LMFDB - Embedded newform 644.2.bc.a.493.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [644,2,Mod(5,644)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(644, base_ring=CyclotomicField(66))

chi = DirichletCharacter(H, H._module([0, 55, 3]))

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

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

chi := DirichletCharacter("644.5");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 644 = 2^{2} \cdot 7 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	644.bc (of order $66$, degree $20$, 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:	$5.14236589017$
Analytic rank:	$0$
Dimension:	$320$
Relative dimension:	$16$ over $\Q(\zeta_{66})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{66}]$

Embedding invariants

Embedding label			493.8
Character	$\chi$	$=$	644.493
Dual form			644.2.bc.a.145.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.118439 + 0.229739i) q^{3} +(-0.622997 + 0.0594890i) q^{5} +(0.286999 + 2.63014i) q^{7} +(1.70142 - 2.38931i) q^{9} +O(q^{10})$	\(q+(0.118439 + 0.229739i) q^{3} +(-0.622997 + 0.0594890i) q^{5} +(0.286999 + 2.63014i) q^{7} +(1.70142 - 2.38931i) q^{9} +(-3.94516 + 1.36543i) q^{11} +(0.970607 + 3.30558i) q^{13} +(-0.0874541 - 0.136081i) q^{15} +(5.73936 + 2.29769i) q^{17} +(-2.59679 + 1.03960i) q^{19} +(-0.570255 + 0.377446i) q^{21} +(2.78284 + 3.90587i) q^{23} +(-4.52506 + 0.872133i) q^{25} +(1.51796 + 0.218249i) q^{27} +(0.381185 + 2.65120i) q^{29} +(-1.34970 + 0.0642943i) q^{31} +(-0.780955 - 0.744639i) q^{33} +(-0.335264 - 1.62150i) q^{35} +(-0.255259 - 0.181769i) q^{37} +(-0.644465 + 0.614496i) q^{39} +(6.43896 + 2.94057i) q^{41} +(-3.31192 + 5.15345i) q^{43} +(-0.917842 + 1.58975i) q^{45} +(5.79716 - 3.34699i) q^{47} +(-6.83526 + 1.50969i) q^{49} +(0.151893 + 1.59069i) q^{51} +(5.82618 + 6.11032i) q^{53} +(2.37660 - 1.08536i) q^{55} +(-0.546398 - 0.473457i) q^{57} +(-5.01885 - 1.21756i) q^{59} +(-4.54952 - 2.34544i) q^{61} +(6.77252 + 3.78924i) q^{63} +(-0.801332 - 2.00163i) q^{65} +(-0.182148 - 0.945073i) q^{67} +(-0.567736 + 1.10193i) q^{69} +(5.78935 + 6.68126i) q^{71} +(8.97225 - 11.4091i) q^{73} +(-0.736306 - 0.936289i) q^{75} +(-4.72354 - 9.98445i) q^{77} +(-2.29705 + 2.40908i) q^{79} +(-2.74841 - 7.94102i) q^{81} +(-0.796330 - 1.74372i) q^{83} +(-3.71230 - 1.09003i) q^{85} +(-0.563937 + 0.401578i) q^{87} +(0.322705 - 6.77440i) q^{89} +(-8.41558 + 3.50153i) q^{91} +(-0.174628 - 0.302465i) q^{93} +(1.55595 - 0.802148i) q^{95} +(1.68127 - 3.68147i) q^{97} +(-3.44993 + 11.7494i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 320 q - 20 q^{9}+O(q^{10}) $ 320 * q - 20 * q^9	$ 320 q - 20 q^{9} + 66 q^{21} + 21 q^{23} - 8 q^{25} - 12 q^{29} - 6 q^{31} - 38 q^{35} + 44 q^{37} - 20 q^{39} - 88 q^{43} - 42 q^{47} - 74 q^{49} + 44 q^{51} - 88 q^{57} + 55 q^{63} + 77 q^{65} - 32 q^{71} - 36 q^{73} + 24 q^{75} + 105 q^{77} + 44 q^{79} - 36 q^{81} + 60 q^{85} - 96 q^{87} - 20 q^{93} - 31 q^{95} + 242 q^{99}+O(q^{100}) $ 320 * q - 20 * q^9 + 66 * q^21 + 21 * q^23 - 8 * q^25 - 12 * q^29 - 6 * q^31 - 38 * q^35 + 44 * q^37 - 20 * q^39 - 88 * q^43 - 42 * q^47 - 74 * q^49 + 44 * q^51 - 88 * q^57 + 55 * q^63 + 77 * q^65 - 32 * q^71 - 36 * q^73 + 24 * q^75 + 105 * q^77 + 44 * q^79 - 36 * q^81 + 60 * q^85 - 96 * q^87 - 20 * q^93 - 31 * q^95 + 242 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/644\mathbb{Z}\right)^\times$.

$n$	$185$	$281$	$323$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{3}{22}\right)$	$1$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	0.118439	+	0.229739i	0.0683807	+	0.132640i	0.920548	−	0.390629i	$-0.127743\pi$
$3$	0.118439	+	0.229739i	0.0683807	+	0.132640i	−0.852167	+	0.523269i	$0.824712\pi$
$4$		0			0
$5$	−0.622997	+	0.0594890i	−0.278613	+	0.0266043i	−0.233427	−	0.972374i	$-0.574994\pi$
$5$	−0.622997	+	0.0594890i	−0.278613	+	0.0266043i	−0.0451858	+	0.998979i	$0.514388\pi$
$6$		0			0
$7$	0.286999	+	2.63014i	0.108475	+	0.994099i
$7$	0.286999	+	2.63014i	0.108475	+	0.994099i
$8$		0			0
$9$	1.70142	−	2.38931i	0.567139	−	0.796436i
$10$		0			0
$11$	−3.94516	+	1.36543i	−1.18951	+	0.411694i	−0.848922	−	0.528518i	$-0.822748\pi$
$11$	−3.94516	+	1.36543i	−1.18951	+	0.411694i	−0.340590	+	0.940212i	$0.610627\pi$
$12$		0			0
$13$	0.970607	+	3.30558i	0.269198	+	0.916804i	0.977507	+	0.210902i	$0.0676401\pi$
$13$	0.970607	+	3.30558i	0.269198	+	0.916804i	−0.708309	+	0.705902i	$0.750542\pi$
$14$		0			0
$15$	−0.0874541	−	0.136081i	−0.0225805	−	0.0351360i
$16$		0			0
$17$	5.73936	+	2.29769i	1.39200	+	0.557273i	0.941957	−	0.335734i	$-0.108984\pi$
$17$	5.73936	+	2.29769i	1.39200	+	0.557273i	0.450043	+	0.893007i	$0.351409\pi$
$18$		0			0
$19$	−2.59679	+	1.03960i	−0.595745	+	0.238500i	−0.649885	−	0.760033i	$-0.725183\pi$
$19$	−2.59679	+	1.03960i	−0.595745	+	0.238500i	0.0541393	+	0.998533i	$0.482759\pi$
$20$		0			0
$21$	−0.570255	+	0.377446i	−0.124440	+	0.0823654i
$22$		0			0
$23$	2.78284	+	3.90587i	0.580262	+	0.814430i
$23$	2.78284	+	3.90587i	0.580262	+	0.814430i
$24$		0			0
$25$	−4.52506	+	0.872133i	−0.905011	+	0.174427i
$26$		0			0
$27$	1.51796	+	0.218249i	0.292131	+	0.0420021i
$28$		0			0
$29$	0.381185	+	2.65120i	0.0707842	+	0.492315i	0.994117	+	0.108314i	$0.0345451\pi$
$29$	0.381185	+	2.65120i	0.0707842	+	0.492315i	−0.923333	+	0.384001i	$0.874546\pi$
$30$		0			0
$31$	−1.34970	+	0.0642943i	−0.242414	+	0.0115476i	−0.168437	−	0.985712i	$-0.553872\pi$
$31$	−1.34970	+	0.0642943i	−0.242414	+	0.0115476i	−0.0739767	+	0.997260i	$0.523569\pi$
$32$		0			0
$33$	−0.780955	−	0.744639i	−0.135947	−	0.129625i
$34$		0			0
$35$	−0.335264	−	1.62150i	−0.0566699	−	0.274083i
$36$		0			0
$37$	−0.255259	−	0.181769i	−0.0419644	−	0.0298827i	0.558882	−	0.829247i	$-0.311230\pi$
$37$	−0.255259	−	0.181769i	−0.0419644	−	0.0298827i	−0.600847	+	0.799364i	$0.705170\pi$
$38$		0			0
$39$	−0.644465	+	0.614496i	−0.103197	+	0.0983982i
$40$		0			0
$41$	6.43896	+	2.94057i	1.00560	+	0.459240i	0.848983	−	0.528420i	$-0.177215\pi$
$41$	6.43896	+	2.94057i	1.00560	+	0.459240i	0.156613	+	0.987660i	$0.449942\pi$
$42$		0			0
$43$	−3.31192	+	5.15345i	−0.505063	+	0.785893i	−0.996373	−	0.0850913i	$-0.972882\pi$
$43$	−3.31192	+	5.15345i	−0.505063	+	0.785893i	0.491310	+	0.870985i	$0.336518\pi$
$44$		0			0
$45$	−0.917842	+	1.58975i	−0.136824	+	0.236986i
$46$		0			0
$47$	5.79716	−	3.34699i	0.845603	−	0.488209i	−0.0135621	−	0.999908i	$-0.504317\pi$
$47$	5.79716	−	3.34699i	0.845603	−	0.488209i	0.859165	+	0.511699i	$0.170984\pi$
$48$		0			0
$49$	−6.83526	+	1.50969i	−0.976466	+	0.215670i
$50$		0			0
$51$	0.151893	+	1.59069i	0.0212693	+	0.222742i
$52$		0			0
$53$	5.82618	+	6.11032i	0.800287	+	0.839317i	0.989786	−	0.142564i	$-0.0455348\pi$
$53$	5.82618	+	6.11032i	0.800287	+	0.839317i	−0.189499	+	0.981881i	$0.560686\pi$
$54$		0			0
$55$	2.37660	−	1.08536i	0.320461	−	0.146349i
$56$		0			0
$57$	−0.546398	−	0.473457i	−0.0723722	−	0.0627109i
$58$		0			0
$59$	−5.01885	−	1.21756i	−0.653398	−	0.158513i	−0.104662	−	0.994508i	$-0.533376\pi$
$59$	−5.01885	−	1.21756i	−0.653398	−	0.158513i	−0.548737	+	0.835995i	$0.684891\pi$
$60$		0			0
$61$	−4.54952	−	2.34544i	−0.582506	−	0.300303i	0.141674	−	0.989913i	$-0.454751\pi$
$61$	−4.54952	−	2.34544i	−0.582506	−	0.300303i	−0.724181	+	0.689610i	$0.757782\pi$
$62$		0			0
$63$	6.77252	+	3.78924i	0.853257	+	0.477399i
$64$		0			0
$65$	−0.801332	−	2.00163i	−0.0993930	−	0.248272i
$66$		0			0
$67$	−0.182148	−	0.945073i	−0.0222529	−	0.115459i	0.969104	−	0.246653i	$-0.0793309\pi$
$67$	−0.182148	−	0.945073i	−0.0222529	−	0.115459i	−0.991357	+	0.131194i	$0.958119\pi$
$68$		0			0
$69$	−0.567736	+	1.10193i	−0.0683473	+	0.132657i
$70$		0			0
$71$	5.78935	+	6.68126i	0.687069	+	0.792920i	0.986945	−	0.161058i	$-0.0514907\pi$
$71$	5.78935	+	6.68126i	0.687069	+	0.792920i	−0.299876	+	0.953978i	$0.596945\pi$
$72$		0			0
$73$	8.97225	−	11.4091i	1.05012	−	1.33534i	0.110215	−	0.993908i	$-0.464846\pi$
$73$	8.97225	−	11.4091i	1.05012	−	1.33534i	0.939907	−	0.341431i	$-0.110912\pi$
$74$		0			0
$75$	−0.736306	−	0.936289i	−0.0850213	−	0.108113i
$76$		0			0
$77$	−4.72354	−	9.98445i	−0.538297	−	1.13783i
$78$		0			0
$79$	−2.29705	+	2.40908i	−0.258438	+	0.271042i	−0.840152	−	0.542352i	$-0.817534\pi$
$79$	−2.29705	+	2.40908i	−0.258438	+	0.271042i	0.581713	+	0.813394i	$0.302383\pi$
$80$		0			0
$81$	−2.74841	−	7.94102i	−0.305379	−	0.882336i
$82$		0			0
$83$	−0.796330	−	1.74372i	−0.0874086	−	0.191398i	0.860880	−	0.508809i	$-0.169914\pi$
$83$	−0.796330	−	1.74372i	−0.0874086	−	0.191398i	−0.948288	+	0.317411i	$0.897187\pi$
$84$		0			0
$85$	−3.71230	−	1.09003i	−0.402655	−	0.118230i
$86$		0			0
$87$	−0.563937	+	0.401578i	−0.0604604	+	0.0430537i
$88$		0			0
$89$	0.322705	−	6.77440i	0.0342066	−	0.718085i	−0.915004	−	0.403444i	$-0.867813\pi$
$89$	0.322705	−	6.77440i	0.0342066	−	0.718085i	0.949211	−	0.314641i	$-0.101884\pi$
$90$		0			0
$91$	−8.41558	+	3.50153i	−0.882193	+	0.367060i
$92$		0			0
$93$	−0.174628	−	0.302465i	−0.0181081	−	0.0313642i
$94$		0			0
$95$	1.55595	−	0.802148i	0.159637	−	0.0822987i
$96$		0			0
$97$	1.68127	−	3.68147i	0.170707	−	0.373797i	−0.804871	−	0.593450i	$-0.797765\pi$
$97$	1.68127	−	3.68147i	0.170707	−	0.373797i	0.975578	+	0.219653i	$0.0704926\pi$
$98$		0			0
$99$	−3.44993	+	11.7494i	−0.346731	+	1.18086i
$100$		0			0
$101$	1.14665	−	12.0082i	0.114096	−	1.19486i	−0.739219	−	0.673466i	$-0.764805\pi$
$101$	1.14665	−	12.0082i	0.114096	−	1.19486i	0.853314	−	0.521397i	$-0.174589\pi$
$102$		0			0
$103$	−8.02709	−	1.54709i	−0.790932	−	0.152440i	−0.222242	−	0.974992i	$-0.571338\pi$
$103$	−8.02709	−	1.54709i	−0.790932	−	0.152440i	−0.568690	+	0.822552i	$0.692550\pi$
$104$		0			0
$105$	0.332813	−	0.269071i	0.0324793	−	0.0262587i
$106$		0			0
$107$	−0.929412	+	1.80281i	−0.0898497	+	0.174284i	−0.929478	−	0.368877i	$-0.879742\pi$
$107$	−0.929412	+	1.80281i	−0.0898497	+	0.174284i	0.839629	+	0.543161i	$0.182773\pi$
$108$		0			0
$109$	3.42961	−	8.56674i	0.328497	−	0.820545i	−0.668544	−	0.743672i	$-0.733082\pi$
$109$	3.42961	−	8.56674i	0.328497	−	0.820545i	0.997041	−	0.0768727i	$-0.0244935\pi$
$110$		0			0
$111$	0.0115269	−	0.0801717i	0.00109409	−	0.00760956i
$112$		0			0
$113$	−9.82358	+	8.51218i	−0.924125	+	0.800759i	−0.980270	−	0.197664i	$-0.936665\pi$
$113$	−9.82358	+	8.51218i	−0.924125	+	0.800759i	0.0561450	+	0.998423i	$0.482119\pi$
$114$		0			0
$115$	−1.96606	−	2.26780i	−0.183336	−	0.211473i
$116$		0			0
$117$	9.54947	+	3.30510i	0.882849	+	0.305557i
$118$		0			0
$119$	−4.39607	+	15.7548i	−0.402987	+	1.44424i
$120$		0			0
$121$	5.05333	−	3.97398i	0.459394	−	0.361271i
$122$		0			0
$123$	0.0870574	+	1.82756i	0.00784970	+	0.164786i
$124$		0			0
$125$	5.76962	−	1.69411i	0.516050	−	0.151526i
$126$		0			0
$127$	6.08384	−	7.02113i	0.539854	−	0.623024i	−0.418635	−	0.908155i	$-0.637491\pi$
$127$	6.08384	−	7.02113i	0.539854	−	0.623024i	0.958489	+	0.285130i	$0.0920368\pi$
$128$		0			0
$129$	−1.57621	−	0.150510i	−0.138778	−	0.0132516i
$130$		0			0
$131$	6.92649	−	1.68035i	0.605170	−	0.146813i	0.0785453	−	0.996911i	$-0.474972\pi$
$131$	6.92649	−	1.68035i	0.605170	−	0.146813i	0.526625	+	0.850098i	$0.323457\pi$
$132$		0			0
$133$	−3.47957	−	6.53156i	−0.301717	−	0.566358i
$134$		0			0
$135$	−0.958666	−	0.0456669i	−0.0825089	−	0.00393038i
$136$		0			0
$137$	1.03174	+	0.595674i	0.0881473	+	0.0508919i	0.543426	−	0.839457i	$-0.317127\pi$
$137$	1.03174	+	0.595674i	0.0881473	+	0.0508919i	−0.455278	+	0.890349i	$0.650460\pi$
$138$		0			0
$139$			0.772908i			0.0655572i	0.999463	+	0.0327786i	$0.0104356\pi$
$139$			0.772908i			0.0655572i	−0.999463	+	0.0327786i	$0.989564\pi$
$140$		0			0
$141$	1.45554	+	0.935422i	0.122579	+	0.0787767i
$142$		0			0
$143$	−8.34277	−	11.7158i	−0.697657	−	0.979722i
$144$		0			0
$145$	−0.395194	−	1.62901i	−0.0328191	−	0.135282i
$146$		0			0
$147$	−1.15640	−	1.39152i	−0.0953780	−	0.114771i
$148$		0			0
$149$	1.58054	−	8.20062i	0.129483	−	0.671821i	−0.857944	−	0.513743i	$-0.828258\pi$
$149$	1.58054	−	8.20062i	0.129483	−	0.671821i	0.987427	−	0.158077i	$-0.0505295\pi$
$150$		0			0
$151$	4.96253	−	20.4558i	0.403845	−	1.66467i	−0.299711	−	0.954030i	$-0.596890\pi$
$151$	4.96253	−	20.4558i	0.403845	−	1.66467i	0.703556	−	0.710640i	$-0.251595\pi$
$152$		0			0
$153$	15.2550	−	9.80376i	1.23329	−	0.792587i
$154$		0			0
$155$	0.837037	−	0.120348i	0.0672325	−	0.00966657i
$156$		0			0
$157$	6.81436	+	5.35887i	0.543845	+	0.427685i	0.851916	−	0.523679i	$-0.175441\pi$
$157$	6.81436	+	5.35887i	0.543845	+	0.427685i	−0.308070	+	0.951364i	$0.599683\pi$
$158$		0			0
$159$	−0.713735	+	2.06220i	−0.0566028	+	0.163543i
$160$		0			0
$161$	−9.47431	+	8.44023i	−0.746680	+	0.665183i
$162$		0			0
$163$	3.29497	−	9.52020i	0.258082	−	0.745680i	−0.739300	−	0.673376i	$-0.764844\pi$
$163$	3.29497	−	9.52020i	0.258082	−	0.745680i	0.997383	−	0.0723040i	$-0.0230352\pi$
$164$		0			0
$165$	0.530831	+	0.417450i	0.0413251	+	0.0324984i
$166$		0			0
$167$	−3.27928	+	0.471489i	−0.253758	+	0.0364849i	−0.268020	−	0.963413i	$-0.586369\pi$
$167$	−3.27928	+	0.471489i	−0.253758	+	0.0364849i	0.0142617	+	0.999898i	$0.495460\pi$
$168$		0			0
$169$	0.951486	−	0.611483i	0.0731912	−	0.0470371i
$170$		0			0
$171$	−1.93431	+	7.97333i	−0.147920	+	0.609736i
$172$		0			0
$173$	3.78773	−	19.6526i	0.287976	−	1.49416i	−0.493237	−	0.869895i	$-0.664186\pi$
$173$	3.78773	−	19.6526i	0.287976	−	1.49416i	0.781213	−	0.624265i	$-0.214602\pi$
$174$		0			0
$175$	−3.59252	−	11.6512i	−0.271569	−	0.880750i
$176$		0			0
$177$	−0.314705	−	1.29723i	−0.0236547	−	0.0975060i
$178$		0			0
$179$	−7.37530	−	10.3572i	−0.551256	−	0.774130i	0.441111	−	0.897453i	$-0.354585\pi$
$179$	−7.37530	−	10.3572i	−0.551256	−	0.774130i	−0.992367	+	0.123322i	$0.960645\pi$
$180$		0			0
$181$	15.1251	+	9.72029i	1.12424	+	0.722504i	0.964350	−	0.264631i	$-0.0852503\pi$
$181$	15.1251	+	9.72029i	1.12424	+	0.722504i	0.159888	+	0.987135i	$0.448887\pi$
$182$		0			0
$183$		−	1.32299i		−	0.0977986i
$184$		0			0
$185$	0.169839	+	0.0980567i	0.0124868	+	0.00720927i
$186$		0			0
$187$	−25.7801	−	1.22806i	−1.88523	−	0.0898044i
$188$		0			0
$189$	−0.138374	+	4.05507i	−0.0100653	+	0.294963i
$190$		0			0
$191$	−10.2710	+	2.49171i	−0.743180	+	0.180294i	−0.589434	−	0.807817i	$-0.700649\pi$
$191$	−10.2710	+	2.49171i	−0.743180	+	0.180294i	−0.153746	+	0.988110i	$0.549134\pi$
$192$		0			0
$193$	−25.7669	−	2.46045i	−1.85475	−	0.177107i	−0.892819	−	0.450415i	$-0.851276\pi$
$193$	−25.7669	−	2.46045i	−1.85475	−	0.177107i	−0.961926	+	0.273309i	$0.911882\pi$
$194$		0			0
$195$	0.364944	−	0.421168i	0.0261342	−	0.0301605i
$196$		0			0
$197$	5.92241	−	1.73898i	0.421954	−	0.123897i	−0.0638602	−	0.997959i	$-0.520341\pi$
$197$	5.92241	−	1.73898i	0.421954	−	0.123897i	0.485815	+	0.874062i	$0.338523\pi$
$198$		0			0
$199$	0.520455	+	10.9257i	0.0368941	+	0.774502i	0.939193	+	0.343391i	$0.111575\pi$
$199$	0.520455	+	10.9257i	0.0368941	+	0.774502i	−0.902299	+	0.431112i	$0.858121\pi$
$200$		0			0
$201$	0.195547	−	0.153780i	0.0137928	−	0.0108468i
$202$		0			0
$203$	−6.86362	+	1.76346i	−0.481732	+	0.123771i
$204$		0			0
$205$	−4.18639	−	1.44892i	−0.292390	−	0.101197i
$206$		0			0
$207$	14.0671	−	0.00353786i	0.977731	−	0.000245899i
$208$		0			0
$209$	8.82527	−	7.64714i	0.610457	−	0.528964i
$210$		0			0
$211$	−3.55138	+	24.7004i	−0.244487	+	1.70044i	0.384578	+	0.923092i	$0.374347\pi$
$211$	−3.55138	+	24.7004i	−0.244487	+	1.70044i	−0.629065	+	0.777352i	$0.716562\pi$
$212$		0			0
$213$	−0.849265	+	2.12136i	−0.0581907	+	0.145353i
$214$		0			0
$215$	1.75674	−	3.40761i	0.119809	−	0.232397i
$216$		0			0
$217$	−0.556466	−	3.53146i	−0.0377754	−	0.239731i
$218$		0			0
$219$	3.68379	+	0.709993i	0.248928	+	0.0479769i
$220$		0			0
$221$	−2.02456	+	21.2021i	−0.136186	+	1.42621i
$222$		0			0
$223$	1.57854	−	5.37602i	0.105707	−	0.360005i	−0.889604	−	0.456733i	$-0.849020\pi$
$223$	1.57854	−	5.37602i	0.105707	−	0.360005i	0.995311	+	0.0967280i	$0.0308377\pi$
$224$		0			0
$225$	−5.61522	+	12.2956i	−0.374348	+	0.819708i
$226$		0			0
$227$	−4.52279	+	2.33166i	−0.300188	+	0.154758i	−0.601740	−	0.798692i	$-0.705526\pi$
$227$	−4.52279	+	2.33166i	−0.300188	+	0.154758i	0.301552	+	0.953450i	$0.402495\pi$
$228$		0			0
$229$	−9.73303	−	16.8581i	−0.643177	−	1.11402i	−0.984719	−	0.174149i	$-0.944283\pi$
$229$	−9.73303	−	16.8581i	−0.643177	−	1.11402i	0.341542	−	0.939866i	$-0.389051\pi$
$230$		0			0
$231$	1.73437	−	2.26773i	0.114113	−	0.149206i
$232$		0			0
$233$	0.0988018	−	2.07411i	0.00647272	−	0.135879i	−0.993318	−	0.115411i	$-0.963181\pi$
$233$	0.0988018	−	2.07411i	0.00647272	−	0.135879i	0.999791	−	0.0204678i	$-0.00651557\pi$
$234$		0			0
$235$	−3.41251	+	2.43003i	−0.222607	+	0.158518i
$236$		0			0
$237$	−0.825520	−	0.242394i	−0.0536233	−	0.0157452i
$238$		0			0
$239$	6.71103	+	14.6951i	0.434100	+	0.950547i	0.992644	+	0.121072i	$0.0386332\pi$
$239$	6.71103	+	14.6951i	0.434100	+	0.950547i	−0.558543	+	0.829475i	$0.688640\pi$
$240$		0			0
$241$	0.969779	+	2.80199i	0.0624689	+	0.180492i	0.971916	−	0.235327i	$-0.0756161\pi$
$241$	0.969779	+	2.80199i	0.0624689	+	0.180492i	−0.909447	+	0.415819i	$0.863495\pi$
$242$		0			0
$243$	4.67369	−	4.90163i	0.299817	−	0.314439i
$244$		0			0
$245$	4.16854	−	1.34716i	0.266318	−	0.0860667i
$246$		0			0
$247$	−5.95695	−	7.57488i	−0.379032	−	0.481978i
$248$		0			0
$249$	0.306285	−	0.389473i	0.0194100	−	0.0246818i
$250$		0			0
$251$	20.6386	+	23.8182i	1.30270	+	1.50339i	0.729525	+	0.683954i	$0.239741\pi$
$251$	20.6386	+	23.8182i	1.30270	+	1.50339i	0.573170	+	0.819436i	$0.305713\pi$
$252$		0			0
$253$	−16.3120	−	11.6095i	−1.02552	−	0.729884i
$254$		0			0
$255$	−0.189258	−	0.981962i	−0.0118518	−	0.0614929i
$256$		0			0
$257$	−2.33724	−	5.83815i	−0.145793	−	0.364174i	0.837439	−	0.546530i	$-0.184052\pi$
$257$	−2.33724	−	5.83815i	−0.145793	−	0.364174i	−0.983232	+	0.182357i	$0.941627\pi$
$258$		0			0
$259$	0.404820	−	0.723535i	0.0251543	−	0.0449583i
$260$		0			0
$261$	6.98308	+	3.60003i	0.432242	+	0.222836i
$262$		0			0
$263$	23.6747	+	5.74341i	1.45984	+	0.354154i	0.885569	−	0.464509i	$-0.153769\pi$
$263$	23.6747	+	5.74341i	1.45984	+	0.354154i	0.574275	+	0.818663i	$0.305284\pi$
$264$		0			0
$265$	−3.99319	−	3.46012i	−0.245300	−	0.212553i
$266$		0			0
$267$	1.59457	−	0.728215i	0.0975860	−	0.0445660i
$268$		0			0
$269$	20.8138	+	21.8289i	1.26904	+	1.33093i	0.919032	+	0.394182i	$0.128972\pi$
$269$	20.8138	+	21.8289i	1.26904	+	1.33093i	0.350006	+	0.936747i	$0.386179\pi$
$270$		0			0
$271$	−2.06778	−	21.6548i	−0.125609	−	1.31544i	−0.810047	−	0.586365i	$-0.800558\pi$
$271$	−2.06778	−	21.6548i	−0.125609	−	1.31544i	0.684438	−	0.729071i	$-0.260048\pi$
$272$		0			0
$273$	−1.80117	−	1.51867i	−0.109012	−	0.0919143i
$274$		0			0
$275$	16.6613	−	9.61938i	1.00471	−	0.580070i
$276$		0			0
$277$	−14.7085	+	25.4759i	−0.883749	+	1.53070i	−0.0366073	+	0.999330i	$0.511655\pi$
$277$	−14.7085	+	25.4759i	−0.883749	+	1.53070i	−0.847141	+	0.531368i	$0.821678\pi$
$278$		0			0
$279$	−2.14279	+	3.33425i	−0.128286	+	0.199616i
$280$		0			0
$281$	14.4996	+	6.62173i	0.864972	+	0.395020i	0.797944	−	0.602732i	$-0.205921\pi$
$281$	14.4996	+	6.62173i	0.864972	+	0.395020i	0.0670281	+	0.997751i	$0.478648\pi$
$282$		0			0
$283$	13.4912	−	12.8638i	0.801969	−	0.764676i	−0.173495	−	0.984835i	$-0.555506\pi$
$283$	13.4912	−	12.8638i	0.801969	−	0.764676i	0.975464	+	0.220158i	$0.0706575\pi$
$284$		0			0
$285$	0.368570	+	0.262458i	0.0218322	+	0.0155466i
$286$		0			0
$287$	−5.88615	+	17.7793i	−0.347448	+	1.04948i
$288$		0			0
$289$	15.3574	+	14.6433i	0.903377	+	0.861368i
$290$		0			0
$291$	1.04491	−	0.0497751i	0.0612536	−	0.00291787i
$292$		0			0
$293$	−3.08781	−	21.4762i	−0.180392	−	1.25465i	−0.855838	−	0.517244i	$-0.826958\pi$
$293$	−3.08781	−	21.4762i	−0.180392	−	1.25465i	0.675446	−	0.737409i	$-0.263951\pi$
$294$		0			0
$295$	3.19916	+	0.459970i	0.186262	+	0.0267805i
$296$		0			0
$297$	−6.28659	+	1.21164i	−0.364785	+	0.0703066i
$298$		0			0
$299$	−10.2101	+	12.9900i	−0.590468	+	0.751229i
$300$		0			0
$301$	−14.5048	−	7.23178i	−0.836043	−	0.416833i
$302$		0			0
$303$	2.89457	−	1.15881i	0.166289	−	0.0665719i
$304$		0			0
$305$	2.97387	+	1.19056i	0.170283	+	0.0681711i
$306$		0			0
$307$	16.3142	+	25.3853i	0.931098	+	1.44882i	0.893264	+	0.449533i	$0.148410\pi$
$307$	16.3142	+	25.3853i	0.931098	+	1.44882i	0.0378348	+	0.999284i	$0.487954\pi$
$308$		0			0
$309$	−0.595290	−	2.02737i	−0.0338649	−	0.115333i
$310$		0			0
$311$	23.4001	−	8.09885i	1.32690	−	0.459244i	0.430538	−	0.902572i	$-0.358324\pi$
$311$	23.4001	−	8.09885i	1.32690	−	0.459244i	0.896359	+	0.443329i	$0.146203\pi$
$312$		0			0
$313$	−18.3413	+	25.7568i	−1.03671	+	1.45586i	−0.152770	+	0.988262i	$0.548820\pi$
$313$	−18.3413	+	25.7568i	−1.03671	+	1.45586i	−0.883942	+	0.467597i	$0.845120\pi$
$314$		0			0
$315$	−4.44468	−	1.95780i	−0.250429	−	0.110309i
$316$		0			0
$317$	−13.7976	+	1.31751i	−0.774951	+	0.0739988i	−0.475035	−	0.879967i	$-0.657565\pi$
$317$	−13.7976	+	1.31751i	−0.774951	+	0.0739988i	−0.299916	+	0.953966i	$0.596959\pi$
$318$		0			0
$319$	−5.12388	−	9.93893i	−0.286882	−	0.556473i
$320$		0			0
$321$	−0.524255			−0.0292610
$322$		0			0
$323$	−17.2926			−0.962187
$324$		0			0
$325$	−7.27496	−	14.1115i	−0.403542	−	0.782763i
$326$		0			0
$327$	2.37432	−	0.226720i	0.131300	−	0.0125376i
$328$		0			0
$329$	10.4668	+	14.2868i	0.577055	+	0.787654i
$330$		0			0
$331$	−11.6966	+	16.4256i	−0.642905	+	0.902834i	−0.999506	−	0.0314225i	$-0.989996\pi$
$331$	−11.6966	+	16.4256i	−0.642905	+	0.902834i	0.356601	+	0.934257i	$0.383936\pi$
$332$		0			0
$333$	−0.868606	+	0.300627i	−0.0475993	+	0.0164743i
$334$		0			0
$335$	0.169699	+	0.577942i	0.00927165	+	0.0315764i
$336$		0			0
$337$	18.6939	+	29.0882i	1.01832	+	1.58454i	0.792037	+	0.610474i	$0.209021\pi$
$337$	18.6939	+	29.0882i	1.01832	+	1.58454i	0.226282	+	0.974062i	$0.427343\pi$
$338$		0			0
$339$	−3.11908	−	1.24869i	−0.169405	−	0.0678195i
$340$		0			0
$341$	5.23702	−	2.09658i	0.283600	−	0.113536i
$342$		0			0
$343$	−5.93241	−	17.5444i	−0.320320	−	0.947309i
$344$		0			0
$345$	0.288145	−	0.720276i	0.0155132	−	0.0387784i
$346$		0			0
$347$	−21.2819	+	4.10174i	−1.14247	+	0.220193i	−0.725166	−	0.688574i	$-0.758237\pi$
$347$	−21.2819	+	4.10174i	−1.14247	+	0.220193i	−0.417304	+	0.908767i	$0.637025\pi$
$348$		0			0
$349$	−7.89776	−	1.13553i	−0.422757	−	0.0607833i	−0.0723469	−	0.997380i	$-0.523049\pi$
$349$	−7.89776	−	1.13553i	−0.422757	−	0.0607833i	−0.350411	+	0.936596i	$0.613958\pi$
$350$		0			0
$351$	0.751898	+	5.22957i	0.0401334	+	0.279134i
$352$		0			0
$353$	−5.37565	+	0.256074i	−0.286117	+	0.0136294i	−0.190150	−	0.981755i	$-0.560897\pi$
$353$	−5.37565	+	0.256074i	−0.286117	+	0.0136294i	−0.0959670	+	0.995385i	$0.530594\pi$
$354$		0			0
$355$	−4.00421	−	3.81801i	−0.212521	−	0.202639i
$356$		0			0
$357$	−4.14015	+	0.856026i	−0.219120	+	0.0453057i
$358$		0			0
$359$	21.7816	+	15.5106i	1.14959	+	0.818617i	0.985808	−	0.167880i	$-0.0536920\pi$
$359$	21.7816	+	15.5106i	1.14959	+	0.818617i	0.163780	+	0.986497i	$0.447631\pi$
$360$		0			0
$361$	−8.08838	+	7.71225i	−0.425704	+	0.405908i
$362$		0			0
$363$	1.51149	+	0.690275i	0.0793327	+	0.0362300i
$364$		0			0
$365$	−4.91097	+	7.64162i	−0.257052	+	0.399980i
$366$		0			0
$367$	3.78031	−	6.54770i	0.197331	−	0.341787i	−0.750331	−	0.661062i	$-0.770106\pi$
$367$	3.78031	−	6.54770i	0.197331	−	0.341787i	0.947662	+	0.319275i	$0.103439\pi$
$368$		0			0
$369$	17.9813	−	10.3815i	0.936069	−	0.540440i
$370$		0			0
$371$	−14.3989	+	17.0773i	−0.747553	+	0.886610i
$372$		0			0
$373$	0.377907	+	3.95762i	0.0195673	+	0.204918i	0.999969	+	0.00790772i	$0.00251713\pi$
$373$	0.377907	+	3.95762i	0.0195673	+	0.204918i	−0.980401	+	0.197010i	$0.936877\pi$
$374$		0			0
$375$	1.07255	+	1.12486i	0.0553863	+	0.0580875i
$376$		0			0
$377$	−8.39378	+	3.83331i	−0.432302	+	0.197426i
$378$		0			0
$379$	−25.2134	−	21.8475i	−1.29512	−	1.12223i	−0.985189	−	0.171473i	$-0.945147\pi$
$379$	−25.2134	−	21.8475i	−1.29512	−	1.12223i	−0.309935	−	0.950758i	$-0.600307\pi$
$380$		0			0
$381$	2.33359	+	0.566124i	0.119554	+	0.0290034i
$382$		0			0
$383$	19.2716	+	9.93522i	0.984735	+	0.507666i	0.873865	−	0.486169i	$-0.161606\pi$
$383$	19.2716	+	9.93522i	0.984735	+	0.507666i	0.110870	+	0.993835i	$0.464636\pi$
$384$		0			0
$385$	3.53672	+	5.93929i	0.180248	+	0.302694i
$386$		0			0
$387$	6.67821	+	16.6814i	0.339473	+	0.847962i
$388$		0			0
$389$	−1.44576	−	7.50129i	−0.0733027	−	0.380331i	−0.999990	−	0.00449697i	$-0.998569\pi$
$389$	−1.44576	−	7.50129i	−0.0733027	−	0.380331i	0.926687	−	0.375834i	$-0.122644\pi$
$390$		0			0
$391$	6.99722	+	28.8113i	0.353865	+	1.45705i
$392$		0			0
$393$	1.20641	+	1.39227i	0.0608552	+	0.0702306i
$394$		0			0
$395$	1.28774	−	1.63750i	0.0647934	−	0.0823914i
$396$		0			0
$397$	23.9036	+	30.3959i	1.19969	+	1.52552i	0.789773	+	0.613400i	$0.210199\pi$
$397$	23.9036	+	30.3959i	1.19969	+	1.52552i	0.409913	+	0.912125i	$0.365559\pi$
$398$		0			0
$399$	1.08844	−	1.57298i	0.0544902	−	0.0787477i
$400$		0			0
$401$	−3.60332	+	3.77905i	−0.179941	+	0.188717i	−0.807527	−	0.589830i	$-0.799195\pi$
$401$	−3.60332	+	3.77905i	−0.179941	+	0.188717i	0.627586	+	0.778547i	$0.284043\pi$
$402$		0			0
$403$	−1.52256	−	4.39916i	−0.0758443	−	0.219138i
$404$		0			0
$405$	2.18466	+	4.78374i	0.108557	+	0.237706i
$406$		0			0
$407$	1.25523	+	0.368570i	0.0622197	+	0.0182693i
$408$		0			0
$409$	16.7824	−	11.9507i	0.829837	−	0.590924i	−0.0842492	−	0.996445i	$-0.526849\pi$
$409$	16.7824	−	11.9507i	0.829837	−	0.590924i	0.914086	+	0.405521i	$0.132910\pi$
$410$		0			0
$411$	−0.0146519	+	0.307582i	−0.000722726	+	0.0151719i
$412$		0			0
$413$	1.76195	−	13.5497i	0.0866998	−	0.666737i
$414$		0			0
$415$	0.599844	+	1.03896i	0.0294452	+	0.0510006i
$416$		0			0
$417$	−0.177567	+	0.0915423i	−0.00869551	+	0.00448285i
$418$		0			0
$419$	4.12230	−	9.02658i	0.201387	−	0.440977i	−0.781811	−	0.623515i	$-0.785704\pi$
$419$	4.12230	−	9.02658i	0.201387	−	0.440977i	0.983199	+	0.182538i	$0.0584313\pi$
$420$		0			0
$421$	−1.72868	+	5.88733i	−0.0842506	+	0.286931i	−0.990832	−	0.135100i	$-0.956864\pi$
$421$	−1.72868	+	5.88733i	−0.0842506	+	0.286931i	0.906581	+	0.422031i	$0.138683\pi$
$422$		0			0
$423$	1.86640	−	19.5458i	0.0907475	−	0.950351i
$424$		0			0
$425$	−27.9748	−	5.39171i	−1.35698	−	0.261536i
$426$		0			0
$427$	4.86313	−	12.6390i	0.235343	−	0.611644i
$428$		0			0
$429$	1.70347	−	3.30426i	0.0822441	−	0.159531i
$430$		0			0
$431$	10.4054	−	25.9913i	0.501208	−	1.25196i	−0.434974	−	0.900443i	$-0.643243\pi$
$431$	10.4054	−	25.9913i	0.501208	−	1.25196i	0.936182	−	0.351515i	$-0.114333\pi$
$432$		0			0
$433$	2.44090	−	16.9769i	0.117302	−	0.815856i	−0.843203	−	0.537595i	$-0.819333\pi$
$433$	2.44090	−	16.9769i	0.117302	−	0.815856i	0.960506	−	0.278261i	$-0.0897579\pi$
$434$		0			0
$435$	0.327442	−	0.283730i	0.0156996	−	0.0136038i
$436$		0			0
$437$	−11.2870	−	7.24970i	−0.539930	−	0.346800i
$438$		0			0
$439$	−10.7094	−	3.70656i	−0.511132	−	0.176904i	0.0593146	−	0.998239i	$-0.481109\pi$
$439$	−10.7094	−	3.70656i	−0.511132	−	0.176904i	−0.570446	+	0.821335i	$0.693230\pi$
$440$		0			0
$441$	−8.02252	+	18.9002i	−0.382025	+	0.900008i
$442$		0			0
$443$	−8.70155	+	6.84298i	−0.413423	+	0.325120i	−0.803113	−	0.595826i	$-0.796825\pi$
$443$	−8.70155	+	6.84298i	−0.413423	+	0.325120i	0.389690	+	0.920946i	$0.372582\pi$
$444$		0			0
$445$	0.201959	+	4.23963i	0.00957376	+	0.200978i
$446$		0			0
$447$	2.07120	−	0.608160i	0.0979645	−	0.0287650i
$448$		0			0
$449$	13.2326	−	15.2712i	0.624484	−	0.720693i	−0.352068	−	0.935974i	$-0.614521\pi$
$449$	13.2326	−	15.2712i	0.624484	−	0.720693i	0.976552	+	0.215282i	$0.0690669\pi$
$450$		0			0
$451$	−29.4179	−	2.80907i	−1.38524	−	0.132274i
$452$		0			0
$453$	5.28726	−	1.28268i	0.248417	−	0.0602654i
$454$		0			0
$455$	5.03458	−	2.68208i	0.236025	−	0.125738i
$456$		0			0
$457$	14.1916	+	0.676029i	0.663855	+	0.0316233i	0.376805	−	0.926292i	$-0.377023\pi$
$457$	14.1916	+	0.676029i	0.663855	+	0.0316233i	0.287049	+	0.957916i	$0.407326\pi$
$458$		0			0
$459$	8.21063	+	4.74041i	0.383239	+	0.221263i
$460$		0			0
$461$		−	12.3102i		−	0.573341i	−0.958029	−	0.286671i	$-0.907451\pi$
$461$		−	12.3102i		−	0.573341i	0.958029	−	0.286671i	$-0.0925486\pi$
$462$		0			0
$463$	−15.6870	−	10.0814i	−0.729038	−	0.468524i	0.122732	−	0.992440i	$-0.460834\pi$
$463$	−15.6870	−	10.0814i	−0.729038	−	0.468524i	−0.851770	+	0.523915i	$0.824471\pi$
$464$		0			0
$465$	0.126786	+	0.178047i	0.00587958	+	0.00825671i
$466$		0			0
$467$	0.831100	+	3.42584i	0.0384587	+	0.158529i	0.987803	−	0.155709i	$-0.0497662\pi$
$467$	0.831100	+	3.42584i	0.0384587	+	0.158529i	−0.949344	+	0.314238i	$0.898251\pi$
$468$		0			0
$469$	2.43340	−	0.750309i	0.112364	−	0.0346460i
$470$		0			0
$471$	−0.424059	+	2.20023i	−0.0195396	+	0.101381i
$472$		0			0
$473$	6.02937	−	24.8534i	0.277231	−	1.14276i
$474$		0			0
$475$	10.8440	−	6.96900i	0.497555	−	0.319759i
$476$		0			0
$477$	24.5122	−	3.52432i	1.12234	−	0.161368i
$478$		0			0
$479$	−5.40542	−	4.25087i	−0.246980	−	0.194227i	0.486993	−	0.873406i	$-0.338094\pi$
$479$	−5.40542	−	4.25087i	−0.246980	−	0.194227i	−0.733973	+	0.679179i	$0.762336\pi$
$480$		0			0
$481$	0.353097	−	1.02021i	0.0160999	−	0.0465175i
$482$		0			0
$483$	−3.06118	−	1.17697i	−0.139288	−	0.0535540i
$484$		0			0
$485$	−0.828421	+	2.39357i	−0.0376167	+	0.108686i
$486$		0			0
$487$	12.2332	+	9.62029i	0.554339	+	0.435937i	0.855624	−	0.517597i	$-0.173173\pi$
$487$	12.2332	+	9.62029i	0.554339	+	0.435937i	−0.301286	+	0.953534i	$0.597416\pi$
$488$		0			0
$489$	2.57742	−	0.370577i	0.116555	−	0.0167581i
$490$		0			0
$491$	0.356969	−	0.229410i	0.0161098	−	0.0103531i	−0.532561	−	0.846392i	$-0.678770\pi$
$491$	0.356969	−	0.229410i	0.0161098	−	0.0103531i	0.548671	+	0.836038i	$0.315134\pi$
$492$		0			0
$493$	−3.90389	+	16.0920i	−0.175822	+	0.724749i
$494$		0			0
$495$	1.45034	−	7.52507i	0.0651879	−	0.338227i
$496$		0			0
$497$	−15.9111	+	17.1443i	−0.713711	+	0.769027i
$498$		0			0
$499$	−9.61625	−	39.6387i	−0.430483	−	1.77447i	−0.611762	−	0.791042i	$-0.709539\pi$
$499$	−9.61625	−	39.6387i	−0.430483	−	1.77447i	0.181280	−	0.983432i	$-0.441976\pi$
$500$		0			0
$501$	−0.496714	−	0.697537i	−0.0221915	−	0.0311636i
$502$		0			0
$503$	8.90177	+	5.72082i	0.396910	+	0.255079i	0.723837	−	0.689971i	$-0.242377\pi$
$503$	8.90177	+	5.72082i	0.396910	+	0.255079i	−0.326927	+	0.945050i	$0.606013\pi$
$504$		0			0
$505$			7.54930i			0.335940i
$506$		0			0
$507$	0.253175	+	0.146170i	0.0112439	+	0.00649166i
$508$		0			0
$509$	−8.65367	−	0.412225i	−0.383567	−	0.0182715i	−0.145087	−	0.989419i	$-0.546346\pi$
$509$	−8.65367	−	0.412225i	−0.383567	−	0.0182715i	−0.238480	+	0.971147i	$0.576649\pi$
$510$		0			0
$511$	32.5827	+	20.3239i	1.44137	+	0.899074i
$512$		0			0
$513$	−4.16871	+	1.01132i	−0.184053	+	0.0446508i
$514$		0			0
$515$	5.09289	+	0.486312i	0.224419	+	0.0214295i
$516$		0			0
$517$	−18.3007	+	21.1201i	−0.804862	+	0.928860i
$518$		0			0
$519$	4.96359	−	1.45744i	0.217878	−	0.0639746i
$520$		0			0
$521$	2.07547	+	43.5695i	0.0909281	+	1.90882i	0.340153	+	0.940370i	$0.389521\pi$
$521$	2.07547	+	43.5695i	0.0909281	+	1.90882i	−0.249225	+	0.968446i	$0.580176\pi$
$522$		0			0
$523$	−8.21749	+	6.46231i	−0.359326	+	0.282577i	−0.781459	−	0.623957i	$-0.785524\pi$
$523$	−8.21749	+	6.46231i	−0.359326	+	0.282577i	0.422133	+	0.906534i	$0.361282\pi$
$524$		0			0
$525$	2.25125	−	2.20530i	0.0982527	−	0.0962472i
$526$		0			0
$527$	−7.89417	−	2.73220i	−0.343875	−	0.119016i
$528$		0			0
$529$	−7.51163	+	21.7388i	−0.326593	+	0.945165i
$530$		0			0
$531$	−11.4483	+	9.91999i	−0.496813	+	0.430491i
$532$		0			0
$533$	−3.47062	+	24.1387i	−0.150329	+	1.04556i
$534$		0			0
$535$	0.471774	−	1.17843i	0.0203966	−	0.0509482i
$536$		0			0
$537$	1.50592	−	2.92109i	0.0649855	−	0.126054i
$538$		0			0
$539$	24.9049	−	15.2891i	1.07273	−	0.658548i
$540$		0			0
$541$	−40.0799	−	7.72477i	−1.72317	−	0.332114i	−0.770805	−	0.637072i	$-0.780146\pi$
$541$	−40.0799	−	7.72477i	−1.72317	−	0.332114i	−0.952366	+	0.304958i	$0.901358\pi$
$542$		0			0
$543$	−0.441738	+	4.62609i	−0.0189568	+	0.198524i
$544$		0			0
$545$	−1.62701	+	5.54108i	−0.0696934	+	0.237354i
$546$		0			0
$547$	16.1096	−	35.2752i	0.688798	−	1.50826i	−0.164246	−	0.986419i	$-0.552519\pi$
$547$	16.1096	−	35.2752i	0.688798	−	1.50826i	0.853044	−	0.521838i	$-0.174754\pi$
$548$		0			0
$549$	−13.3446	+	6.87963i	−0.569534	+	0.293615i
$550$		0			0
$551$	−3.74604	−	6.48833i	−0.159587	−	0.276412i
$552$		0			0
$553$	−6.99546	−	5.35016i	−0.297477	−	0.227512i
$554$		0			0
$555$	−0.00241192	+	0.0506325i	−0.000102380	+	0.00214923i
$556$		0			0
$557$	−0.0110096	+	0.00783992i	−0.000466493	+	0.000332188i	−0.580290	−	0.814410i	$-0.697061\pi$
$557$	−0.0110096	+	0.00783992i	−0.000466493	+	0.000332188i	0.579824	+	0.814742i	$0.303121\pi$
$558$		0			0
$559$	−20.2497	−	5.94586i	−0.856472	−	0.251483i
$560$		0			0
$561$	−2.77123	−	6.06815i	−0.117001	−	0.256197i
$562$		0			0
$563$	−14.0041	−	40.4623i	−0.590204	−	1.70528i	−0.702569	−	0.711616i	$-0.747964\pi$
$563$	−14.0041	−	40.4623i	−0.590204	−	1.70528i	0.112364	−	0.993667i	$-0.464158\pi$
$564$		0			0
$565$	5.61368	−	5.88746i	0.236169	−	0.247687i
$566$		0			0
$567$	20.0972	−	9.50778i	0.844003	−	0.399289i
$568$		0			0
$569$	−11.5365	−	14.6698i	−0.483635	−	0.614991i	0.481595	−	0.876394i	$-0.340057\pi$
$569$	−11.5365	−	14.6698i	−0.483635	−	0.614991i	−0.965230	+	0.261402i	$0.915815\pi$
$570$		0			0
$571$	15.8854	−	20.2000i	0.664785	−	0.845343i	−0.330350	−	0.943858i	$-0.607167\pi$
$571$	15.8854	−	20.2000i	0.664785	−	0.845343i	0.995136	+	0.0985154i	$0.0314094\pi$
$572$		0			0
$573$	−1.78892	−	2.06453i	−0.0747333	−	0.0862469i
$574$		0			0
$575$	−15.9989	−	15.2473i	−0.667202	−	0.635855i
$576$		0			0
$577$	2.46940	+	12.8125i	0.102803	+	0.533391i	0.996419	+	0.0845583i	$0.0269479\pi$
$577$	2.46940	+	12.8125i	0.102803	+	0.533391i	−0.893616	+	0.448833i	$0.851840\pi$
$578$		0			0
$579$	−2.48655	−	6.21109i	−0.103337	−	0.258124i
$580$		0			0
$581$	4.35768	−	2.59490i	0.180787	−	0.107655i
$582$		0			0
$583$	−31.3285	−	16.1509i	−1.29749	−	0.668904i
$584$		0			0
$585$	−6.14591	−	1.49098i	−0.254102	−	0.0616445i
$586$		0			0
$587$	−24.2737	−	21.0333i	−1.00188	−	0.868138i	−0.0106089	−	0.999944i	$-0.503377\pi$
$587$	−24.2737	−	21.0333i	−1.00188	−	0.868138i	−0.991276	+	0.131806i	$0.957922\pi$
$588$		0			0
$589$	3.43806	−	1.57011i	0.141663	−	0.0646953i
$590$		0			0
$591$	1.10096	+	1.15465i	0.0452873	+	0.0474959i
$592$		0			0
$593$	−3.67663	−	38.5034i	−0.150981	−	1.58115i	−0.680436	−	0.732807i	$-0.738210\pi$
$593$	−3.67663	−	38.5034i	−0.150981	−	1.58115i	0.529455	−	0.848338i	$-0.322396\pi$
$594$		0			0
$595$	1.80150	−	10.0767i	0.0738544	−	0.413104i
$596$		0			0
$597$	−2.44842	+	1.41360i	−0.100207	+	0.0578547i
$598$		0			0
$599$	9.71008	−	16.8184i	0.396743	−	0.687179i	−0.596579	−	0.802554i	$-0.703474\pi$
$599$	9.71008	−	16.8184i	0.396743	−	0.687179i	0.993322	+	0.115375i	$0.0368071\pi$
$600$		0			0
$601$	7.86830	−	12.2433i	0.320955	−	0.499415i	−0.642862	−	0.765982i	$-0.722253\pi$
$601$	7.86830	−	12.2433i	0.320955	−	0.499415i	0.963816	+	0.266567i	$0.0858893\pi$
$602$		0			0
$603$	−2.56798	−	1.17276i	−0.104576	−	0.0477584i
$604$		0			0
$605$	−2.91180	+	2.77640i	−0.118382	+	0.112877i
$606$		0			0
$607$	−9.00149	−	6.40993i	−0.365359	−	0.260171i	0.382602	−	0.923913i	$-0.375028\pi$
$607$	−9.00149	−	6.40993i	−0.365359	−	0.260171i	−0.747962	+	0.663742i	$0.768967\pi$
$608$		0			0
$609$	−1.21806	−	1.36798i	−0.0493581	−	0.0554334i
$610$		0			0
$611$	16.6905	+	15.9144i	0.675227	+	0.643827i
$612$		0			0
$613$	4.95930	−	0.236241i	0.200304	−	0.00954167i	0.0528100	−	0.998605i	$-0.483182\pi$
$613$	4.95930	−	0.236241i	0.200304	−	0.00954167i	0.147494	+	0.989063i	$0.452879\pi$
$614$		0			0
$615$	−0.162956	−	1.13339i	−0.00657103	−	0.0457025i
$616$		0			0
$617$	−6.10211	−	0.877351i	−0.245662	−	0.0353208i	0.0183839	−	0.999831i	$-0.494148\pi$
$617$	−6.10211	−	0.877351i	−0.245662	−	0.0353208i	−0.264046	+	0.964510i	$0.585057\pi$
$618$		0			0
$619$	21.4553	−	4.13518i	0.862363	−	0.166207i	0.261152	−	0.965298i	$-0.415898\pi$
$619$	21.4553	−	4.13518i	0.862363	−	0.166207i	0.601210	+	0.799091i	$0.294685\pi$
$620$		0			0
$621$	3.37177	+	6.53629i	0.135305	+	0.262292i
$622$		0			0
$623$	17.9102	−	1.09549i	0.717559	−	0.0438897i
$624$		0			0
$625$	17.8975	−	7.16507i	0.715899	−	0.286603i
$626$		0			0
$627$	2.80210	+	1.12179i	0.111905	+	0.0448001i
$628$		0			0
$629$	−1.04738	−	1.62975i	−0.0417616	−	0.0649823i
$630$		0			0
$631$	5.96210	+	20.3050i	0.237347	+	0.808331i	0.988890	+	0.148647i	$0.0474918\pi$
$631$	5.96210	+	20.3050i	0.237347	+	0.808331i	−0.751543	+	0.659684i	$0.770690\pi$
$632$		0			0
$633$	−6.09527	+	2.10959i	−0.242265	+	0.0838488i
$634$		0			0
$635$	−3.37254	+	4.73607i	−0.133835	+	0.187945i
$636$		0			0
$637$	−11.6248	−	21.1292i	−0.460590	−	0.837170i
$638$		0			0
$639$	25.8137	−	2.46491i	1.02117	−	0.0975103i
$640$		0			0
$641$	−9.81979	−	19.0477i	−0.387858	−	0.752340i	0.611381	−	0.791336i	$-0.290614\pi$
$641$	−9.81979	−	19.0477i	−0.387858	−	0.752340i	−0.999239	+	0.0389961i	$0.987584\pi$
$642$		0			0
$643$	−21.0422			−0.829822			−0.414911	−	0.909862i	$-0.636187\pi$
$643$	−21.0422			−0.829822			−0.414911	+	0.909862i	$0.636187\pi$
$644$		0			0
$645$	0.990928			0.0390178
$646$		0			0
$647$	−4.33962	−	8.41769i	−0.170608	−	0.330933i	0.787994	−	0.615683i	$-0.211120\pi$
$647$	−4.33962	−	8.41769i	−0.170608	−	0.330933i	−0.958602	+	0.284750i	$0.908090\pi$
$648$		0			0
$649$	21.4627	−	2.04944i	0.842484	−	0.0804474i
$650$		0			0
$651$	0.745407	−	0.546104i	0.0292148	−	0.0214035i
$652$		0			0
$653$	9.81206	−	13.7791i	0.383976	−	0.539218i	−0.576677	−	0.816973i	$-0.695651\pi$
$653$	9.81206	−	13.7791i	0.383976	−	0.539218i	0.960652	+	0.277754i	$0.0895901\pi$
$654$		0			0
$655$	−4.21522	+	1.45890i	−0.164702	+	0.0570040i
$656$		0			0
$657$	−11.9944	−	40.8492i	−0.467946	−	1.59368i
$658$		0			0
$659$	8.10701	+	12.6148i	0.315804	+	0.491401i	0.962476	−	0.271367i	$-0.0874759\pi$
$659$	8.10701	+	12.6148i	0.315804	+	0.491401i	−0.646671	+	0.762769i	$0.723840\pi$
$660$		0			0
$661$	27.0686	+	10.8366i	1.05285	+	0.421497i	0.832558	−	0.553938i	$-0.186876\pi$
$661$	27.0686	+	10.8366i	1.05285	+	0.421497i	0.220290	+	0.975435i	$0.429300\pi$
$662$		0			0
$663$	−5.11074	+	2.04603i	−0.198485	+	0.0794613i
$664$		0			0
$665$	2.55632	+	3.86215i	0.0991297	+	0.149768i
$666$		0			0
$667$	−9.29446	+	8.86671i	−0.359883	+	0.343320i
$668$		0			0
$669$	1.42204	−	0.274077i	0.0549794	−	0.0105964i
$670$		0			0
$671$	21.1512	+	3.04108i	0.816531	+	0.117399i
$672$		0			0
$673$	−4.11313	−	28.6074i	−0.158549	−	1.10273i	−0.901309	−	0.433177i	$-0.857393\pi$
$673$	−4.11313	−	28.6074i	−0.158549	−	1.10273i	0.742760	−	0.669558i	$-0.233516\pi$
$674$		0			0
$675$	−7.05918	+	0.336270i	−0.271708	+	0.0129430i
$676$		0			0
$677$	28.8280	+	27.4874i	1.10795	+	1.05643i	0.998046	+	0.0624860i	$0.0199029\pi$
$677$	28.8280	+	27.4874i	1.10795	+	1.05643i	0.109904	+	0.993942i	$0.464946\pi$
$678$		0			0
$679$	10.1653	+	3.36540i	0.390109	+	0.129152i
$680$		0			0
$681$	−1.07135	−	0.762904i	−0.0410542	−	0.0292346i
$682$		0			0
$683$	−3.79683	+	3.62027i	−0.145282	+	0.138526i	−0.759235	−	0.650816i	$-0.774427\pi$
$683$	−3.79683	+	3.62027i	−0.145282	+	0.138526i	0.613953	+	0.789342i	$0.289578\pi$
$684$		0			0
$685$	−0.678206	−	0.309726i	−0.0259129	−	0.0118340i
$686$		0			0
$687$	2.72020	−	4.23272i	0.103782	−	0.161488i
$688$		0			0
$689$	−14.5432	+	25.1896i	−0.554053	+	0.959649i
$690$		0			0
$691$	3.76140	−	2.17165i	0.143091	−	0.0826134i	−0.426746	−	0.904372i	$-0.640340\pi$
$691$	3.76140	−	2.17165i	0.143091	−	0.0826134i	0.569836	+	0.821758i	$0.307007\pi$
$692$		0			0
$693$	−31.8927	−	5.70174i	−1.21150	−	0.216591i
$694$		0			0
$695$	−0.0459795	−	0.481520i	−0.00174410	−	0.0182651i
$696$		0			0
$697$	30.1990	+	31.6718i	1.14387	+	1.19965i
$698$		0			0
$699$	0.488206	−	0.222956i	0.0184656	−	0.00843297i
$700$		0			0
$701$	−5.47555	−	4.74459i	−0.206809	−	0.179201i	0.545298	−	0.838242i	$-0.316417\pi$
$701$	−5.47555	−	4.74459i	−0.206809	−	0.179201i	−0.752106	+	0.659042i	$0.770962\pi$
$702$		0			0
$703$	0.851823	+	0.206650i	0.0321271	+	0.00779396i
$704$		0			0
$705$	−0.962448	−	0.496176i	−0.0362479	−	0.0186871i
$706$		0			0
$707$	31.9124	−	0.430503i	1.20019	−	0.0161907i
$708$		0			0
$709$	−2.38222	−	5.95049i	−0.0894660	−	0.223475i	0.876886	−	0.480698i	$-0.159617\pi$
$709$	−2.38222	−	5.95049i	−0.0894660	−	0.223475i	−0.966352	+	0.257223i	$0.917193\pi$
$710$		0			0
$711$	1.84778	+	9.58721i	0.0692973	+	0.359548i
$712$		0			0
$713$	−4.00713	−	5.09285i	−0.150068	−	0.190729i
$714$		0			0
$715$	5.89448	+	6.80259i	0.220441	+	0.254403i
$716$		0			0
$717$	−2.58120	+	3.28226i	−0.0963966	+	0.122578i
$718$		0			0
$719$	23.1298	+	29.4119i	0.862596	+	1.09688i	0.994408	+	0.105606i	$0.0336782\pi$
$719$	23.1298	+	29.4119i	0.862596	+	1.09688i	−0.131812	+	0.991275i	$0.542079\pi$
$720$		0			0
$721$	1.76531	−	21.5564i	0.0657436	−	0.802801i
$722$		0			0
$723$	−0.528868	+	0.554661i	−0.0196688	+	0.0206281i
$724$		0			0
$725$	−4.03708	−	11.6644i	−0.149933	−	0.433204i
$726$		0			0
$727$	−18.2215	−	39.8994i	−0.675797	−	1.47979i	−0.867036	−	0.498245i	$-0.833978\pi$
$727$	−18.2215	−	39.8994i	−0.675797	−	1.47979i	0.191240	−	0.981543i	$-0.438749\pi$
$728$		0			0
$729$	−22.5088	−	6.60917i	−0.833658	−	0.244784i
$730$		0			0
$731$	−30.8494	+	21.9677i	−1.14100	+	0.812506i
$732$		0			0
$733$	−1.94344	+	40.7978i	−0.0717825	+	1.50690i	0.619890	+	0.784689i	$0.287177\pi$
$733$	−1.94344	+	40.7978i	−0.0717825	+	1.50690i	−0.691673	+	0.722211i	$0.743126\pi$
$734$		0			0
$735$	0.803212	+	0.798122i	0.0296269	+	0.0294392i
$736$		0			0
$737$	2.00904	+	3.47976i	0.0740039	+	0.128179i
$738$		0			0
$739$	−42.5034	+	21.9120i	−1.56351	+	0.806046i	−0.999801	−	0.0199264i	$-0.993657\pi$
$739$	−42.5034	+	21.9120i	−1.56351	+	0.806046i	−0.563710	+	0.825973i	$0.690627\pi$
$740$		0			0
$741$	1.03471	−	2.26571i	0.0380111	−	0.0832328i
$742$		0			0
$743$	9.16766	−	31.2222i	0.336329	−	1.14543i	−0.601657	−	0.798755i	$-0.705492\pi$
$743$	9.16766	−	31.2222i	0.336329	−	1.14543i	0.937985	−	0.346675i	$-0.112689\pi$
$744$		0			0
$745$	−0.496825	+	5.20299i	−0.0182023	+	0.190623i
$746$		0			0
$747$	−5.52118	−	1.06412i	−0.202009	−	0.0389341i
$748$		0			0
$749$	−5.00838	−	1.92708i	−0.183002	−	0.0704140i
$750$		0			0
$751$	15.3235	−	29.7234i	0.559162	−	1.08462i	−0.424640	−	0.905362i	$-0.639599\pi$
$751$	15.3235	−	29.7234i	0.559162	−	1.08462i	0.983802	−	0.179260i	$-0.0573704\pi$
$752$		0			0
$753$	−3.02756	+	7.56249i	−0.110331	+	0.275592i
$754$		0			0
$755$	−1.87474	+	13.0391i	−0.0682289	+	0.474543i
$756$		0			0
$757$	−15.6071	+	13.5237i	−0.567251	+	0.491526i	−0.890621	−	0.454747i	$-0.849730\pi$
$757$	−15.6071	+	13.5237i	−0.567251	+	0.491526i	0.323369	+	0.946273i	$0.395184\pi$
$758$		0			0
$759$	0.735192	−	5.12252i	0.0266858	−	0.185936i
$760$		0			0
$761$	27.6739	+	9.57802i	1.00318	+	0.347203i	0.778782	−	0.627295i	$-0.215838\pi$
$761$	27.6739	+	9.57802i	1.00318	+	0.347203i	0.224396	+	0.974498i	$0.427959\pi$
$762$		0			0
$763$	23.5160	+	6.56170i	0.851337	+	0.237549i
$764$		0			0
$765$	−8.92058	+	7.01522i	−0.322524	+	0.253636i
$766$		0			0
$767$	−0.846584	−	17.7720i	−0.0305684	−	0.641710i
$768$		0			0
$769$	−31.7226	+	9.31459i	−1.14395	+	0.335893i	−0.798175	−	0.602426i	$-0.794201\pi$
$769$	−31.7226	+	9.31459i	−1.14395	+	0.335893i	−0.345771	+	0.938319i	$0.612383\pi$
$770$		0			0
$771$	1.06443	−	1.22842i	0.0383346	−	0.0442405i
$772$		0			0
$773$	29.7400	+	2.83983i	1.06967	+	0.102142i	0.615009	−	0.788520i	$-0.289153\pi$
$773$	29.7400	+	2.83983i	1.06967	+	0.102142i	0.454666	+	0.890662i	$0.349759\pi$
$774$		0			0
$775$	6.05141	−	1.46806i	0.217373	−	0.0527342i
$776$		0			0
$777$	0.214171	+	0.00730832i	0.00768334	+	0.000262185i
$778$		0			0
$779$	−19.7777	−	0.942126i	−0.708608	−	0.0337552i
$780$		0			0
$781$	−31.9628	−	18.4537i	−1.14372	−	0.660326i
$782$		0			0
$783$			4.10760i			0.146794i
$784$		0			0
$785$	−4.56412	−	2.93318i	−0.162901	−	0.104690i
$786$		0			0
$787$	−10.4672	−	14.6991i	−0.373115	−	0.523967i	0.584739	−	0.811221i	$-0.301197\pi$
$787$	−10.4672	−	14.6991i	−0.373115	−	0.523967i	−0.957854	+	0.287255i	$0.907257\pi$
$788$		0			0
$789$	1.48451	+	6.11925i	0.0528501	+	0.217851i
$790$		0			0
$791$	−25.2076	−	23.3944i	−0.896278	−	0.831809i
$792$		0			0
$793$	3.33725	−	17.3153i	0.118509	−	0.614885i
$794$		0			0
$795$	0.321977	−	1.32721i	0.0114193	−	0.0470711i
$796$		0			0
$797$	−11.8046	+	7.58638i	−0.418142	+	0.268724i	−0.732750	−	0.680498i	$-0.761763\pi$
$797$	−11.8046	+	7.58638i	−0.418142	+	0.268724i	0.314608	+	0.949222i	$0.398127\pi$
$798$		0			0
$799$	40.9624	−	5.88950i	1.44914	−	0.208356i
$800$		0			0
$801$	−15.6371	−	12.2971i	−0.552509	−	0.434498i
$802$		0			0
$803$	−19.8186	+	57.2620i	−0.699382	+	2.02073i
$804$		0			0
$805$	5.40037	−	5.82186i	0.190338	−	0.205194i
$806$		0			0
$807$	−2.54979	+	7.36713i	−0.0897568	+	0.259335i
$808$		0			0
$809$	13.9436	+	10.9653i	0.490230	+	0.385521i	0.832451	−	0.554098i	$-0.186937\pi$
$809$	13.9436	+	10.9653i	0.490230	+	0.385521i	−0.342221	+	0.939619i	$0.611179\pi$
$810$		0			0
$811$	−21.3690	+	3.07240i	−0.750368	+	0.107887i	−0.506879	−	0.862017i	$-0.669201\pi$
$811$	−21.3690	+	3.07240i	−0.750368	+	0.107887i	−0.243489	+	0.969904i	$0.578292\pi$
$812$		0			0
$813$	4.73005	−	3.03982i	0.165890	−	0.106611i
$814$		0			0
$815$	−1.48641	+	6.12708i	−0.0520668	+	0.214622i
$816$		0			0
$817$	3.24285	−	16.8255i	0.113453	−	0.588650i
$818$		0			0
$819$	−5.95220	+	26.0650i	−0.207987	+	0.910784i
$820$		0			0
$821$	8.97755	+	37.0060i	0.313319	+	1.29152i	0.882892	+	0.469576i	$0.155593\pi$
$821$	8.97755	+	37.0060i	0.313319	+	1.29152i	−0.569573	+	0.821941i	$0.692891\pi$
$822$		0			0
$823$	0.536220	+	0.753016i	0.0186915	+	0.0262485i	0.823816	−	0.566857i	$-0.191841\pi$
$823$	0.536220	+	0.753016i	0.0186915	+	0.0262485i	−0.805124	+	0.593106i	$0.797902\pi$
$824$		0			0
$825$	4.18329	+	2.68844i	0.145643	+	0.0935994i
$826$		0			0
$827$		−	34.7248i		−	1.20750i	−0.797174	−	0.603750i	$-0.793672\pi$
$827$		−	34.7248i		−	1.20750i	0.797174	−	0.603750i	$-0.206328\pi$
$828$		0			0
$829$	30.4238	+	17.5652i	1.05666	+	0.610065i	0.924507	−	0.381164i	$-0.124477\pi$
$829$	30.4238	+	17.5652i	1.05666	+	0.610065i	0.132156	+	0.991229i	$0.457810\pi$
$830$		0			0
$831$	−7.59487	−	0.361788i	−0.263463	−	0.0125503i
$832$		0			0
$833$	−42.6989	−	7.04068i	−1.47943	−	0.243945i
$834$		0			0
$835$	2.01493	−	0.488818i	0.0697296	−	0.0169162i
$836$		0			0
$837$	−2.06282	−	0.196976i	−0.0713016	−	0.00680848i
$838$		0			0
$839$	−17.2966	+	19.9614i	−0.597145	+	0.689142i	−0.971200	−	0.238264i	$-0.923422\pi$
$839$	−17.2966	+	19.9614i	−0.597145	+	0.689142i	0.374055	+	0.927406i	$0.377967\pi$
$840$		0			0
$841$	20.9417	−	6.14905i	0.722129	−	0.212036i
$842$		0			0
$843$	0.196040	+	4.11539i	0.00675199	+	0.141742i
$844$		0			0
$845$	−0.556397	+	0.437555i	−0.0191406	+	0.0150524i
$846$		0			0
$847$	11.9024	+	12.1504i	0.408972	+	0.417494i
$848$		0			0
$849$	4.55322	+	1.57588i	0.156266	+	0.0540842i
$850$		0			0
$851$	−0.000377964	−	1.50284i	−1.29564e−5	−	0.0515168i
$852$		0			0
$853$	22.6303	−	19.6092i	0.774845	−	0.671407i	−0.174846	−	0.984596i	$-0.555943\pi$
$853$	22.6303	−	19.6092i	0.774845	−	0.671407i	0.949691	+	0.313189i	$0.101397\pi$
$854$		0			0
$855$	0.730744	−	5.08244i	0.0249909	−	0.173816i
$856$		0			0
$857$	−5.43057	+	13.5649i	−0.185505	+	0.463368i	−0.991746	−	0.128219i	$-0.959074\pi$
$857$	−5.43057	+	13.5649i	−0.185505	+	0.463368i	0.806241	+	0.591587i	$0.201498\pi$
$858$		0			0
$859$	−7.84130	+	15.2100i	−0.267542	+	0.518958i	−0.983888	−	0.178787i	$-0.942783\pi$
$859$	−7.84130	+	15.2100i	−0.267542	+	0.518958i	0.716346	+	0.697745i	$0.245813\pi$
$860$		0			0
$861$	−4.78175	+	0.753480i	−0.162962	+	0.0256785i
$862$		0			0
$863$	49.0113	+	9.44616i	1.66837	+	0.321551i	0.934019	−	0.357224i	$-0.116277\pi$
$863$	49.0113	+	9.44616i	1.66837	+	0.321551i	0.734346	+	0.678775i	$0.237489\pi$
$864$		0			0
$865$	−1.19063	+	12.4689i	−0.0404827	+	0.423954i
$866$		0			0
$867$	−1.54522	+	5.26253i	−0.0524784	+	0.178725i
$868$		0			0
$869$	5.77280	−	12.6407i	0.195829	−	0.428806i
$870$		0			0
$871$	2.94722	−	1.51940i	0.0998629	−	0.0514829i
$872$		0			0
$873$	−5.93563	−	10.2808i	−0.200890	−	0.347953i
$874$		0			0
$875$	6.11163	+	14.6887i	0.206611	+	0.496568i
$876$		0			0
$877$	0.0251179	−	0.527289i	0.000848170	−	0.0178053i	−0.998404	−	0.0564827i	$-0.982011\pi$
$877$	0.0251179	−	0.527289i	0.000848170	−	0.0178053i	0.999252	+	0.0386774i	$0.0123145\pi$
$878$		0			0
$879$	4.56821	−	3.25301i	0.154082	−	0.109721i
$880$		0			0
$881$	2.02965	+	0.595960i	0.0683808	+	0.0200784i	0.315744	−	0.948844i	$-0.397746\pi$
$881$	2.02965	+	0.595960i	0.0683808	+	0.0200784i	−0.247363	+	0.968923i	$0.579564\pi$
$882$		0			0
$883$	−19.9390	−	43.6604i	−0.671002	−	1.46929i	−0.871903	−	0.489678i	$-0.837114\pi$
$883$	−19.9390	−	43.6604i	−0.671002	−	1.46929i	0.200901	−	0.979611i	$-0.435613\pi$
$884$		0			0
$885$	0.273232	+	0.789451i	0.00918458	+	0.0265371i
$886$		0			0
$887$	31.0955	−	32.6120i	1.04408	−	1.09500i	0.0487212	−	0.998812i	$-0.484485\pi$
$887$	31.0955	−	32.6120i	1.04408	−	1.09500i	0.995363	−	0.0961914i	$-0.0306661\pi$
$888$		0			0
$889$	20.2126	+	13.9863i	0.677909	+	0.469085i
$890$		0			0
$891$	21.6859	+	27.5759i	0.726505	+	0.923826i
$892$		0			0
$893$	−11.5745	+	14.7182i	−0.387326	+	0.492525i
$894$		0			0
$895$	5.21093	+	6.01373i	0.174182	+	0.201017i
$896$		0			0
$897$	−4.19358	−	0.807153i	−0.140020	−	0.0269501i
$898$		0			0
$899$	−0.684944	−	3.55383i	−0.0228442	−	0.118527i
$900$		0			0
$901$	19.3989	+	48.4561i	0.646271	+	1.61431i
$902$		0			0
$903$	−0.0565082	−	4.18885i	−0.00188048	−	0.139396i
$904$		0			0
$905$	−10.0011	−	5.15594i	−0.332449	−	0.171389i
$906$		0			0
$907$	46.4700	+	11.2735i	1.54301	+	0.374331i	0.914864	−	0.403763i	$-0.132298\pi$
$907$	46.4700	+	11.2735i	1.54301	+	0.374331i	0.628148	+	0.778094i	$0.283813\pi$
$908$		0			0
$909$	−26.7404	−	23.1707i	−0.886924	−	0.768524i
$910$		0			0
$911$	−24.5112	+	11.1939i	−0.812094	+	0.370871i	−0.777777	−	0.628540i	$-0.783653\pi$
$911$	−24.5112	+	11.1939i	−0.812094	+	0.370871i	−0.0343166	+	0.999411i	$0.510925\pi$
$912$		0			0
$913$	5.52259	+	5.79193i	0.182771	+	0.191685i
$914$		0			0
$915$	0.0787037	+	0.824222i	0.00260186	+	0.0272480i
$916$		0			0
$917$	6.40744	+	17.7354i	0.211592	+	0.585673i
$918$		0			0
$919$	−28.7082	+	16.5747i	−0.946997	+	0.546749i	−0.892147	−	0.451746i	$-0.850801\pi$
$919$	−28.7082	+	16.5747i	−0.946997	+	0.546749i	−0.0548502	+	0.998495i	$0.517468\pi$
$920$		0			0
$921$	−3.89978	+	6.75461i	−0.128502	+	0.222572i
$922$		0			0
$923$	−16.4663	+	25.6221i	−0.541995	+	0.843360i
$924$		0			0
$925$	1.31359	+	0.599897i	0.0431906	+	0.0197245i
$926$		0			0
$927$	−17.3539	+	16.5469i	−0.569977	+	0.543472i
$928$		0			0
$929$	−2.94730	−	2.09876i	−0.0966977	−	0.0688581i	0.530685	−	0.847569i	$-0.321935\pi$
$929$	−2.94730	−	2.09876i	−0.0966977	−	0.0688581i	−0.627383	+	0.778711i	$0.715874\pi$
$930$		0			0
$931$	16.1803	−	11.0263i	0.530288	−	0.361372i
$932$		0			0
$933$	4.63210	+	4.41670i	0.151648	+	0.144596i
$934$		0			0
$935$	16.1340	−	0.768556i	0.527638	−	0.0251345i
$936$		0			0
$937$	5.11697	+	35.5893i	0.167164	+	1.16265i	0.884710	+	0.466142i	$0.154356\pi$
$937$	5.11697	+	35.5893i	0.167164	+	1.16265i	−0.717546	+	0.696511i	$0.754735\pi$
$938$		0			0
$939$	−8.08967	−	1.16312i	−0.263996	−	0.0379569i
$940$		0			0
$941$	2.27655	−	0.438769i	0.0742134	−	0.0143035i	−0.152009	−	0.988379i	$-0.548574\pi$
$941$	2.27655	−	0.438769i	0.0742134	−	0.0143035i	0.226223	+	0.974076i	$0.427362\pi$
$942$		0			0
$943$	6.43308	+	33.3329i	0.209490	+	1.08547i
$944$		0			0
$945$	−0.155026	−	2.53453i	−0.00504298	−	0.0824483i
$946$		0			0
$947$	10.4217	−	4.17223i	0.338661	−	0.135579i	−0.196098	−	0.980584i	$-0.562827\pi$
$947$	10.4217	−	4.17223i	0.338661	−	0.135579i	0.534758	+	0.845005i	$0.320403\pi$
$948$		0			0
$949$	46.4224	+	18.5847i	1.50694	+	0.603286i
$950$		0			0
$951$	−1.93686	−	3.01381i	−0.0628069	−	0.0977295i
$952$		0			0
$953$	−6.39504	−	21.7795i	−0.207156	−	0.705508i	−0.995874	−	0.0907522i	$-0.971073\pi$
$953$	−6.39504	−	21.7795i	−0.207156	−	0.705508i	0.788718	−	0.614755i	$-0.210745\pi$
$954$		0			0
$955$	6.25055	−	2.16334i	0.202263	−	0.0700039i
$956$		0			0
$957$	1.67650	−	2.35431i	0.0541935	−	0.0761041i
$958$		0			0
$959$	−1.27060	+	2.88457i	−0.0410297	+	0.0931476i
$960$		0			0
$961$	−29.0421	+	2.77318i	−0.936841	+	0.0894574i
$962$		0			0
$963$	2.72614	+	5.28798i	0.0878488	+	0.170403i
$964$		0			0
$965$	16.1991			0.521468
$966$		0			0
$967$	9.60372			0.308835			0.154417	−	0.988006i	$-0.450650\pi$
$967$	9.60372			0.308835			0.154417	+	0.988006i	$0.450650\pi$
$968$		0			0
$969$	−2.04812	−	3.97280i	−0.0657950	−	0.127625i
$970$		0			0
$971$	−5.31213	+	0.507247i	−0.170474	+	0.0162783i	−0.179944	−	0.983677i	$-0.557592\pi$
$971$	−5.31213	+	0.507247i	−0.170474	+	0.0162783i	0.00946981	+	0.999955i	$0.496986\pi$
$972$		0			0
$973$	−2.03286	+	0.221823i	−0.0651703	+	0.00711133i
$974$		0			0
$975$	2.38032	−	3.34269i	0.0762312	−	0.107052i
$976$		0			0
$977$	−55.9691	+	19.3711i	−1.79061	+	0.619736i	−0.790637	+	0.612285i	$0.790251\pi$
$977$	−55.9691	+	19.3711i	−1.79061	+	0.619736i	−0.999972	+	0.00745091i	$0.997628\pi$
$978$		0			0
$979$	7.97688	+	27.1668i	0.254942	+	0.868254i
$980$		0			0
$981$	−14.6334	−	22.7700i	−0.467208	−	0.726990i
$982$		0			0
$983$	−38.8652	−	15.5593i	−1.23961	−	0.496264i	−0.343103	−	0.939298i	$-0.611478\pi$
$983$	−38.8652	−	15.5593i	−1.23961	−	0.496264i	−0.896505	+	0.443034i	$0.853902\pi$
$984$		0			0
$985$	−3.58620	+	1.43570i	−0.114266	+	0.0457451i
$986$		0			0
$987$	−2.04255	+	4.09675i	−0.0650151	+	0.130401i
$988$		0			0
$989$	−29.3452	+	1.40528i	−0.933124	+	0.0446854i
$990$		0			0
$991$	25.9667	−	5.00467i	0.824859	−	0.158978i	0.240681	−	0.970604i	$-0.422629\pi$
$991$	25.9667	−	5.00467i	0.824859	−	0.158978i	0.584178	+	0.811626i	$0.301417\pi$
$992$		0			0
$993$	−5.15895	−	0.741745i	−0.163714	−	0.0235386i
$994$		0			0
$995$	−0.974202	−	6.77572i	−0.0308843	−	0.214805i
$996$		0			0
$997$	62.5509	−	2.97967i	1.98101	−	0.0943670i	0.984359	−	0.176172i	$-0.0563716\pi$
$997$	62.5509	−	2.97967i	1.98101	−	0.0943670i	0.996648	+	0.0818053i	$0.0260686\pi$
$998$		0			0
$999$	−0.347802	−	0.331628i	−0.0110040	−	0.0104923i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	644.2.bc.a.493.8	yes	320
7.5	odd	6	inner	644.2.bc.a.33.8	✓	320
23.7	odd	22	inner	644.2.bc.a.605.8	yes	320
161.145	even	66	inner	644.2.bc.a.145.8	yes	320

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
644.2.bc.a.33.8	✓	320	7.5	odd	6	inner
644.2.bc.a.145.8	yes	320	161.145	even	66	inner
644.2.bc.a.493.8	yes	320	1.1	even	1	trivial
644.2.bc.a.605.8	yes	320	23.7	odd	22	inner

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:	\( N \)	\(=\)	\( 644 = 2^{2} \cdot 7 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	644.bc (of order \(66\), degree \(20\), minimal)

\(f(q)\)	\(=\)	\(q+(0.118439 + 0.229739i) q^{3} +(-0.622997 + 0.0594890i) q^{5} +(0.286999 + 2.63014i) q^{7} +(1.70142 - 2.38931i) q^{9} +O(q^{10})\)	\(q+(0.118439 + 0.229739i) q^{3} +(-0.622997 + 0.0594890i) q^{5} +(0.286999 + 2.63014i) q^{7} +(1.70142 - 2.38931i) q^{9} +(-3.94516 + 1.36543i) q^{11} +(0.970607 + 3.30558i) q^{13} +(-0.0874541 - 0.136081i) q^{15} +(5.73936 + 2.29769i) q^{17} +(-2.59679 + 1.03960i) q^{19} +(-0.570255 + 0.377446i) q^{21} +(2.78284 + 3.90587i) q^{23} +(-4.52506 + 0.872133i) q^{25} +(1.51796 + 0.218249i) q^{27} +(0.381185 + 2.65120i) q^{29} +(-1.34970 + 0.0642943i) q^{31} +(-0.780955 - 0.744639i) q^{33} +(-0.335264 - 1.62150i) q^{35} +(-0.255259 - 0.181769i) q^{37} +(-0.644465 + 0.614496i) q^{39} +(6.43896 + 2.94057i) q^{41} +(-3.31192 + 5.15345i) q^{43} +(-0.917842 + 1.58975i) q^{45} +(5.79716 - 3.34699i) q^{47} +(-6.83526 + 1.50969i) q^{49} +(0.151893 + 1.59069i) q^{51} +(5.82618 + 6.11032i) q^{53} +(2.37660 - 1.08536i) q^{55} +(-0.546398 - 0.473457i) q^{57} +(-5.01885 - 1.21756i) q^{59} +(-4.54952 - 2.34544i) q^{61} +(6.77252 + 3.78924i) q^{63} +(-0.801332 - 2.00163i) q^{65} +(-0.182148 - 0.945073i) q^{67} +(-0.567736 + 1.10193i) q^{69} +(5.78935 + 6.68126i) q^{71} +(8.97225 - 11.4091i) q^{73} +(-0.736306 - 0.936289i) q^{75} +(-4.72354 - 9.98445i) q^{77} +(-2.29705 + 2.40908i) q^{79} +(-2.74841 - 7.94102i) q^{81} +(-0.796330 - 1.74372i) q^{83} +(-3.71230 - 1.09003i) q^{85} +(-0.563937 + 0.401578i) q^{87} +(0.322705 - 6.77440i) q^{89} +(-8.41558 + 3.50153i) q^{91} +(-0.174628 - 0.302465i) q^{93} +(1.55595 - 0.802148i) q^{95} +(1.68127 - 3.68147i) q^{97} +(-3.44993 + 11.7494i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 320 q - 20 q^{9}+O(q^{10}) \) 320 * q - 20 * q^9	\( 320 q - 20 q^{9} + 66 q^{21} + 21 q^{23} - 8 q^{25} - 12 q^{29} - 6 q^{31} - 38 q^{35} + 44 q^{37} - 20 q^{39} - 88 q^{43} - 42 q^{47} - 74 q^{49} + 44 q^{51} - 88 q^{57} + 55 q^{63} + 77 q^{65} - 32 q^{71} - 36 q^{73} + 24 q^{75} + 105 q^{77} + 44 q^{79} - 36 q^{81} + 60 q^{85} - 96 q^{87} - 20 q^{93} - 31 q^{95} + 242 q^{99}+O(q^{100}) \) 320 * q - 20 * q^9 + 66 * q^21 + 21 * q^23 - 8 * q^25 - 12 * q^29 - 6 * q^31 - 38 * q^35 + 44 * q^37 - 20 * q^39 - 88 * q^43 - 42 * q^47 - 74 * q^49 + 44 * q^51 - 88 * q^57 + 55 * q^63 + 77 * q^65 - 32 * q^71 - 36 * q^73 + 24 * q^75 + 105 * q^77 + 44 * q^79 - 36 * q^81 + 60 * q^85 - 96 * q^87 - 20 * q^93 - 31 * q^95 + 242 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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