375i	0.771809	−	0.635854i	$-0.219352\pi$
$571$	−3.93707	−	6.81920i	−0.164761	−	0.285375i	−0.936570	+	0.350479i	$0.886019\pi$
$572$		0			0
$573$	−0.0670662	−	0.382080i	−0.00280173	−	0.0159616i
$574$		0			0
$575$			28.8239i			1.20204i
$576$		0			0
$577$	−2.77842	−	1.60412i	−0.115667	−	0.0667805i	0.441050	−	0.897482i	$-0.354606\pi$
$577$	−2.77842	−	1.60412i	−0.115667	−	0.0667805i	−0.556717	+	0.830702i	$0.687939\pi$
$578$		0			0
$579$	15.4793	−	42.4268i	0.643297	−	1.76320i
$580$		0			0
$581$	15.1088	−	25.5987i	0.626817	−	1.06201i
$582$		0			0
$583$	2.37794	−	4.11871i	0.0984840	−	0.170579i
$584$		0			0
$585$	−21.9385	+	26.0633i	−0.907046	+	1.07758i
$586$		0			0
$587$	2.37708	+	4.11722i	0.0981125	+	0.169936i	0.910903	−	0.412620i	$-0.135386\pi$
$587$	2.37708	+	4.11722i	0.0981125	+	0.169936i	−0.812791	+	0.582556i	$0.802053\pi$
$588$		0			0
$589$	5.88332	−	10.1902i	0.242418	−	0.419880i
$590$		0			0
$591$	−2.07504	+	1.73843i	−0.0853556	+	0.0715094i
$592$		0			0
$593$	13.0354	+	22.5780i	0.535300	+	0.927166i	0.999149	+	0.0412519i	$0.0131346\pi$
$593$	13.0354	+	22.5780i	0.535300	+	0.927166i	−0.463849	+	0.885914i	$0.653532\pi$
$594$		0			0
$595$	54.8703	+	0.526519i	2.24946	+	0.0215852i
$596$		0			0
$597$	−4.65840	−	26.5392i	−0.190656	−	1.08618i
$598$		0			0
$599$	23.8178	−	13.7512i	0.973168	−	0.561859i	0.0729672	−	0.997334i	$-0.476753\pi$
$599$	23.8178	−	13.7512i	0.973168	−	0.561859i	0.900200	+	0.435476i	$0.143420\pi$
$600$		0			0
$601$	−26.8647	+	15.5104i	−1.09584	+	0.632681i	−0.935124	−	0.354320i	$-0.884712\pi$
$601$	−26.8647	+	15.5104i	−1.09584	+	0.632681i	−0.160712	+	0.987001i	$0.551379\pi$
$602$		0			0
$603$	22.1357	−	8.01795i	0.901435	−	0.326516i
$604$		0			0
$605$	27.1903			1.10544
$606$		0			0
$607$		−	39.2304i		−	1.59231i	−0.605092	−	0.796156i	$-0.706864\pi$
$607$		−	39.2304i		−	1.59231i	0.605092	−	0.796156i	$-0.293136\pi$
$608$		0			0
$609$	−5.00801	−	30.2316i	−0.202935	−	1.22505i
$610$		0			0
$611$	−22.0440	+	12.7271i	−0.891803	+	0.514883i
$612$		0			0
$613$	−11.5364	+	19.9817i	−0.465951	+	0.807051i	−0.999244	−	0.0388795i	$-0.987621\pi$
$613$	−11.5364	+	19.9817i	−0.465951	+	0.807051i	0.533293	+	0.845931i	$0.320954\pi$
$614$		0			0
$615$	60.6692	−	10.6492i	2.44642	−	0.429418i
$616$		0			0
$617$	5.15715	+	2.97748i	0.207619	+	0.119869i	0.600204	−	0.799847i	$-0.295086\pi$
$617$	5.15715	+	2.97748i	0.207619	+	0.119869i	−0.392585	+	0.919716i	$0.628419\pi$
$618$		0			0
$619$			32.3650i			1.30086i	0.759567	+	0.650429i	$0.225411\pi$
$619$			32.3650i			1.30086i	−0.759567	+	0.650429i	$0.774589\pi$
$620$		0			0
$621$	−9.95902	−	17.3424i	−0.399642	−	0.695926i
$622$		0			0
$623$	−18.5526	+	31.4337i	−0.743296	+	1.25936i
$624$		0			0
$625$	−6.35758			−0.254303
$626$		0			0
$627$	2.60679	−	7.14490i	0.104105	−	0.285340i
$628$		0			0
$629$	10.6268			0.423719
$630$		0			0
$631$	35.6689			1.41996			0.709978	−	0.704224i	$-0.248705\pi$
$631$	35.6689			1.41996			0.709978	+	0.704224i	$0.248705\pi$
$632$		0			0
$633$	−23.8227	+	4.18158i	−0.946868	+	0.166203i
$634$		0			0
$635$	−63.3459			−2.51380
$636$		0			0
$637$	−19.6918	+	10.8707i	−0.780218	+	0.430711i
$638$		0			0
$639$	−22.5347	−	4.00944i	−0.891457	−	0.158611i
$640$		0			0
$641$		−	24.8536i		−	0.981659i	−0.871256	−	0.490829i	$-0.836694\pi$
$641$		−	24.8536i		−	0.981659i	0.871256	−	0.490829i	$-0.163306\pi$
$642$		0			0
$643$	−14.8270	−	8.56038i	−0.584720	−	0.337588i	0.178287	−	0.983979i	$-0.442944\pi$
$643$	−14.8270	−	8.56038i	−0.584720	−	0.337588i	−0.763007	+	0.646390i	$0.776278\pi$
$644$		0			0
$645$	−9.91224	+	27.1682i	−0.390294	+	1.06975i
$646$		0			0
$647$	−16.7208	+	28.9613i	−0.657363	+	1.13859i	0.323933	+	0.946080i	$0.394995\pi$
$647$	−16.7208	+	28.9613i	−0.657363	+	1.13859i	−0.981296	+	0.192506i	$0.938339\pi$
$648$		0			0
$649$	−13.8761	+	8.01138i	−0.544686	+	0.314474i
$650$		0			0
$651$	−3.64900	−	22.0278i	−0.143016	−	0.863337i
$652$		0			0
$653$			26.4238i			1.03404i	0.855972	+	0.517022i	$0.172959\pi$
$653$			26.4238i			1.03404i	−0.855972	+	0.517022i	$0.827041\pi$
$654$		0			0
$655$	−59.9745			−2.34340
$656$		0			0
$657$	26.2502	−	31.1856i	1.02412	−	1.21667i
$658$		0			0
$659$	−25.8862	+	14.9454i	−1.00838	+	0.582191i	−0.910718	−	0.413029i	$-0.864471\pi$
$659$	−25.8862	+	14.9454i	−1.00838	+	0.582191i	−0.0976658	+	0.995219i	$0.531138\pi$
$660$		0			0
$661$	−3.92629	+	2.26684i	−0.152715	+	0.0881699i	−0.574410	−	0.818568i	$-0.694769\pi$
$661$	−3.92629	+	2.26684i	−0.152715	+	0.0881699i	0.421695	+	0.906738i	$0.361435\pi$
$662$		0			0
$663$	−30.6842	−	11.1950i	−1.19168	−	0.434779i
$664$		0			0
$665$	−19.4459	−	11.4773i	−0.754079	−	0.445069i
$666$		0			0
$667$	12.8682	+	22.2883i	0.498257	+	0.863006i
$668$		0			0
$669$	40.2529	+	14.6862i	1.55627	+	0.567800i
$670$		0			0
$671$	−9.43172	+	16.3362i	−0.364107	+	0.630652i
$672$		0			0
$673$	4.12239	+	7.14019i	0.158907	+	0.275234i	0.934475	−	0.356030i	$-0.115870\pi$
$673$	4.12239	+	7.14019i	0.158907	+	0.275234i	−0.775568	+	0.631264i	$0.782536\pi$
$674$		0			0
$675$	−33.7466	+	19.3793i	−1.29891	+	0.745910i
$676$		0			0
$677$	2.75631	−	4.77407i	0.105934	−	0.183483i	−0.808186	−	0.588928i	$-0.799550\pi$
$677$	2.75631	−	4.77407i	0.105934	−	0.183483i	0.914119	+	0.405445i	$0.132884\pi$
$678$		0			0
$679$	36.3026	+	21.4264i	1.39317	+	0.822268i
$680$		0			0
$681$	6.94253	+	8.28680i	0.266038	+	0.317551i
$682$		0			0
$683$	−24.0097	−	13.8620i	−0.918706	−	0.530415i	−0.0354840	−	0.999370i	$-0.511297\pi$
$683$	−24.0097	−	13.8620i	−0.918706	−	0.530415i	−0.883222	+	0.468955i	$0.844631\pi$
$684$		0			0
$685$		−	19.6540i		−	0.750942i
$686$		0			0
$687$	−21.0537	+	17.6384i	−0.803248	+	0.672947i
$688$		0			0
$689$	4.20235	+	7.27868i	0.160097	+	0.277296i
$690$		0			0
$691$	−36.5312	−	21.0913i	−1.38971	−	0.802351i	−0.396430	−	0.918065i	$-0.629751\pi$
$691$	−36.5312	−	21.0913i	−1.38971	−	0.802351i	−0.993283	+	0.115714i	$0.963084\pi$
$692$		0			0
$693$	−4.78464	−	13.6159i	−0.181754	−	0.517225i
$694$		0			0
$695$	43.9994	+	25.4031i	1.66899	+	0.963593i
$696$		0			0
$697$	29.5284	+	51.1447i	1.11847	+	1.93724i
$698$		0			0
$699$	5.53461	+	2.01929i	0.209338	+	0.0763764i
$700$		0			0
$701$			1.07738i			0.0406922i	0.999793	+	0.0203461i	$0.00647681\pi$
$701$			1.07738i			0.0406922i	−0.999793	+	0.0203461i	$0.993523\pi$
$702$		0			0
$703$	−3.78710	−	2.18648i	−0.142833	−	0.0824648i
$704$		0			0
$705$	−47.7581	+	8.38294i	−1.79867	+	0.315720i
$706$		0			0
$707$	−14.4717	−	25.6306i	−0.544265	−	0.963938i
$708$		0			0
$709$	10.9806	−	19.0189i	0.412385	−	0.714271i	−0.582765	−	0.812640i	$-0.698029\pi$
$709$	10.9806	−	19.0189i	0.412385	−	0.714271i	0.995150	+	0.0983694i	$0.0313627\pi$
$710$		0			0
$711$	−4.22889	−	3.55963i	−0.158596	−	0.133496i
$712$		0			0
$713$	9.37617	+	16.2400i	0.351140	+	0.608193i
$714$		0			0
$715$	10.3240	−	17.8817i	0.386095	−	0.668737i
$716$		0			0
$717$	5.65275	+	32.2041i	0.211106	+	1.20268i
$718$		0			0
$719$	5.89267	+	10.2064i	0.219760	+	0.380635i	0.954734	−	0.297460i	$-0.0961394\pi$
$719$	5.89267	+	10.2064i	0.219760	+	0.380635i	−0.734975	+	0.678094i	$0.762806\pi$
$720$		0			0
$721$	1.38930	−	0.784436i	0.0517403	−	0.0292139i
$722$		0			0
$723$	14.8496	−	12.4407i	0.552263	−	0.462676i
$724$		0			0
$725$	43.3709	−	25.0402i	1.61075	−	0.929970i
$726$		0			0
$727$	10.1963	−	5.88682i	0.378159	−	0.218330i	−0.298858	−	0.954298i	$-0.596606\pi$
$727$	10.1963	−	5.88682i	0.378159	−	0.218330i	0.677017	+	0.735967i	$0.263272\pi$
$728$		0			0
$729$	13.6084	−	23.3198i	0.504016	−	0.863694i
$730$		0			0
$731$	−27.7274			−1.02554
$732$		0			0
$733$			43.7655i			1.61652i	0.588829	+	0.808258i	$0.299589\pi$
$733$			43.7655i			1.61652i	−0.588829	+	0.808258i	$0.700411\pi$
$734$		0			0
$735$	−42.3368	+	6.59654i	−1.56162	+	0.243317i
$736$		0			0
$737$	−12.3575	+	7.13462i	−0.455195	+	0.262807i
$738$		0			0
$739$	−13.9728	+	24.2016i	−0.513998	+	0.890270i	0.485870	+	0.874031i	$0.338503\pi$
$739$	−13.9728	+	24.2016i	−0.513998	+	0.890270i	−0.999868	+	0.0162393i	$0.994831\pi$
$740$		0			0
$741$	8.63159	+	10.3029i	0.317089	+	0.378487i
$742$		0			0
$743$	−31.0951	−	17.9528i	−1.14077	−	0.658623i	−0.194147	−	0.980972i	$-0.562194\pi$
$743$	−31.0951	−	17.9528i	−1.14077	−	0.658623i	−0.946621	+	0.322350i	$0.895527\pi$
$744$		0			0
$745$		−	22.6923i		−	0.831382i
$746$		0			0
$747$	−31.6900	+	11.4787i	−1.15948	+	0.419984i
$748$		0			0
$749$	−29.8200	−	17.6002i	−1.08960	−	0.643099i
$750$		0			0
$751$	2.35031			0.0857642			0.0428821	−	0.999080i	$-0.486346\pi$
$751$	2.35031			0.0857642			0.0428821	+	0.999080i	$0.486346\pi$
$752$		0			0
$753$	−17.1894	−	20.5178i	−0.626417	−	0.747709i
$754$		0			0
$755$	−56.5178			−2.05689
$756$		0			0
$757$	8.88061			0.322771			0.161386	−	0.986891i	$-0.448404\pi$
$757$	8.88061			0.322771			0.161386	+	0.986891i	$0.448404\pi$
$758$		0			0
$759$	7.78399	+	9.29119i	0.282541	+	0.337249i
$760$		0			0
$761$	26.9766			0.977902			0.488951	−	0.872311i	$-0.337380\pi$
$761$	26.9766			0.977902			0.488951	+	0.872311i	$0.337380\pi$
$762$		0			0
$763$	7.25223	+	0.0695902i	0.262548	+	0.00251933i
$764$		0			0
$765$	−47.6013	−	40.0679i	−1.72103	−	1.44866i
$766$		0			0
$767$		−	28.3158i		−	1.02243i
$768$		0			0
$769$	7.88232	+	4.55086i	0.284244	+	0.164108i	0.635343	−	0.772230i	$-0.280859\pi$
$769$	7.88232	+	4.55086i	0.284244	+	0.164108i	−0.351099	+	0.936338i	$0.614192\pi$
$770$		0			0
$771$	−11.8403	−	14.1329i	−0.426419	−	0.508985i
$772$		0			0
$773$	−6.46864	+	11.2040i	−0.232661	+	0.402980i	−0.958590	−	0.284789i	$-0.908077\pi$
$773$	−6.46864	+	11.2040i	−0.232661	+	0.402980i	0.725929	+	0.687769i	$0.241410\pi$
$774$		0			0
$775$	31.6015	−	18.2451i	1.13516	−	0.655384i
$776$		0			0
$777$	−8.18643	+	1.35612i	−0.293686	+	0.0486505i
$778$		0			0
$779$		−	24.3020i		−	0.870710i
$780$		0			0
$781$	13.8726			0.496399
$782$		0			0
$783$	−17.4431	+	30.0510i	−0.623366	+	1.07394i
$784$		0			0
$785$	−42.6245	+	24.6093i	−1.52134	+	0.878343i
$786$		0			0
$787$	−21.5265	+	12.4283i	−0.767336	+	0.443022i	−0.831923	−	0.554890i	$-0.812760\pi$
$787$	−21.5265	+	12.4283i	−0.767336	+	0.443022i	0.0645875	+	0.997912i	$0.479427\pi$
$788$		0			0
$789$	−14.7208	+	12.3328i	−0.524073	+	0.439059i
$790$		0			0
$791$	0.194975	−	20.3190i	0.00693250	−	0.722460i
$792$		0			0
$793$	−16.6680	−	28.8697i	−0.591896	−	1.02519i
$794$		0			0
$795$	2.76796	+	15.7692i	0.0981693	+	0.559277i
$796$		0			0
$797$	6.71671	−	11.6337i	0.237918	−	0.412086i	−0.722199	−	0.691686i	$-0.756868\pi$
$797$	6.71671	−	11.6337i	0.237918	−	0.412086i	0.960117	+	0.279600i	$0.0902017\pi$
$798$		0			0
$799$	−23.2444	−	40.2605i	−0.822328	−	1.42431i
$800$		0			0
$801$	38.9134	−	14.0951i	1.37494	−	0.498028i
$802$		0			0
$803$	−12.3530	+	21.3961i	−0.435928	+	0.755050i
$804$		0			0
$805$	31.3359	−	17.6931i	1.10445	−	0.623600i
$806$		0			0
$807$	−10.7185	+	1.88141i	−0.377309	+	0.0662288i
$808$		0			0
$809$	−9.38524	−	5.41857i	−0.329967	−	0.190507i	0.325859	−	0.945418i	$-0.394346\pi$
$809$	−9.38524	−	5.41857i	−0.329967	−	0.190507i	−0.655827	+	0.754912i	$0.727680\pi$
$810$		0			0
$811$		−	35.3334i		−	1.24072i	−0.784316	−	0.620361i	$-0.786986\pi$
$811$		−	35.3334i		−	1.24072i	0.784316	−	0.620361i	$-0.213014\pi$
$812$		0			0
$813$	−1.79343	−	0.654327i	−0.0628983	−	0.0229483i
$814$		0			0
$815$	−27.5475	−	47.7137i	−0.964948	−	1.67134i
$816$		0			0
$817$	9.88127	+	5.70496i	0.345702	+	0.199591i
$818$		0			0
$819$	25.0664	+	4.70846i	0.875890	+	0.164527i
$820$		0			0
$821$	−16.6412	−	9.60782i	−0.580783	−	0.335315i	0.180661	−	0.983545i	$-0.442176\pi$
$821$	−16.6412	−	9.60782i	−0.580783	−	0.335315i	−0.761445	+	0.648230i	$0.775510\pi$
$822$		0			0
$823$	14.9074	+	25.8204i	0.519639	+	0.900041i	0.999739	+	0.0228278i	$0.00726695\pi$
$823$	14.9074	+	25.8204i	0.519639	+	0.900041i	−0.480100	+	0.877214i	$0.659400\pi$
$824$		0			0
$825$	18.0798	−	15.1469i	0.629456	−	0.527347i
$826$		0			0
$827$			0.356137i			0.0123841i	0.999981	+	0.00619205i	$0.00197100\pi$
$827$			0.356137i			0.0123841i	−0.999981	+	0.00619205i	$0.998029\pi$
$828$		0			0
$829$	−17.5571	−	10.1366i	−0.609783	−	0.352058i	0.163098	−	0.986610i	$-0.447851\pi$
$829$	−17.5571	−	10.1366i	−0.609783	−	0.352058i	−0.772880	+	0.634552i	$0.781185\pi$
$830$		0			0
$831$	−17.0869	−	20.3955i	−0.592739	−	0.707510i
$832$		0			0
$833$	−19.8539	−	35.9646i	−0.687896	−	1.24610i
$834$		0			0
$835$	23.2795	−	40.3213i	0.805620	−	1.39538i
$836$		0			0
$837$	−12.7096	+	21.8962i	−0.439309	+	0.756843i
$838$		0			0
$839$	0.662663	+	1.14777i	0.0228777	+	0.0396253i	0.877238	−	0.480056i	$-0.159384\pi$
$839$	0.662663	+	1.14777i	0.0228777	+	0.0396253i	−0.854360	+	0.519682i	$0.826051\pi$
$840$		0			0
$841$	7.85791	−	13.6103i	0.270962	−	0.469321i
$842$		0			0
$843$	35.5353	+	12.9649i	1.22390	+	0.446536i
$844$		0			0
$845$	−4.72626	−	8.18612i	−0.162588	−	0.281611i
$846$		0			0
$847$	−10.0084	−	17.7258i	−0.343894	−	0.609064i
$848$		0			0
$849$	18.0262	+	6.57681i	0.618659	+	0.225716i
$850$		0			0
$851$	6.03545	−	3.48457i	0.206893	−	0.119449i
$852$		0			0
$853$	−41.7558	+	24.1077i	−1.42969	+	0.825432i	−0.997096	−	0.0761571i	$-0.975735\pi$
$853$	−41.7558	+	24.1077i	−1.42969	+	0.825432i	−0.432594	+	0.901589i	$0.642402\pi$
$854$		0			0
$855$	8.71972	+	24.0731i	0.298208	+	0.823282i
$856$		0			0
$857$	−20.8773			−0.713155			−0.356578	−	0.934266i	$-0.616056\pi$
$857$	−20.8773			−0.713155			−0.356578	+	0.934266i	$0.616056\pi$
$858$		0			0
$859$			13.7094i			0.467758i	0.972266	+	0.233879i	$0.0751419\pi$
$859$			13.7094i			0.467758i	−0.972266	+	0.233879i	$0.924858\pi$
$860$		0			0
$861$	−29.2740	−	35.6313i	−0.997657	−	1.21431i
$862$		0			0
$863$	−28.1125	+	16.2307i	−0.956959	+	0.552501i	−0.895236	−	0.445593i	$-0.852993\pi$
$863$	−28.1125	+	16.2307i	−0.956959	+	0.552501i	−0.0617233	+	0.998093i	$0.519660\pi$
$864$		0			0
$865$	−19.8047	+	34.3027i	−0.673379	+	1.16633i
$866$		0			0
$867$	10.3542	−	28.3795i	0.351646	−	0.963819i
$868$		0			0
$869$	2.90139	+	1.67512i	0.0984228	+	0.0568244i
$870$		0			0
$871$		−	25.2169i		−	0.854444i
$872$		0			0
$873$	−16.2784	−	44.9409i	−0.550941	−	1.52102i
$874$		0			0
$875$	−11.4434	−	20.2671i	−0.386856	−	0.685154i
$876$		0			0
$877$	21.9338			0.740653			0.370326	−	0.928902i	$-0.379246\pi$
$877$	21.9338			0.740653			0.370326	+	0.928902i	$0.379246\pi$
$878$		0			0
$879$	43.1030	−	7.56583i	1.45383	−	0.255189i
$880$		0			0
$881$	21.8019			0.734526			0.367263	−	0.930117i	$-0.380295\pi$
$881$	21.8019			0.734526			0.367263	+	0.930117i	$0.380295\pi$
$882$		0			0
$883$	24.4085			0.821411			0.410705	−	0.911768i	$-0.365283\pi$
$883$	24.4085			0.821411			0.410705	+	0.911768i	$0.365283\pi$
$884$		0			0
$885$	18.4876	−	50.6723i	0.621454	−	1.70333i
$886$		0			0
$887$	33.7444			1.13303			0.566513	−	0.824053i	$-0.308292\pi$
$887$	33.7444			1.13303			0.566513	+	0.824053i	$0.308292\pi$
$888$		0			0
$889$	23.3169	+	41.2961i	0.782024	+	1.38503i
$890$		0			0
$891$	−5.64455	+	15.3602i	−0.189099	+	0.514585i
$892$		0			0
$893$			19.1303i			0.640170i
$894$		0			0
$895$	−32.6113	−	18.8281i	−1.09007	−	0.629355i
$896$		0			0
$897$	−21.0978	+	3.70328i	−0.704436	+	0.123649i
$898$		0			0
$899$	16.2907	−	28.2164i	0.543326	−	0.941068i
$900$		0			0
$901$	−13.2936	+	7.67505i	−0.442873	+	0.255693i
$902$		0			0
$903$	21.3600	−	3.53837i	0.710815	−	0.117750i
$904$		0			0
$905$			42.0183i			1.39674i
$906$		0			0
$907$	−15.0566			−0.499948			−0.249974	−	0.968253i	$-0.580422\pi$
$907$	−15.0566			−0.499948			−0.249974	+	0.968253i	$0.580422\pi$
$908$		0			0
$909$	−5.84637	+	32.8589i	−0.193912	+	1.08986i
$910$		0			0
$911$	21.5047	−	12.4157i	0.712481	−	0.411351i	−0.0994977	−	0.995038i	$-0.531724\pi$
$911$	21.5047	−	12.4157i	0.712481	−	0.411351i	0.811979	+	0.583686i	$0.198390\pi$
$912$		0			0
$913$	17.6913	−	10.2141i	0.585498	−	0.338038i
$914$		0			0
$915$	−10.9787	−	62.5462i	−0.362944	−	2.06771i
$916$		0			0
$917$	22.0759	+	39.0983i	0.729012	+	1.29114i
$918$		0			0
$919$	12.0689	+	20.9039i	0.398115	+	0.689555i	0.993493	−	0.113890i	$-0.0363312\pi$
$919$	12.0689	+	20.9039i	0.398115	+	0.689555i	−0.595378	+	0.803445i	$0.702998\pi$
$920$		0			0
$921$	−16.2194	+	13.5883i	−0.534447	+	0.447750i
$922$		0			0
$923$	−12.2580	+	21.2314i	−0.403476	+	0.698840i
$924$		0			0
$925$	−6.78064	−	11.7444i	−0.222946	−	0.386154i
$926$		0			0
$927$	−1.78111	−	0.316901i	−0.0584994	−	0.0104084i
$928$		0			0
$929$	−13.3310	+	23.0900i	−0.437376	+	0.757558i	−0.997486	−	0.0708606i	$-0.977425\pi$
$929$	−13.3310	+	23.0900i	−0.437376	+	0.757558i	0.560110	+	0.828418i	$0.310759\pi$
$930$		0			0
$931$	−0.324397	+	16.9017i	−0.0106317	+	0.553932i
$932$		0			0
$933$	−5.63360	+	15.4410i	−0.184436	+	0.505515i
$934$		0			0
$935$	32.6586	+	18.8555i	1.06805	+	0.616640i
$936$		0			0
$937$			8.17165i			0.266956i	0.991052	+	0.133478i	$0.0426146\pi$
$937$			8.17165i			0.266956i	−0.991052	+	0.133478i	$0.957385\pi$
$938$		0			0
$939$	4.05790	+	23.1181i	0.132424	+	0.754430i
$940$		0			0
$941$	16.0136	+	27.7363i	0.522028	+	0.904179i	0.999672	+	0.0256254i	$0.00815770\pi$
$941$	16.0136	+	27.7363i	0.522028	+	0.904179i	−0.477644	+	0.878554i	$0.658509\pi$
$942$		0			0
$943$	33.5410	+	19.3649i	1.09224	+	0.630608i
$944$		0			0
$945$	41.7830	+	24.7920i	1.35920	+	0.806483i
$946$		0			0
$947$	15.5020	+	8.95009i	0.503748	+	0.290839i	0.730260	−	0.683169i	$-0.239399\pi$
$947$	15.5020	+	8.95009i	0.503748	+	0.290839i	−0.226512	+	0.974008i	$0.572732\pi$
$948$		0			0
$949$	−21.8305	−	37.8116i	−0.708650	−	1.22742i
$950$		0			0
$951$	4.75640	+	27.0975i	0.154237	+	0.878697i
$952$		0			0
$953$		−	11.2737i		−	0.365191i	−0.983188	−	0.182596i	$-0.941550\pi$
$953$		−	11.2737i		−	0.365191i	0.983188	−	0.182596i	$-0.0584499\pi$
$954$		0			0
$955$	−0.685459	−	0.395750i	−0.0221809	−	0.0128062i
$956$		0			0
$957$	7.21812	−	19.7840i	0.233329	−	0.639525i
$958$		0			0
$959$	−12.8128	+	7.23442i	−0.413746	+	0.233612i
$960$		0			0
$961$	−3.63003	+	6.28740i	−0.117098	+	0.202819i
$962$		0			0
$963$	13.3716	+	36.9158i	0.430893	+	1.18959i
$964$		0			0
$965$	−46.0738	−	79.8022i	−1.48317	−	2.56892i
$966$		0			0
$967$	−15.3313	+	26.5546i	−0.493022	+	0.853939i	−0.999968	−	0.00803913i	$-0.997441\pi$
$967$	−15.3313	+	26.5546i	−0.493022	+	0.853939i	0.506946	+	0.861978i	$0.330774\pi$
$968$		0			0
$969$	−18.8170	+	15.7645i	−0.604488	+	0.506429i
$970$		0			0
$971$	−19.0807	−	33.0488i	−0.612330	−	1.06059i	−0.990847	−	0.134992i	$-0.956899\pi$
$971$	−19.0807	−	33.0488i	−0.612330	−	1.06059i	0.378517	−	0.925595i	$-0.376434\pi$
$972$		0			0
$973$	0.364967	−	38.0345i	0.0117003	−	1.21933i
$974$		0			0
$975$	7.20624	+	41.0543i	0.230784	+	1.31479i
$976$		0			0
$977$	26.5862	−	15.3496i	0.850568	−	0.491076i	−0.0102745	−	0.999947i	$-0.503271\pi$
$977$	26.5862	−	15.3496i	0.850568	−	0.491076i	0.860842	+	0.508872i	$0.169937\pi$
$978$		0			0
$979$	−21.7239	+	12.5423i	−0.694299	+	0.400854i
$980$		0			0
$981$	−6.29148	−	5.29580i	−0.200872	−	0.169082i
$982$		0			0
$983$	−25.8057			−0.823073			−0.411536	−	0.911393i	$-0.635008\pi$
$983$	−25.8057			−0.823073			−0.411536	+	0.911393i	$0.635008\pi$
$984$		0			0
$985$			5.52328i			0.175986i
$986$		0			0
$987$	23.0442	+	28.0486i	0.733505	+	0.892796i
$988$		0			0
$989$	−15.7476	+	9.09191i	−0.500746	+	0.289106i
$990$		0			0
$991$	11.4388	−	19.8126i	0.363366	−	0.629369i	−0.625146	−	0.780508i	$-0.714961\pi$
$991$	11.4388	−	19.8126i	0.363366	−	0.629369i	0.988513	+	0.151139i	$0.0482940\pi$
$992$		0			0
$993$	18.7212	−	3.28612i	0.594100	−	0.104282i
$994$		0			0
$995$	−47.6118	−	27.4887i	−1.50940	−	0.871450i
$996$		0			0
$997$		−	41.5407i		−	1.31561i	−0.753189	−	0.657804i	$-0.771486\pi$
$997$		−	41.5407i		−	1.31561i	0.753189	−	0.657804i	$-0.228514\pi$
$998$		0			0
$999$	8.13752	+	4.72342i	0.257460	+	0.149443i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1008.2.df.e.689.18		48
3.2	odd	2		3024.2.df.e.17.3		48
4.3	odd	2		504.2.cx.a.185.7	yes	48
7.5	odd	6		1008.2.ca.e.257.24		48
9.2	odd	6		1008.2.ca.e.353.24		48
9.7	even	3		3024.2.ca.e.2033.3		48
12.11	even	2		1512.2.cx.a.17.3		48
21.5	even	6		3024.2.ca.e.2609.3		48
28.19	even	6		504.2.bs.a.257.1	✓	48
36.7	odd	6		1512.2.bs.a.521.3		48
36.11	even	6		504.2.bs.a.353.1	yes	48
63.47	even	6	inner	1008.2.df.e.929.18		48
63.61	odd	6		3024.2.df.e.1601.3		48
84.47	odd	6		1512.2.bs.a.1097.3		48
252.47	odd	6		504.2.cx.a.425.7	yes	48
252.187	even	6		1512.2.cx.a.89.3		48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
504.2.bs.a.257.1	✓	48	28.19	even	6
504.2.bs.a.353.1	yes	48	36.11	even	6
504.2.cx.a.185.7	yes	48	4.3	odd	2
504.2.cx.a.425.7	yes	48	252.47	odd	6
1008.2.ca.e.257.24		48	7.5	odd	6
1008.2.ca.e.353.24		48	9.2	odd	6
1008.2.df.e.689.18		48	1.1	even	1	trivial
1008.2.df.e.929.18		48	63.47	even	6	inner
1512.2.bs.a.521.3		48	36.7	odd	6
1512.2.bs.a.1097.3		48	84.47	odd	6
1512.2.cx.a.17.3		48	12.11	even	2
1512.2.cx.a.89.3		48	252.187	even	6
3024.2.ca.e.2033.3		48	9.7	even	3
3024.2.ca.e.2609.3		48	21.5	even	6
3024.2.df.e.17.3		48	3.2	odd	2
3024.2.df.e.1601.3		48	63.61	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 1008 = 2^{4} \cdot 3^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1008.df (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(1.11231 + 1.32769i) q^{3} +3.53401 q^{5} +(-1.30083 - 2.30388i) q^{7} +(-0.525517 + 2.95361i) q^{9} +O(q^{10})\)	\(q+(1.11231 + 1.32769i) q^{3} +3.53401 q^{5} +(-1.30083 - 2.30388i) q^{7} +(-0.525517 + 2.95361i) q^{9} -1.81827i q^{11} +(2.78280 + 1.60665i) q^{13} +(3.93093 + 4.69207i) q^{15} +(-2.93434 + 5.08242i) q^{17} +(2.09143 - 1.20749i) q^{19} +(1.61190 - 4.28973i) q^{21} +3.84871i q^{23} +7.48923 q^{25} +(-4.50602 + 2.58762i) q^{27} +(5.79110 - 3.34349i) q^{29} +(4.21959 - 2.43618i) q^{31} +(2.41410 - 2.02249i) q^{33} +(-4.59714 - 8.14192i) q^{35} +(-0.905385 - 1.56817i) q^{37} +(0.962213 + 5.48178i) q^{39} +(5.03152 - 8.71485i) q^{41} +(2.36232 + 4.09166i) q^{43} +(-1.85718 + 10.4381i) q^{45} +(-3.96076 + 6.86023i) q^{47} +(-3.61569 + 5.99390i) q^{49} +(-10.0118 + 1.75736i) q^{51} +(2.26517 + 1.30780i) q^{53} -6.42580i q^{55} +(3.92950 + 1.43366i) q^{57} +(-4.40604 - 7.63149i) q^{59} +(-8.98447 - 5.18718i) q^{61} +(7.48837 - 2.63142i) q^{63} +(9.83443 + 5.67791i) q^{65} +(-3.92384 - 6.79630i) q^{67} +(-5.10990 + 4.28098i) q^{69} +7.62952i q^{71} +(-11.7672 - 6.79382i) q^{73} +(8.33037 + 9.94337i) q^{75} +(-4.18907 + 2.36526i) q^{77} +(-0.921268 + 1.59568i) q^{79} +(-8.44766 - 3.10435i) q^{81} +(5.61748 + 9.72975i) q^{83} +(-10.3700 + 17.9613i) q^{85} +(10.8806 + 3.96977i) q^{87} +(-6.89792 - 11.9475i) q^{89} +(0.0815748 - 8.50119i) q^{91} +(7.92800 + 2.89251i) q^{93} +(7.39114 - 4.26728i) q^{95} +(-13.7982 + 7.96638i) q^{97} +(5.37048 + 0.955533i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q + 2 q^{9}+O(q^{10}) \) 48 * q + 2 * q^9	\( 48 q + 2 q^{9} - 8 q^{15} - 10 q^{21} + 48 q^{25} - 18 q^{27} + 18 q^{29} - 18 q^{31} + 12 q^{33} + 4 q^{39} - 6 q^{41} + 6 q^{43} - 18 q^{45} - 18 q^{47} - 12 q^{49} - 6 q^{51} - 12 q^{53} + 4 q^{57} + 18 q^{61} + 32 q^{63} - 36 q^{65} - 12 q^{77} - 6 q^{79} + 6 q^{81} + 54 q^{87} - 18 q^{89} - 6 q^{91} + 4 q^{93} + 54 q^{95} + 64 q^{99}+O(q^{100}) \) 48 * q + 2 * q^9 - 8 * q^15 - 10 * q^21 + 48 * q^25 - 18 * q^27 + 18 * q^29 - 18 * q^31 + 12 * q^33 + 4 * q^39 - 6 * q^41 + 6 * q^43 - 18 * q^45 - 18 * q^47 - 12 * q^49 - 6 * q^51 - 12 * q^53 + 4 * q^57 + 18 * q^61 + 32 * q^63 - 36 * q^65 - 12 * q^77 - 6 * q^79 + 6 * q^81 + 54 * q^87 - 18 * q^89 - 6 * q^91 + 4 * q^93 + 54 * q^95 + 64 * q^99

Introduction

L-functions

Modular forms

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