LMFDB - Embedded newform 816.2.u.a.205.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [816,2,Mod(205,816)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(816, base_ring=CyclotomicField(4))

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

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

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

chi := DirichletCharacter("816.205");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 816 = 2^{4} \cdot 3 \cdot 17 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	816.u (of order $4$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$6.51579280494$
Analytic rank:	$0$
Dimension:	$64$
Relative dimension:	$32$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			205.2
Character	$\chi$	$=$	816.205
Dual form			816.2.u.a.613.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.40827 + 0.129521i) q^{2} +(0.707107 + 0.707107i) q^{3} +(1.96645 - 0.364802i) q^{4} +(-0.644405 + 0.644405i) q^{5} +(-1.08738 - 0.904212i) q^{6} -1.28446i q^{7} +(-2.72204 + 0.768437i) q^{8} +1.00000i q^{9} +(0.824032 - 0.990961i) q^{10} +(-0.233825 + 0.233825i) q^{11} +(1.64844 + 1.13253i) q^{12} +(-0.0350841 - 0.0350841i) q^{13} +(0.166366 + 1.80887i) q^{14} -0.911327 q^{15} +(3.73384 - 1.43473i) q^{16} -1.00000 q^{17} +(-0.129521 - 1.40827i) q^{18} +(3.41141 + 3.41141i) q^{19} +(-1.03211 + 1.50227i) q^{20} +(0.908254 - 0.908254i) q^{21} +(0.299003 - 0.359574i) q^{22} +6.04012i q^{23} +(-2.46814 - 1.38141i) q^{24} +4.16948i q^{25} +(0.0539520 + 0.0448637i) q^{26} +(-0.707107 + 0.707107i) q^{27} +(-0.468576 - 2.52583i) q^{28} +(2.00185 + 2.00185i) q^{29} +(1.28339 - 0.118036i) q^{30} +2.07555 q^{31} +(-5.07242 + 2.50410i) q^{32} -0.330678 q^{33} +(1.40827 - 0.129521i) q^{34} +(0.827716 + 0.827716i) q^{35} +(0.364802 + 1.96645i) q^{36} +(5.06780 - 5.06780i) q^{37} +(-5.24603 - 4.36233i) q^{38} -0.0496164i q^{39} +(1.25891 - 2.24928i) q^{40} +6.69303i q^{41} +(-1.16143 + 1.39670i) q^{42} +(-5.15228 + 5.15228i) q^{43} +(-0.374505 + 0.545104i) q^{44} +(-0.644405 - 0.644405i) q^{45} +(-0.782325 - 8.50612i) q^{46} -0.433973 q^{47} +(3.65473 + 1.62572i) q^{48} +5.35015 q^{49} +(-0.540038 - 5.87176i) q^{50} +(-0.707107 - 0.707107i) q^{51} +(-0.0817898 - 0.0561923i) q^{52} +(-0.118525 + 0.118525i) q^{53} +(0.904212 - 1.08738i) q^{54} -0.301356i q^{55} +(0.987031 + 3.49636i) q^{56} +4.82446i q^{57} +(-3.07842 - 2.55986i) q^{58} +(-0.216815 + 0.216815i) q^{59} +(-1.79208 + 0.332454i) q^{60} +(-4.08768 - 4.08768i) q^{61} +(-2.92293 + 0.268828i) q^{62} +1.28446 q^{63} +(6.81901 - 4.18344i) q^{64} +0.0452167 q^{65} +(0.465684 - 0.0428299i) q^{66} +(-5.47442 - 5.47442i) q^{67} +(-1.96645 + 0.364802i) q^{68} +(-4.27101 + 4.27101i) q^{69} +(-1.27285 - 1.05844i) q^{70} +3.98814i q^{71} +(-0.768437 - 2.72204i) q^{72} +13.1366i q^{73} +(-6.48044 + 7.79321i) q^{74} +(-2.94827 + 2.94827i) q^{75} +(7.95285 + 5.46387i) q^{76} +(0.300340 + 0.300340i) q^{77} +(0.00642638 + 0.0698733i) q^{78} -5.14921 q^{79} +(-1.48156 + 3.33065i) q^{80} -1.00000 q^{81} +(-0.866891 - 9.42559i) q^{82} +(2.55760 + 2.55760i) q^{83} +(1.45470 - 2.11737i) q^{84} +(0.644405 - 0.644405i) q^{85} +(6.58847 - 7.92313i) q^{86} +2.83104i q^{87} +(0.456801 - 0.816161i) q^{88} +5.77616i q^{89} +(0.990961 + 0.824032i) q^{90} +(-0.0450643 + 0.0450643i) q^{91} +(2.20345 + 11.8776i) q^{92} +(1.46763 + 1.46763i) q^{93} +(0.611152 - 0.0562089i) q^{94} -4.39666 q^{95} +(-5.35741 - 1.81608i) q^{96} +7.68003 q^{97} +(-7.53446 + 0.692959i) q^{98} +(-0.233825 - 0.233825i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 64 q + 4 q^{4} + 12 q^{10} + 8 q^{11} - 8 q^{12} + 20 q^{14} + 24 q^{15} + 28 q^{16} - 64 q^{17} - 4 q^{18} - 48 q^{22} - 20 q^{26} + 16 q^{29} + 8 q^{30} - 24 q^{31} + 40 q^{32} - 24 q^{35} + 16 q^{37}+ \cdots + 8 q^{99}+O(q^{100}) $ 64 * q + 4 * q^4 + 12 * q^10 + 8 * q^11 - 8 * q^12 + 20 * q^14 + 24 * q^15 + 28 * q^16 - 64 * q^17 - 4 * q^18 - 48 * q^22 - 20 * q^26 + 16 * q^29 + 8 * q^30 - 24 * q^31 + 40 * q^32 - 24 * q^35 + 16 * q^37 - 12 * q^38 - 56 * q^40 + 8 * q^42 + 8 * q^43 + 24 * q^44 + 52 * q^46 + 64 * q^47 - 64 * q^49 + 68 * q^50 + 44 * q^52 - 16 * q^53 - 56 * q^56 + 4 * q^58 + 4 * q^60 + 76 * q^62 - 8 * q^63 + 52 * q^64 + 8 * q^66 + 16 * q^67 - 4 * q^68 - 136 * q^70 + 4 * q^72 - 84 * q^74 - 16 * q^75 - 20 * q^76 + 32 * q^77 + 24 * q^78 + 40 * q^79 + 56 * q^80 - 64 * q^81 + 64 * q^83 - 52 * q^84 - 44 * q^86 - 96 * q^88 - 20 * q^90 - 56 * q^91 + 32 * q^92 + 88 * q^94 - 48 * q^95 + 72 * q^98 + 8 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/816\mathbb{Z}\right)^\times$.

$n$	$241$	$511$	$545$	$613$
$\chi(n)$	$1$	$1$	$1$	$e\left(\frac{3}{4}\right)$

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 $

$2$	−1.40827	+	0.129521i	−0.995797	+	0.0915855i
$2$	−1.40827	+	0.129521i	−0.995797	+	0.0915855i
$3$	0.707107	+	0.707107i	0.408248	+	0.408248i
$3$	0.707107	+	0.707107i	0.408248	+	0.408248i
$4$	1.96645	−	0.364802i	0.983224	−	0.182401i
$5$	−0.644405	+	0.644405i	−0.288187	+	0.288187i	−0.836363	−	0.548176i	$-0.815322\pi$
$5$	−0.644405	+	0.644405i	−0.288187	+	0.288187i	0.548176	+	0.836363i	$0.315322\pi$
$6$	−1.08738	−	0.904212i	−0.443922	−	0.369143i
$7$		−	1.28446i		−	0.485482i	−0.970091	−	0.242741i	$-0.921953\pi$
$7$		−	1.28446i		−	0.485482i	0.970091	−	0.242741i	$-0.0780465\pi$
$8$	−2.72204	+	0.768437i	−0.962387	+	0.271684i
$9$			1.00000i			0.333333i
$10$	0.824032	−	0.990961i	0.260582	−	0.313369i
$11$	−0.233825	+	0.233825i	−0.0705009	+	0.0705009i	−0.741478	−	0.670977i	$-0.765875\pi$
$11$	−0.233825	+	0.233825i	−0.0705009	+	0.0705009i	0.670977	+	0.741478i	$0.265875\pi$
$12$	1.64844	+	1.13253i	0.475865	+	0.326935i
$13$	−0.0350841	−	0.0350841i	−0.00973057	−	0.00973057i	0.702225	−	0.711955i	$-0.252190\pi$
$13$	−0.0350841	−	0.0350841i	−0.00973057	−	0.00973057i	−0.711955	+	0.702225i	$0.752190\pi$
$14$	0.166366	+	1.80887i	0.0444631	+	0.483442i
$15$	−0.911327			−0.235304
$16$	3.73384	−	1.43473i	0.933460	−	0.358682i
$17$	−1.00000			−0.242536
$17$	−1.00000			−0.242536
$18$	−0.129521	−	1.40827i	−0.0305285	−	0.331932i
$19$	3.41141	+	3.41141i	0.782631	+	0.782631i	0.980274	−	0.197643i	$-0.0633288\pi$
$19$	3.41141	+	3.41141i	0.782631	+	0.782631i	−0.197643	+	0.980274i	$0.563329\pi$
$20$	−1.03211	+	1.50227i	−0.230787	+	0.335918i
$21$	0.908254	−	0.908254i	0.198197	−	0.198197i
$22$	0.299003	−	0.359574i	0.0637477	−	0.0766614i
$23$			6.04012i			1.25945i	0.776817	+	0.629726i	$0.216833\pi$
$23$			6.04012i			1.25945i	−0.776817	+	0.629726i	$0.783167\pi$
$24$	−2.46814	−	1.38141i	−0.503807	−	0.281978i
$25$			4.16948i			0.833897i
$26$	0.0539520	+	0.0448637i	0.0105809	+	0.00879850i
$27$	−0.707107	+	0.707107i	−0.136083	+	0.136083i
$28$	−0.468576	−	2.52583i	−0.0885525	−	0.477338i
$29$	2.00185	+	2.00185i	0.371734	+	0.371734i	0.868108	−	0.496375i	$-0.165336\pi$
$29$	2.00185	+	2.00185i	0.371734	+	0.371734i	−0.496375	+	0.868108i	$0.665336\pi$
$30$	1.28339	−	0.118036i	0.234315	−	0.0215504i
$31$	2.07555			0.372780			0.186390	−	0.982476i	$-0.440321\pi$
$31$	2.07555			0.372780			0.186390	+	0.982476i	$0.440321\pi$
$32$	−5.07242	+	2.50410i	−0.896686	+	0.442666i
$33$	−0.330678			−0.0575637
$34$	1.40827	−	0.129521i	0.241516	−	0.0222127i
$35$	0.827716	+	0.827716i	0.139909	+	0.139909i
$36$	0.364802	+	1.96645i	0.0608004	+	0.327741i
$37$	5.06780	−	5.06780i	0.833140	−	0.833140i	−0.154805	−	0.987945i	$-0.549475\pi$
$37$	5.06780	−	5.06780i	0.833140	−	0.833140i	0.987945	+	0.154805i	$0.0494748\pi$
$38$	−5.24603	−	4.36233i	−0.851019	−	0.707664i
$39$		−	0.0496164i		−	0.00794498i
$40$	1.25891	−	2.24928i	0.199051	−	0.355643i
$41$			6.69303i			1.04528i	0.852555	+	0.522638i	$0.175052\pi$
$41$			6.69303i			1.04528i	−0.852555	+	0.522638i	$0.824948\pi$
$42$	−1.16143	+	1.39670i	−0.179212	+	0.215516i
$43$	−5.15228	+	5.15228i	−0.785715	+	0.785715i	−0.980789	−	0.195073i	$-0.937506\pi$
$43$	−5.15228	+	5.15228i	−0.785715	+	0.785715i	0.195073	+	0.980789i	$0.437506\pi$
$44$	−0.374505	+	0.545104i	−0.0564587	+	0.0821776i
$45$	−0.644405	−	0.644405i	−0.0960623	−	0.0960623i
$46$	−0.782325	−	8.50612i	−0.115347	−	1.25416i
$47$	−0.433973			−0.0633015			−0.0316508	−	0.999499i	$-0.510076\pi$
$47$	−0.433973			−0.0633015			−0.0316508	+	0.999499i	$0.510076\pi$
$48$	3.65473	+	1.62572i	0.527515	+	0.234652i
$49$	5.35015			0.764307
$50$	−0.540038	−	5.87176i	−0.0763728	−	0.830392i
$51$	−0.707107	−	0.707107i	−0.0990148	−	0.0990148i
$52$	−0.0817898	−	0.0561923i	−0.0113422	−	0.00779247i
$53$	−0.118525	+	0.118525i	−0.0162807	+	0.0162807i	−0.715200	−	0.698920i	$-0.753665\pi$
$53$	−0.118525	+	0.118525i	−0.0162807	+	0.0162807i	0.698920	+	0.715200i	$0.253665\pi$
$54$	0.904212	−	1.08738i	0.123048	−	0.147974i
$55$		−	0.301356i		−	0.0406348i
$56$	0.987031	+	3.49636i	0.131898	+	0.467221i
$57$			4.82446i			0.639015i
$58$	−3.07842	−	2.55986i	−0.404217	−	0.336126i
$59$	−0.216815	+	0.216815i	−0.0282269	+	0.0282269i	−0.721079	−	0.692852i	$-0.756354\pi$
$59$	−0.216815	+	0.216815i	−0.0282269	+	0.0282269i	0.692852	+	0.721079i	$0.256354\pi$
$60$	−1.79208	+	0.332454i	−0.231356	+	0.0429196i
$61$	−4.08768	−	4.08768i	−0.523374	−	0.523374i	0.395215	−	0.918589i	$-0.370670\pi$
$61$	−4.08768	−	4.08768i	−0.523374	−	0.523374i	−0.918589	+	0.395215i	$0.870670\pi$
$62$	−2.92293	+	0.268828i	−0.371213	+	0.0341412i
$63$	1.28446			0.161827
$64$	6.81901	−	4.18344i	0.852376	−	0.522929i
$65$	0.0452167			0.00560844
$66$	0.465684	−	0.0428299i	0.0573218	−	0.00527200i
$67$	−5.47442	−	5.47442i	−0.668807	−	0.668807i	0.288633	−	0.957440i	$-0.406799\pi$
$67$	−5.47442	−	5.47442i	−0.668807	−	0.668807i	−0.957440	+	0.288633i	$0.906799\pi$
$68$	−1.96645	+	0.364802i	−0.238467	+	0.0442388i
$69$	−4.27101	+	4.27101i	−0.514169	+	0.514169i
$70$	−1.27285	−	1.05844i	−0.152135	−	0.126508i
$71$			3.98814i			0.473305i	0.971594	+	0.236653i	$0.0760504\pi$
$71$			3.98814i			0.473305i	−0.971594	+	0.236653i	$0.923950\pi$
$72$	−0.768437	−	2.72204i	−0.0905612	−	0.320796i
$73$			13.1366i			1.53752i	0.639535	+	0.768762i	$0.279127\pi$
$73$			13.1366i			1.53752i	−0.639535	+	0.768762i	$0.720873\pi$
$74$	−6.48044	+	7.79321i	−0.753335	+	0.905943i
$75$	−2.94827	+	2.94827i	−0.340437	+	0.340437i
$76$	7.95285	+	5.46387i	0.912254	+	0.626749i
$77$	0.300340	+	0.300340i	0.0342269	+	0.0342269i
$78$	0.00642638	+	0.0698733i	0.000727645	+	0.00791159i
$79$	−5.14921			−0.579332			−0.289666	−	0.957128i	$-0.593544\pi$
$79$	−5.14921			−0.579332			−0.289666	+	0.957128i	$0.593544\pi$
$80$	−1.48156	+	3.33065i	−0.165643	+	0.372378i
$81$	−1.00000			−0.111111
$82$	−0.866891	−	9.42559i	−0.0957321	−	1.04088i
$83$	2.55760	+	2.55760i	0.280733	+	0.280733i	0.833401	−	0.552669i	$-0.186390\pi$
$83$	2.55760	+	2.55760i	0.280733	+	0.280733i	−0.552669	+	0.833401i	$0.686390\pi$
$84$	1.45470	−	2.11737i	0.158721	−	0.231024i
$85$	0.644405	−	0.644405i	0.0698956	−	0.0698956i
$86$	6.58847	−	7.92313i	0.710453	−	0.854373i
$87$			2.83104i			0.303519i
$88$	0.456801	−	0.816161i	0.0486951	−	0.0870030i
$89$			5.77616i			0.612272i	0.951988	+	0.306136i	$0.0990362\pi$
$89$			5.77616i			0.612272i	−0.951988	+	0.306136i	$0.900964\pi$
$90$	0.990961	+	0.824032i	0.104456	+	0.0868606i
$91$	−0.0450643	+	0.0450643i	−0.00472402	+	0.00472402i
$92$	2.20345	+	11.8776i	0.229725	+	1.23832i
$93$	1.46763	+	1.46763i	0.152187	+	0.152187i
$94$	0.611152	−	0.0562089i	0.0630355	−	0.00579750i
$95$	−4.39666			−0.451088
$96$	−5.35741	−	1.81608i	−0.546788	−	0.185353i
$97$	7.68003			0.779789			0.389895	−	0.920859i	$-0.372511\pi$
$97$	7.68003			0.779789			0.389895	+	0.920859i	$0.372511\pi$
$98$	−7.53446	+	0.692959i	−0.761095	+	0.0699995i
$99$	−0.233825	−	0.233825i	−0.0235003	−	0.0235003i
$100$	1.52104	+	8.19907i	0.152104	+	0.819907i
$101$	2.53027	−	2.53027i	0.251771	−	0.251771i	−0.569925	−	0.821696i	$-0.693028\pi$
$101$	2.53027	−	2.53027i	0.251771	−	0.251771i	0.821696	+	0.569925i	$0.193028\pi$
$102$	1.08738	+	0.904212i	0.107667	+	0.0895303i
$103$		−	3.80999i		−	0.375410i	−0.982225	−	0.187705i	$-0.939895\pi$
$103$		−	3.80999i		−	0.375410i	0.982225	−	0.187705i	$-0.0601048\pi$
$104$	0.122460	+	0.0685404i	0.0120082	+	0.00672094i
$105$			1.17057i			0.114236i
$106$	0.151564	−	0.182267i	0.0147212	−	0.0177033i
$107$	−3.81586	+	3.81586i	−0.368893	+	0.368893i	−0.867073	−	0.498181i	$-0.834002\pi$
$107$	−3.81586	+	3.81586i	−0.368893	+	0.368893i	0.498181	+	0.867073i	$0.334002\pi$
$108$	−1.13253	+	1.64844i	−0.108978	+	0.158622i
$109$	12.5434	+	12.5434i	1.20144	+	1.20144i	0.973728	+	0.227713i	$0.0731247\pi$
$109$	12.5434	+	12.5434i	1.20144	+	1.20144i	0.227713	+	0.973728i	$0.426875\pi$
$110$	0.0390321	+	0.424391i	0.00372156	+	0.0404641i
$111$	7.16695			0.680256
$112$	−1.84286	−	4.79598i	−0.174134	−	0.453178i
$113$	9.26089			0.871191			0.435595	−	0.900143i	$-0.356538\pi$
$113$	9.26089			0.871191			0.435595	+	0.900143i	$0.356538\pi$
$114$	−0.624871	−	6.79414i	−0.0585245	−	0.636330i
$115$	−3.89228	−	3.89228i	−0.362957	−	0.362957i
$116$	4.66681	+	3.20625i	0.433302	+	0.297693i
$117$	0.0350841	−	0.0350841i	0.00324352	−	0.00324352i
$118$	0.277252	−	0.333416i	0.0255231	−	0.0306934i
$119$			1.28446i			0.117747i
$120$	2.48067	−	0.700297i	0.226453	−	0.0639281i
$121$			10.8907i			0.990059i
$122$	6.28600	+	5.22712i	0.569108	+	0.473241i
$123$	−4.73269	+	4.73269i	−0.426732	+	0.426732i
$124$	4.08146	−	0.757165i	0.366526	−	0.0679954i
$125$	−5.90886	−	5.90886i	−0.528505	−	0.528505i
$126$	−1.80887	+	0.166366i	−0.161147	+	0.0148210i
$127$	−7.07177			−0.627518			−0.313759	−	0.949503i	$-0.601588\pi$
$127$	−7.07177			−0.627518			−0.313759	+	0.949503i	$0.601588\pi$
$128$	−9.06116	+	6.77461i	−0.800901	+	0.598797i
$129$	−7.28642			−0.641534
$130$	−0.0636774	+	0.00585654i	−0.00558487	+	0.000513652i
$131$	−2.45976	−	2.45976i	−0.214910	−	0.214910i	0.591440	−	0.806349i	$-0.298560\pi$
$131$	−2.45976	−	2.45976i	−0.214910	−	0.214910i	−0.806349	+	0.591440i	$0.798560\pi$
$132$	−0.650262	+	0.120632i	−0.0565980	+	0.0104997i
$133$	4.38183	−	4.38183i	0.379953	−	0.379953i
$134$	8.41851	+	7.00040i	0.727249	+	0.604743i
$135$		−	0.911327i		−	0.0784345i
$136$	2.72204	−	0.768437i	0.233413	−	0.0658930i
$137$		−	13.1305i		−	1.12182i	−0.827878	−	0.560909i	$-0.810452\pi$
$137$		−	13.1305i		−	1.12182i	0.827878	−	0.560909i	$-0.189548\pi$
$138$	5.46155	−	6.56792i	0.464918	−	0.559098i
$139$	−11.9738	+	11.9738i	−1.01560	+	1.01560i	−0.0157265	+	0.999876i	$0.505006\pi$
$139$	−11.9738	+	11.9738i	−1.01560	+	1.01560i	−0.999876	+	0.0157265i	$0.994994\pi$
$140$	1.92961	+	1.32571i	0.163082	+	0.112043i
$141$	−0.306866	−	0.306866i	−0.0258427	−	0.0258427i
$142$	−0.516550	−	5.61638i	−0.0433479	−	0.471316i
$143$	0.0164071			0.00137203
$144$	1.43473	+	3.73384i	0.119561	+	0.311153i
$145$	−2.58000			−0.214257
$146$	−1.70147	−	18.4999i	−0.140815	−	1.53106i
$147$	3.78313	+	3.78313i	0.312027	+	0.312027i
$148$	8.11681	−	11.8143i	0.667198	−	0.971130i
$149$	9.84698	−	9.84698i	0.806696	−	0.806696i	−0.177436	−	0.984132i	$-0.556780\pi$
$149$	9.84698	−	9.84698i	0.806696	−	0.806696i	0.984132	+	0.177436i	$0.0567804\pi$
$150$	3.77010	−	4.53382i	0.307827	−	0.370185i
$151$		−	1.57680i		−	0.128318i	−0.997940	−	0.0641591i	$-0.979563\pi$
$151$		−	1.57680i		−	0.128318i	0.997940	−	0.0641591i	$-0.0204365\pi$
$152$	−11.9074	−	6.66454i	−0.965821	−	0.540565i
$153$		−	1.00000i		−	0.0808452i
$154$	−0.461860	−	0.384059i	−0.0372177	−	0.0309484i
$155$	−1.33749	+	1.33749i	−0.107430	+	0.107430i
$156$	−0.0181002	−	0.0975680i	−0.00144917	−	0.00781170i
$157$	0.602980	+	0.602980i	0.0481231	+	0.0481231i	0.730759	−	0.682636i	$-0.239166\pi$
$157$	0.602980	+	0.602980i	0.0481231	+	0.0481231i	−0.682636	+	0.730759i	$0.739166\pi$
$158$	7.25148	−	0.666933i	0.576897	−	0.0530584i
$159$	−0.167620			−0.0132931
$160$	1.65504	−	4.88235i	0.130843	−	0.385984i
$161$	7.75832			0.611441
$162$	1.40827	−	0.129521i	0.110644	−	0.0101762i
$163$	−9.63701	−	9.63701i	−0.754829	−	0.754829i	0.220548	−	0.975376i	$-0.429216\pi$
$163$	−9.63701	−	9.63701i	−0.754829	−	0.754829i	−0.975376	+	0.220548i	$0.929216\pi$
$164$	2.44163	+	13.1615i	0.190659	+	1.02774i
$165$	0.213091	−	0.213091i	0.0165891	−	0.0165891i
$166$	−3.93305	−	3.27052i	−0.305264	−	0.253842i
$167$		−	8.85441i		−	0.685174i	−0.939486	−	0.342587i	$-0.888697\pi$
$167$		−	8.85441i		−	0.685174i	0.939486	−	0.342587i	$-0.111303\pi$
$168$	−1.77437	+	3.17024i	−0.136895	+	0.244589i
$169$		−	12.9975i		−	0.999811i
$170$	−0.824032	+	0.990961i	−0.0632004	+	0.0760032i
$171$	−3.41141	+	3.41141i	−0.260877	+	0.260877i
$172$	−8.25213	+	12.0113i	−0.629219	+	0.915850i
$173$	−15.3064	−	15.3064i	−1.16372	−	1.16372i	−0.983654	−	0.180071i	$-0.942367\pi$
$173$	−15.3064	−	15.3064i	−1.16372	−	1.16372i	−0.180071	−	0.983654i	$-0.557633\pi$
$174$	−0.366680	−	3.98687i	−0.0277980	−	0.302244i
$175$	5.35555			0.404842
$176$	−0.537589	+	1.20854i	−0.0405223	+	0.0910971i
$177$	−0.306623			−0.0230472
$178$	−0.748137	−	8.13440i	−0.0560752	−	0.609699i
$179$	−11.5262	−	11.5262i	−0.861510	−	0.861510i	0.130003	−	0.991514i	$-0.458501\pi$
$179$	−11.5262	−	11.5262i	−0.861510	−	0.861510i	−0.991514	+	0.130003i	$0.958501\pi$
$180$	−1.50227	−	1.03211i	−0.111973	−	0.0769289i
$181$	13.3586	−	13.3586i	0.992937	−	0.992937i	−0.00703858	−	0.999975i	$-0.502240\pi$
$181$	13.3586	−	13.3586i	0.992937	−	0.992937i	0.999975	+	0.00703858i	$0.00224047\pi$
$182$	0.0576258	−	0.0692994i	0.00427151	−	0.00513681i
$183$		−	5.78086i		−	0.427333i
$184$	−4.64145	−	16.4414i	−0.342172	−	1.21208i
$185$			6.53143i			0.480200i
$186$	−2.25692	−	1.87674i	−0.165485	−	0.137609i
$187$	0.233825	−	0.233825i	0.0170990	−	0.0170990i
$188$	−0.853386	+	0.158315i	−0.0622396	+	0.0115463i
$189$	0.908254	+	0.908254i	0.0660657	+	0.0660657i
$190$	6.19168	−	0.569461i	0.449192	−	0.0413131i
$191$	11.0961			0.802884			0.401442	−	0.915884i	$-0.368509\pi$
$191$	11.0961			0.802884			0.401442	+	0.915884i	$0.368509\pi$
$192$	7.77990	+	1.86363i	0.561466	+	0.134496i
$193$	12.2474			0.881585			0.440793	−	0.897609i	$-0.354697\pi$
$193$	12.2474			0.881585			0.440793	+	0.897609i	$0.354697\pi$
$194$	−10.8156	+	0.994729i	−0.776512	+	0.0714174i
$195$	0.0319731	+	0.0319731i	0.00228964	+	0.00228964i
$196$	10.5208	−	1.95175i	0.751485	−	0.139411i
$197$	17.3096	−	17.3096i	1.23326	−	1.23326i	0.270556	−	0.962704i	$-0.412792\pi$
$197$	17.3096	−	17.3096i	1.23326	−	1.23326i	0.962704	−	0.270556i	$-0.0872076\pi$
$198$	0.359574	+	0.299003i	0.0255538	+	0.0212492i
$199$		−	5.87278i		−	0.416310i	−0.978096	−	0.208155i	$-0.933254\pi$
$199$		−	5.87278i		−	0.416310i	0.978096	−	0.208155i	$-0.0667459\pi$
$200$	−3.20399	−	11.3495i	−0.226556	−	0.802531i
$201$		−	7.74200i		−	0.546078i
$202$	−3.23557	+	3.89102i	−0.227654	+	0.273771i
$203$	2.57130	−	2.57130i	0.180470	−	0.180470i
$204$	−1.64844	−	1.13253i	−0.115414	−	0.0792933i
$205$	−4.31302	−	4.31302i	−0.301235	−	0.301235i
$206$	0.493476	+	5.36550i	0.0343821	+	0.373832i
$207$	−6.04012			−0.419817
$208$	−0.181334	−	0.0806621i	−0.0125733	−	0.00559291i
$209$	−1.59534			−0.110352
$210$	−0.151614	−	1.64847i	−0.0104623	−	0.113756i
$211$	6.36289	+	6.36289i	0.438039	+	0.438039i	0.891352	−	0.453313i	$-0.149758\pi$
$211$	6.36289	+	6.36289i	0.438039	+	0.438039i	−0.453313	+	0.891352i	$0.649758\pi$
$212$	−0.189835	+	0.276312i	−0.0130379	+	0.0189772i
$213$	−2.82004	+	2.82004i	−0.193226	+	0.193226i
$214$	4.87952	−	5.86799i	0.333557	−	0.401127i
$215$		−	6.64031i		−	0.452866i
$216$	1.38141	−	2.46814i	0.0939928	−	0.167936i
$217$		−	2.66597i		−	0.180978i
$218$	−19.2892	−	16.0399i	−1.30643	−	1.08636i
$219$	−9.28898	+	9.28898i	−0.627691	+	0.627691i
$220$	−0.109935	−	0.592601i	−0.00741184	−	0.0399531i
$221$	0.0350841	+	0.0350841i	0.00236001	+	0.00236001i
$222$	−10.0930	+	0.928273i	−0.677397	+	0.0623016i
$223$	−21.0587			−1.41019			−0.705096	−	0.709112i	$-0.749096\pi$
$223$	−21.0587			−1.41019			−0.705096	+	0.709112i	$0.749096\pi$
$224$	3.21643	+	6.51535i	0.214907	+	0.435325i
$225$	−4.16948			−0.277966
$226$	−13.0418	+	1.19948i	−0.867529	+	0.0797884i
$227$	1.09601	+	1.09601i	0.0727445	+	0.0727445i	0.742543	−	0.669798i	$-0.233619\pi$
$227$	1.09601	+	1.09601i	0.0727445	+	0.0727445i	−0.669798	+	0.742543i	$0.733619\pi$
$228$	1.75997	+	9.48705i	0.116557	+	0.628295i
$229$	10.2822	−	10.2822i	0.679469	−	0.679469i	−0.280411	−	0.959880i	$-0.590471\pi$
$229$	10.2822	−	10.2822i	0.679469	−	0.679469i	0.959880	+	0.280411i	$0.0904708\pi$
$230$	5.98552	+	4.97725i	0.394674	+	0.328190i
$231$			0.424745i			0.0279461i
$232$	−6.98740	−	3.91081i	−0.458745	−	0.256758i
$233$			7.07432i			0.463454i	0.972781	+	0.231727i	$0.0744377\pi$
$233$			7.07432i			0.463454i	−0.972781	+	0.231727i	$0.925562\pi$
$234$	−0.0448637	+	0.0539520i	−0.00293283	+	0.00352695i
$235$	0.279655	−	0.279655i	0.0182427	−	0.0182427i
$236$	−0.347261	+	0.505450i	−0.0226048	+	0.0329020i
$237$	−3.64104	−	3.64104i	−0.236511	−	0.236511i
$238$	−0.166366	−	1.80887i	−0.0107839	−	0.117252i
$239$	6.37531			0.412385			0.206192	−	0.978511i	$-0.433893\pi$
$239$	6.37531			0.412385			0.206192	+	0.978511i	$0.433893\pi$
$240$	−3.40275	+	1.30751i	−0.219646	+	0.0843993i
$241$	6.93889			0.446973			0.223487	−	0.974707i	$-0.428256\pi$
$241$	6.93889			0.446973			0.223487	+	0.974707i	$0.428256\pi$
$242$	−1.41057	−	15.3370i	−0.0906751	−	0.985898i
$243$	−0.707107	−	0.707107i	−0.0453609	−	0.0453609i
$244$	−9.52941	−	6.54702i	−0.610058	−	0.419130i
$245$	−3.44767	+	3.44767i	−0.220263	+	0.220263i
$246$	6.05192	−	7.27788i	0.385856	−	0.464021i
$247$		−	0.239372i		−	0.0152309i
$248$	−5.64973	+	1.59493i	−0.358758	+	0.101278i
$249$			3.61699i			0.229217i
$250$	9.08660	+	7.55595i	0.574687	+	0.477880i
$251$	10.6096	−	10.6096i	0.669674	−	0.669674i	−0.287966	−	0.957640i	$-0.592979\pi$
$251$	10.6096	−	10.6096i	0.669674	−	0.669674i	0.957640	+	0.287966i	$0.0929792\pi$
$252$	2.52583	−	0.468576i	0.159113	−	0.0295175i
$253$	−1.41233	−	1.41233i	−0.0887924	−	0.0887924i
$254$	9.95896	−	0.915946i	0.624881	−	0.0574715i
$255$	0.911327			0.0570695
$256$	11.8831	−	10.7141i	0.742694	−	0.669631i
$257$	15.1482			0.944916			0.472458	−	0.881353i	$-0.343367\pi$
$257$	15.1482			0.944916			0.472458	+	0.881353i	$0.343367\pi$
$258$	10.2613	−	0.943748i	0.638838	−	0.0587552i
$259$	−6.50940	−	6.50940i	−0.404475	−	0.404475i
$260$	0.0889164	−	0.0164952i	0.00551436	−	0.00102299i
$261$	−2.00185	+	2.00185i	−0.123911	+	0.123911i
$262$	3.78259	+	3.14541i	0.233689	+	0.194324i
$263$		−	10.2151i		−	0.629892i	−0.949110	−	0.314946i	$-0.898014\pi$
$263$		−	10.2151i		−	0.629892i	0.949110	−	0.314946i	$-0.101986\pi$
$264$	0.900120	−	0.254106i	0.0553985	−	0.0156391i
$265$		−	0.152756i		−	0.00938376i
$266$	−5.60326	+	6.73834i	−0.343558	+	0.413154i
$267$	−4.08436	+	4.08436i	−0.249959	+	0.249959i
$268$	−12.7622	−	8.76808i	−0.779578	−	0.535596i
$269$	−7.06393	−	7.06393i	−0.430696	−	0.430696i	0.458169	−	0.888865i	$-0.348505\pi$
$269$	−7.06393	−	7.06393i	−0.430696	−	0.430696i	−0.888865	+	0.458169i	$0.848505\pi$
$270$	0.118036	+	1.28339i	0.00718346	+	0.0781049i
$271$	18.9739			1.15258			0.576292	−	0.817244i	$-0.304499\pi$
$271$	18.9739			1.15258			0.576292	+	0.817244i	$0.304499\pi$
$272$	−3.73384	+	1.43473i	−0.226397	+	0.0869933i
$273$	−0.0637305			−0.00385714
$274$	1.70069	+	18.4913i	0.102742	+	1.11710i
$275$	−0.974929	−	0.974929i	−0.0587904	−	0.0587904i
$276$	−6.84064	+	9.95679i	−0.411758	+	0.599328i
$277$	−18.1660	+	18.1660i	−1.09149	+	1.09149i	−0.0961191	+	0.995370i	$0.530643\pi$
$277$	−18.1660	+	18.1660i	−1.09149	+	1.09149i	−0.995370	+	0.0961191i	$0.969357\pi$
$278$	15.3115	−	18.4132i	0.918320	−	1.10435i
$279$			2.07555i			0.124260i
$280$	−2.88912	−	1.61703i	−0.172658	−	0.0966359i
$281$		−	17.9600i		−	1.07140i	−0.844408	−	0.535701i	$-0.820047\pi$
$281$		−	17.9600i		−	1.07140i	0.844408	−	0.535701i	$-0.179953\pi$
$282$	0.471895	+	0.392404i	0.0281009	+	0.0233673i
$283$	−6.10341	+	6.10341i	−0.362810	+	0.362810i	−0.864847	−	0.502036i	$-0.832584\pi$
$283$	−6.10341	+	6.10341i	−0.362810	+	0.362810i	0.502036	+	0.864847i	$0.332584\pi$
$284$	1.45488	+	7.84248i	0.0863315	+	0.465365i
$285$	−3.10891	−	3.10891i	−0.184156	−	0.184156i
$286$	−0.0231056	+	0.00212507i	−0.00136626	+	0.000125658i
$287$	8.59696			0.507462
$288$	−2.50410	−	5.07242i	−0.147555	−	0.298895i
$289$	1.00000			0.0588235
$290$	3.63334	−	0.334166i	0.213357	−	0.0196229i
$291$	5.43060	+	5.43060i	0.318348	+	0.318348i
$292$	4.79226	+	25.8325i	0.280446	+	1.51173i
$293$	11.1199	−	11.1199i	0.649634	−	0.649634i	−0.303271	−	0.952904i	$-0.598079\pi$
$293$	11.1199	−	11.1199i	0.649634	−	0.649634i	0.952904	+	0.303271i	$0.0980786\pi$
$294$	−5.81766	−	4.83767i	−0.339293	−	0.282139i
$295$		−	0.279433i		−	0.0162692i
$296$	−9.90046	+	17.6890i	−0.575453	+	1.02815i
$297$		−	0.330678i		−	0.0191879i
$298$	−12.5918	+	15.1426i	−0.729424	+	0.877187i
$299$	0.211912	−	0.211912i	0.0122552	−	0.0122552i
$300$	−4.72209	+	6.87316i	−0.272630	+	0.396822i
$301$	6.61792	+	6.61792i	0.381451	+	0.381451i
$302$	0.204230	+	2.22056i	0.0117521	+	0.127779i
$303$	3.57834			0.205570
$304$	17.6321	+	7.84320i	1.01127	+	0.449838i
$305$	5.26825			0.301659
$306$	0.129521	+	1.40827i	0.00740425	+	0.0805054i
$307$	−12.1793	−	12.1793i	−0.695111	−	0.695111i	0.268241	−	0.963352i	$-0.413558\pi$
$307$	−12.1793	−	12.1793i	−0.695111	−	0.695111i	−0.963352	+	0.268241i	$0.913558\pi$
$308$	0.700167	+	0.481038i	0.0398957	+	0.0274097i
$309$	2.69407	−	2.69407i	0.153260	−	0.153260i
$310$	1.71032	−	2.05679i	0.0971396	−	0.116818i
$311$			19.2846i			1.09353i	0.837287	+	0.546764i	$0.184141\pi$
$311$			19.2846i			1.09353i	−0.837287	+	0.546764i	$0.815859\pi$
$312$	0.0381271	+	0.135058i	0.00215852	+	0.00764614i
$313$			13.6980i			0.774257i	0.922026	+	0.387129i	$0.126533\pi$
$313$			13.6980i			0.774257i	−0.922026	+	0.387129i	$0.873467\pi$
$314$	−0.927258	−	0.771060i	−0.0523282	−	0.0435134i
$315$	−0.827716	+	0.827716i	−0.0466365	+	0.0466365i
$316$	−10.1257	+	1.87844i	−0.569613	+	0.105671i
$317$	−12.8297	−	12.8297i	−0.720589	−	0.720589i	0.248136	−	0.968725i	$-0.420182\pi$
$317$	−12.8297	−	12.8297i	−0.720589	−	0.720589i	−0.968725	+	0.248136i	$0.920182\pi$
$318$	0.236054	−	0.0217104i	0.0132373	−	0.00121746i
$319$	−0.936163			−0.0524151
$320$	−1.69838	+	7.09003i	−0.0949422	+	0.396345i
$321$	−5.39643			−0.301200
$322$	−10.9258	+	1.00487i	−0.608871	+	0.0559991i
$323$	−3.41141	−	3.41141i	−0.189816	−	0.189816i
$324$	−1.96645	+	0.364802i	−0.109247	+	0.0202668i
$325$	0.146282	−	0.146282i	0.00811429	−	0.00811429i
$326$	14.8197	+	12.3233i	0.820788	+	0.682525i
$327$			17.7391i			0.980972i
$328$	−5.14317	−	18.2187i	−0.283984	−	1.00596i
$329$			0.557423i			0.0307318i
$330$	−0.272490	+	0.327689i	−0.0150001	+	0.0180387i
$331$	−2.41118	+	2.41118i	−0.132530	+	0.132530i	−0.770260	−	0.637730i	$-0.779874\pi$
$331$	−2.41118	+	2.41118i	−0.132530	+	0.132530i	0.637730	+	0.770260i	$0.279874\pi$
$332$	5.96240	+	4.09636i	0.327229	+	0.224817i
$333$	5.06780	+	5.06780i	0.277713	+	0.277713i
$334$	1.14684	+	12.4694i	0.0627520	+	0.682295i
$335$	7.05549			0.385483
$336$	2.08817	−	4.69437i	0.113919	−	0.256099i
$337$	−3.55179			−0.193478			−0.0967391	−	0.995310i	$-0.530841\pi$
$337$	−3.55179			−0.193478			−0.0967391	+	0.995310i	$0.530841\pi$
$338$	1.68346	+	18.3040i	0.0915681	+	0.995609i
$339$	6.54843	+	6.54843i	0.355662	+	0.355662i
$340$	1.03211	−	1.50227i	0.0559740	−	0.0814720i
$341$	−0.485315	+	0.485315i	−0.0262813	+	0.0262813i
$342$	4.36233	−	5.24603i	0.235888	−	0.283673i
$343$		−	15.8633i		−	0.856539i
$344$	10.0655	−	17.9839i	0.542696	−	0.969628i
$345$		−	5.50452i		−	0.296353i
$346$	23.5381	+	19.5730i	1.26541	+	1.05225i
$347$	−14.0357	+	14.0357i	−0.753473	+	0.753473i	−0.975126	−	0.221652i	$-0.928855\pi$
$347$	−14.0357	+	14.0357i	−0.753473	+	0.753473i	0.221652	+	0.975126i	$0.428855\pi$
$348$	1.03277	+	5.56709i	0.0553623	+	0.298427i
$349$	−1.19507	−	1.19507i	−0.0639705	−	0.0639705i	0.674398	−	0.738368i	$-0.264403\pi$
$349$	−1.19507	−	1.19507i	−0.0639705	−	0.0639705i	−0.738368	+	0.674398i	$0.764403\pi$
$350$	−7.54207	+	0.693659i	−0.403140	+	0.0370776i
$351$	0.0496164			0.00264833
$352$	0.600538	−	1.77158i	0.0320088	−	0.0944255i
$353$	3.31248			0.176306			0.0881529	−	0.996107i	$-0.471904\pi$
$353$	3.31248			0.176306			0.0881529	+	0.996107i	$0.471904\pi$
$354$	0.431808	−	0.0397142i	0.0229503	−	0.00211079i
$355$	−2.56998	−	2.56998i	−0.136400	−	0.136400i
$356$	2.10716	+	11.3585i	0.111679	+	0.602001i
$357$	−0.908254	+	0.908254i	−0.0480699	+	0.0480699i
$358$	17.7249	+	14.7391i	0.936791	+	0.778988i
$359$			14.0955i			0.743933i	0.928246	+	0.371967i	$0.121316\pi$
$359$			14.0955i			0.743933i	−0.928246	+	0.371967i	$0.878684\pi$
$360$	2.24928	+	1.25891i	0.118548	+	0.0663505i
$361$			4.27540i			0.225021i
$362$	−17.0823	+	20.5427i	−0.897825	+	1.07970i
$363$	−7.70085	+	7.70085i	−0.404190	+	0.404190i
$364$	−0.0721770	+	0.105056i	−0.00378310	+	0.00550643i
$365$	−8.46530	−	8.46530i	−0.443094	−	0.443094i
$366$	0.748745	+	8.14101i	0.0391375	+	0.425537i
$367$	−10.0915			−0.526772			−0.263386	−	0.964691i	$-0.584839\pi$
$367$	−10.0915			−0.526772			−0.263386	+	0.964691i	$0.584839\pi$
$368$	8.66594	+	22.5528i	0.451743	+	1.17565i
$369$	−6.69303			−0.348425
$370$	−0.845960	−	9.19801i	−0.0439794	−	0.478182i
$371$	0.152241	+	0.152241i	0.00790398	+	0.00790398i
$372$	3.42142	+	2.35063i	0.177393	+	0.121875i
$373$	−14.9814	+	14.9814i	−0.775707	+	0.775707i	−0.979098	−	0.203390i	$-0.934804\pi$
$373$	−14.9814	+	14.9814i	−0.775707	+	0.775707i	0.203390	+	0.979098i	$0.434804\pi$
$374$	−0.299003	+	0.359574i	−0.0154611	+	0.0185931i
$375$		−	8.35640i		−	0.431522i
$376$	1.18129	−	0.333481i	0.0609205	−	0.0171980i
$377$		−	0.140466i		−	0.00723436i
$378$	−1.39670	−	1.16143i	−0.0718387	−	0.0597374i
$379$	−18.0485	+	18.0485i	−0.927090	+	0.927090i	−0.997517	−	0.0704266i	$-0.977564\pi$
$379$	−18.0485	+	18.0485i	−0.927090	+	0.927090i	0.0704266	+	0.997517i	$0.477564\pi$
$380$	−8.64580	+	1.60391i	−0.443520	+	0.0822789i
$381$	−5.00050	−	5.00050i	−0.256183	−	0.256183i
$382$	−15.6263	+	1.43718i	−0.799510	+	0.0735325i
$383$	25.8774			1.32227			0.661137	−	0.750265i	$-0.270074\pi$
$383$	25.8774			1.32227			0.661137	+	0.750265i	$0.270074\pi$
$384$	−11.1976	−	1.61683i	−0.571424	−	0.0825086i
$385$	−0.387081			−0.0197275
$386$	−17.2476	+	1.58630i	−0.877880	+	0.0807404i
$387$	−5.15228	−	5.15228i	−0.261905	−	0.261905i
$388$	15.1024	−	2.80169i	0.766708	−	0.142234i
$389$	−9.99761	+	9.99761i	−0.506899	+	0.506899i	−0.913573	−	0.406674i	$-0.866688\pi$
$389$	−9.99761	+	9.99761i	−0.506899	+	0.506899i	0.406674	+	0.913573i	$0.366688\pi$
$390$	−0.0491679	−	0.0408855i	−0.00248971	−	0.00207032i
$391$		−	6.04012i		−	0.305462i
$392$	−14.5633	+	4.11126i	−0.735559	+	0.207650i
$393$		−	3.47862i		−	0.175473i
$394$	−22.1347	+	26.6186i	−1.11513	+	1.34103i
$395$	3.31818	−	3.31818i	0.166956	−	0.166956i
$396$	−0.545104	−	0.374505i	−0.0273925	−	0.0188196i
$397$	5.23824	+	5.23824i	0.262900	+	0.262900i	0.826231	−	0.563331i	$-0.190481\pi$
$397$	5.23824	+	5.23824i	0.262900	+	0.262900i	−0.563331	+	0.826231i	$0.690481\pi$
$398$	0.760651	+	8.27046i	0.0381280	+	0.414561i
$399$	6.19685			0.310230
$400$	5.98208	+	15.5682i	0.299104	+	0.778409i
$401$	25.8298			1.28988			0.644940	−	0.764233i	$-0.276882\pi$
$401$	25.8298			1.28988			0.644940	+	0.764233i	$0.276882\pi$
$402$	1.00275	+	10.9028i	0.0500129	+	0.543783i
$403$	−0.0728187	−	0.0728187i	−0.00362736	−	0.00362736i
$404$	4.05259	−	5.89868i	0.201624	−	0.293471i
$405$	0.644405	−	0.644405i	0.0320208	−	0.0320208i
$406$	−3.28805	+	3.95413i	−0.163183	+	0.196240i
$407$			2.36995i			0.117474i
$408$	2.46814	+	1.38141i	0.122191	+	0.0683898i
$409$			37.6846i			1.86338i	0.363253	+	0.931691i	$0.381666\pi$
$409$			37.6846i			1.86338i	−0.363253	+	0.931691i	$0.618334\pi$
$410$	6.63253	+	5.51527i	0.327557	+	0.272380i
$411$	9.28469	−	9.28469i	0.457980	−	0.457980i
$412$	−1.38989	−	7.49215i	−0.0684752	−	0.369112i
$413$	0.278491	+	0.278491i	0.0137037	+	0.0137037i
$414$	8.50612	−	0.782325i	0.418053	−	0.0384492i
$415$	−3.29626			−0.161807
$416$	0.265815	+	0.0901073i	0.0130327	+	0.00441787i
$417$	−16.9335			−0.829236
$418$	2.24667	−	0.206631i	0.109888	−	0.0101067i
$419$	−3.08487	−	3.08487i	−0.150706	−	0.150706i	0.627727	−	0.778433i	$-0.283985\pi$
$419$	−3.08487	−	3.08487i	−0.150706	−	0.150706i	−0.778433	+	0.627727i	$0.783985\pi$
$420$	0.427025	+	2.30186i	0.0208367	+	0.112319i
$421$	16.1291	−	16.1291i	0.786087	−	0.786087i	−0.194764	−	0.980850i	$-0.562394\pi$
$421$	16.1291	−	16.1291i	0.786087	−	0.786087i	0.980850	+	0.194764i	$0.0623940\pi$
$422$	−9.78479	−	8.13653i	−0.476316	−	0.396080i
$423$		−	0.433973i		−	0.0211005i
$424$	0.231551	−	0.413709i	0.0112451	−	0.0200915i
$425$		−	4.16948i		−	0.202250i
$426$	3.60613	−	4.33664i	0.174717	−	0.210111i
$427$	−5.25048	+	5.25048i	−0.254089	+	0.254089i
$428$	−6.11165	+	8.89572i	−0.295418	+	0.429991i
$429$	0.0116015	+	0.0116015i	0.000560128	+	0.000560128i
$430$	0.860063	+	9.35135i	0.0414759	+	0.450962i
$431$	6.17892			0.297628			0.148814	−	0.988865i	$-0.452454\pi$
$431$	6.17892			0.297628			0.148814	+	0.988865i	$0.452454\pi$
$432$	−1.62572	+	3.65473i	−0.0782173	+	0.175838i
$433$	2.86617			0.137739			0.0688697	−	0.997626i	$-0.478061\pi$
$433$	2.86617			0.137739			0.0688697	+	0.997626i	$0.478061\pi$
$434$	0.345300	+	3.75440i	0.0165749	+	0.180217i
$435$	−1.82434	−	1.82434i	−0.0874702	−	0.0874702i
$436$	29.2418	+	20.0901i	1.40043	+	0.962142i
$437$	−20.6053	+	20.6053i	−0.985685	+	0.985685i
$438$	11.8783	−	14.2845i	0.567566	−	0.682541i
$439$		−	24.2265i		−	1.15627i	−0.815942	−	0.578134i	$-0.803781\pi$
$439$		−	24.2265i		−	1.15627i	0.815942	−	0.578134i	$-0.196219\pi$
$440$	0.231573	+	0.820303i	0.0110398	+	0.0391064i
$441$			5.35015i			0.254769i
$442$	−0.0539520	−	0.0448637i	−0.00256623	−	0.00213395i
$443$	17.6169	−	17.6169i	0.837005	−	0.837005i	−0.151459	−	0.988464i	$-0.548397\pi$
$443$	17.6169	−	17.6169i	0.837005	−	0.837005i	0.988464	+	0.151459i	$0.0483971\pi$
$444$	14.0934	−	2.61452i	0.668844	−	0.124080i
$445$	−3.72219	−	3.72219i	−0.176449	−	0.176449i
$446$	29.6563	−	2.72755i	1.40426	−	0.129153i
$447$	13.9257			0.658665
$448$	−5.37347	−	8.75877i	−0.253873	−	0.413813i
$449$	11.3565			0.535946			0.267973	−	0.963426i	$-0.413646\pi$
$449$	11.3565			0.535946			0.267973	+	0.963426i	$0.413646\pi$
$450$	5.87176	−	0.540038i	0.276797	−	0.0254576i
$451$	−1.56500	−	1.56500i	−0.0736928	−	0.0736928i
$452$	18.2111	−	3.37839i	0.856576	−	0.158906i
$453$	1.11497	−	1.11497i	0.0523857	−	0.0523857i
$454$	−1.68543	−	1.40152i	−0.0791012	−	0.0657765i
$455$		−	0.0580793i		−	0.00272280i
$456$	−3.70729	−	13.1324i	−0.173610	−	0.614980i
$457$		−	0.753835i		−	0.0352629i	−0.999845	−	0.0176315i	$-0.994387\pi$
$457$		−	0.753835i		−	0.0352629i	0.999845	−	0.0176315i	$-0.00561256\pi$
$458$	−13.1484	+	15.8119i	−0.614384	+	0.738843i
$459$	0.707107	−	0.707107i	0.0330049	−	0.0330049i
$460$	−9.07389	−	6.23406i	−0.423072	−	0.290665i
$461$	−2.66793	−	2.66793i	−0.124258	−	0.124258i	0.642243	−	0.766501i	$-0.278004\pi$
$461$	−2.66793	−	2.66793i	−0.124258	−	0.124258i	−0.766501	+	0.642243i	$0.778004\pi$
$462$	−0.0550135	−	0.598155i	−0.00255946	−	0.0278287i
$463$	12.1249			0.563494			0.281747	−	0.959489i	$-0.409086\pi$
$463$	12.1249			0.563494			0.281747	+	0.959489i	$0.409086\pi$
$464$	10.3467	+	4.60246i	0.480333	+	0.213664i
$465$	−1.89150			−0.0877164
$466$	−0.916277	−	9.96256i	−0.0424457	−	0.461506i
$467$	−11.6520	−	11.6520i	−0.539192	−	0.539192i	0.384100	−	0.923292i	$-0.374512\pi$
$467$	−11.6520	−	11.6520i	−0.539192	−	0.539192i	−0.923292	+	0.384100i	$0.874512\pi$
$468$	0.0561923	−	0.0817898i	0.00259749	−	0.00378073i
$469$	−7.03170	+	7.03170i	−0.324694	+	0.324694i
$470$	−0.357608	+	0.430051i	−0.0164952	+	0.0198368i
$471$			0.852743i			0.0392923i
$472$	0.423570	−	0.756788i	0.0194964	−	0.0348340i
$473$		−	2.40946i		−	0.110787i
$474$	5.59916	+	4.65598i	0.257178	+	0.213856i
$475$	−14.2238	+	14.2238i	−0.652633	+	0.652633i
$476$	0.468576	+	2.52583i	0.0214771	+	0.115771i
$477$	−0.118525	−	0.118525i	−0.00542689	−	0.00542689i
$478$	−8.97816	+	0.825740i	−0.410652	+	0.0377685i
$479$	−7.83529			−0.358004			−0.179002	−	0.983849i	$-0.557287\pi$
$479$	−7.83529			−0.358004			−0.179002	+	0.983849i	$0.557287\pi$
$480$	4.62264	−	2.28205i	0.210993	−	0.104161i
$481$	−0.355598			−0.0162139
$482$	−9.77183	+	0.898735i	−0.445095	+	0.0409363i
$483$	5.48596	+	5.48596i	0.249620	+	0.249620i
$484$	3.97293	+	21.4159i	0.180588	+	0.973450i
$485$	−4.94905	+	4.94905i	−0.224725	+	0.224725i
$486$	1.08738	+	0.904212i	0.0493247	+	0.0410159i
$487$			1.89895i			0.0860495i	0.999074	+	0.0430248i	$0.0136994\pi$
$487$			1.89895i			0.0860495i	−0.999074	+	0.0430248i	$0.986301\pi$
$488$	14.2680	+	7.98571i	0.645881	+	0.361496i
$489$		−	13.6288i		−	0.616315i
$490$	4.40870	−	5.30179i	0.199165	−	0.239510i
$491$	26.1915	−	26.1915i	1.18201	−	1.18201i	0.202784	−	0.979224i	$-0.435001\pi$
$491$	26.1915	−	26.1915i	1.18201	−	1.18201i	0.979224	−	0.202784i	$-0.0649988\pi$
$492$	−7.58009	+	11.0331i	−0.341737	+	0.497410i
$493$	−2.00185	−	2.00185i	−0.0901587	−	0.0901587i
$494$	0.0310038	+	0.337101i	0.00139493	+	0.0151669i
$495$	0.301356			0.0135449
$496$	7.74977	−	2.97785i	0.347975	−	0.133710i
$497$	5.12263			0.229781
$498$	−0.468477	−	5.09369i	−0.0209930	−	0.228254i
$499$	15.1321	+	15.1321i	0.677406	+	0.677406i	0.959412	−	0.282007i	$-0.0910001\pi$
$499$	15.1321	+	15.1321i	0.677406	+	0.677406i	−0.282007	+	0.959412i	$0.591000\pi$
$500$	−13.7750	−	9.46391i	−0.616039	−	0.423239i
$501$	6.26101	−	6.26101i	0.279721	−	0.279721i
$502$	−13.5671	+	16.3154i	−0.605527	+	0.728192i
$503$		−	27.1528i		−	1.21069i	−0.795965	−	0.605343i	$-0.793036\pi$
$503$		−	27.1528i		−	1.21069i	0.795965	−	0.605343i	$-0.206964\pi$
$504$	−3.49636	+	0.987031i	−0.155740	+	0.0439658i
$505$			3.26103i			0.145114i
$506$	2.17187	+	1.80601i	0.0965513	+	0.0802871i
$507$	9.19065	−	9.19065i	0.408171	−	0.408171i
$508$	−13.9063	+	2.57980i	−0.616991	+	0.114460i
$509$	−12.6196	−	12.6196i	−0.559355	−	0.559355i	0.369769	−	0.929124i	$-0.379437\pi$
$509$	−12.6196	−	12.6196i	−0.559355	−	0.559355i	−0.929124	+	0.369769i	$0.879437\pi$
$510$	−1.28339	+	0.118036i	−0.0568296	+	0.00522674i
$511$	16.8735			0.746440
$512$	−15.3469	+	16.6275i	−0.678244	+	0.734837i
$513$	−4.82446			−0.213005
$514$	−21.3327	+	1.96201i	−0.940944	+	0.0865406i
$515$	2.45518	+	2.45518i	0.108188	+	0.108188i
$516$	−14.3284	+	2.65810i	−0.630772	+	0.117017i
$517$	0.101474	−	0.101474i	0.00446281	−	0.00446281i
$518$	10.0101	+	8.32389i	0.439819	+	0.365731i
$519$		−	21.6465i		−	0.950177i
$520$	−0.123082	+	0.0347462i	−0.00539749	+	0.00152372i
$521$			22.7492i			0.996660i	0.866988	+	0.498330i	$0.166053\pi$
$521$			22.7492i			0.996660i	−0.866988	+	0.498330i	$0.833947\pi$
$522$	2.55986	−	3.07842i	0.112042	−	0.134739i
$523$	17.1767	−	17.1767i	0.751085	−	0.751085i	−0.223597	−	0.974682i	$-0.571780\pi$
$523$	17.1767	−	17.1767i	0.751085	−	0.751085i	0.974682	+	0.223597i	$0.0717800\pi$
$524$	−5.73431	−	3.93966i	−0.250504	−	0.172105i
$525$	3.78695	+	3.78695i	0.165276	+	0.165276i
$526$	1.32308	+	14.3857i	0.0576890	+	0.627245i
$527$	−2.07555			−0.0904123
$528$	−1.23470	+	0.474434i	−0.0537334	+	0.0206471i
$529$	−13.4830			−0.586218
$530$	0.0197852	+	0.215122i	0.000859416	+	0.00934432i
$531$	−0.216815	−	0.216815i	−0.00940897	−	0.00940897i
$532$	7.01814	−	10.2151i	0.304275	−	0.442883i
$533$	0.234819	−	0.234819i	0.0101711	−	0.0101711i
$534$	5.22287	−	6.28090i	0.226016	−	0.271801i
$535$		−	4.91791i		−	0.212620i
$536$	19.1083	+	10.6948i	0.825354	+	0.461947i
$537$		−	16.3005i		−	0.703420i
$538$	10.8629	+	9.03299i	0.468331	+	0.389440i
$539$	−1.25100	+	1.25100i	−0.0538843	+	0.0538843i
$540$	−0.332454	−	1.79208i	−0.0143065	−	0.0771187i
$541$	0.609283	+	0.609283i	0.0261951	+	0.0261951i	0.720083	−	0.693888i	$-0.244104\pi$
$541$	0.609283	+	0.609283i	0.0261951	+	0.0261951i	−0.693888	+	0.720083i	$0.744104\pi$
$542$	−26.7204	+	2.45753i	−1.14774	+	0.105560i
$543$	18.8919			0.810729
$544$	5.07242	−	2.50410i	0.217478	−	0.107362i
$545$	−16.1661			−0.692479
$546$	0.0897497	−	0.00825446i	0.00384093	−	0.000353258i
$547$	−27.2265	−	27.2265i	−1.16412	−	1.16412i	−0.983564	−	0.180558i	$-0.942210\pi$
$547$	−27.2265	−	27.2265i	−1.16412	−	1.16412i	−0.180558	−	0.983564i	$-0.557790\pi$
$548$	−4.79005	−	25.8205i	−0.204621	−	1.10300i
$549$	4.08768	−	4.08768i	0.174458	−	0.174458i
$550$	1.49924	+	1.24669i	0.0639277	+	0.0531590i
$551$			13.6582i			0.581860i
$552$	8.34385	−	14.9079i	0.355138	−	0.634521i
$553$			6.61398i			0.281255i
$554$	23.2297	−	27.9355i	0.986937	−	1.18687i
$555$	−4.61842	+	4.61842i	−0.196041	+	0.196041i
$556$	−19.1778	+	27.9139i	−0.813318	+	1.18381i
$557$	−22.7863	−	22.7863i	−0.965485	−	0.965485i	0.0339389	−	0.999424i	$-0.489195\pi$
$557$	−22.7863	−	22.7863i	−0.965485	−	0.965485i	−0.999424	+	0.0339389i	$0.989195\pi$
$558$	−0.268828	−	2.92293i	−0.0113804	−	0.123738i
$559$	0.361526			0.0152909
$560$	4.27811	+	1.90301i	0.180783	+	0.0804168i
$561$	0.330678			0.0139612
$562$	2.32620	+	25.2925i	0.0981249	+	1.06690i
$563$	21.7926	+	21.7926i	0.918449	+	0.918449i	0.996917	−	0.0784678i	$-0.0250028\pi$
$563$	21.7926	+	21.7926i	0.918449	+	0.918449i	−0.0784678	+	0.996917i	$0.525003\pi$
$564$	−0.715381	−	0.491490i	−0.0301230	−	0.0206955i
$565$	−5.96776	+	5.96776i	−0.251066	+	0.251066i
$566$	7.80473	−	9.38578i	0.328057	−	0.394514i
$567$			1.28446i			0.0539424i
$568$	−3.06464	−	10.8559i	−0.128589	−	0.455503i
$569$			23.0080i			0.964547i	0.876021	+	0.482274i	$0.160189\pi$
$569$			23.0080i			0.964547i	−0.876021	+	0.482274i	$0.839811\pi$
$570$	4.78085	+	3.97551i	0.200248	+	0.166516i
$571$	−27.7065	+	27.7065i	−1.15948	+	1.15948i	−0.174893	+	0.984587i	$0.555958\pi$
$571$	−27.7065	+	27.7065i	−1.15948	+	1.15948i	−0.984587	+	0.174893i	$0.944042\pi$
$572$	0.0322636	−	0.00598533i	0.00134901	−	0.000250259i
$573$	7.84611	+	7.84611i	0.327776	+	0.327776i
$574$	−12.1068	+	1.11349i	−0.505330	+	0.0464762i
$575$	−25.1842			−1.05025
$576$	4.18344	+	6.81901i	0.174310	+	0.284125i
$577$	−12.0843			−0.503078			−0.251539	−	0.967847i	$-0.580937\pi$
$577$	−12.0843			−0.503078			−0.251539	+	0.967847i	$0.580937\pi$
$578$	−1.40827	+	0.129521i	−0.0585763	+	0.00538738i
$579$	8.66020	+	8.66020i	0.359906	+	0.359906i
$580$	−5.07344	+	0.941191i	−0.210663	+	0.0390808i
$581$	3.28514	−	3.28514i	0.136291	−	0.136291i
$582$	−8.35114	−	6.94438i	−0.346166	−	0.287854i
$583$		−	0.0554283i		−	0.00229560i
$584$	−10.0947	−	35.7584i	−0.417720	−	1.47969i
$585$			0.0452167i			0.00186948i
$586$	−14.2196	+	17.1001i	−0.587406	+	0.706400i
$587$	20.5183	−	20.5183i	0.846879	−	0.846879i	−0.142863	−	0.989742i	$-0.545631\pi$
$587$	20.5183	−	20.5183i	0.846879	−	0.846879i	0.989742	+	0.142863i	$0.0456309\pi$
$588$	8.81942	+	6.05923i	0.363707	+	0.249879i
$589$	7.08054	+	7.08054i	0.291749	+	0.291749i
$590$	0.0361926	+	0.393518i	0.00149003	+	0.0162009i
$591$	24.4795			1.00695
$592$	11.6514	−	26.1932i	0.478870	−	1.07654i
$593$	−39.3671			−1.61661			−0.808307	−	0.588762i	$-0.799616\pi$
$593$	−39.3671			−1.61661			−0.808307	+	0.588762i	$0.799616\pi$
$594$	0.0428299	+	0.465684i	0.00175733	+	0.0191073i
$595$	−0.827716	−	0.827716i	−0.0339330	−	0.0339330i
$596$	15.7714	−	22.9558i	0.646021	−	0.940305i
$597$	4.15268	−	4.15268i	0.169958	−	0.169958i
$598$	−0.270982	+	0.325876i	−0.0110813	+	0.0133261i
$599$			13.6942i			0.559528i	0.960069	+	0.279764i	$0.0902563\pi$
$599$			13.6942i			0.559528i	−0.960069	+	0.279764i	$0.909744\pi$
$600$	5.75975	−	10.2909i	0.235141	−	0.420123i
$601$		−	28.6299i		−	1.16784i	−0.811812	−	0.583919i	$-0.801519\pi$
$601$		−	28.6299i		−	1.16784i	0.811812	−	0.583919i	$-0.198481\pi$
$602$	−10.1770	−	8.46266i	−0.414783	−	0.344912i
$603$	5.47442	−	5.47442i	0.222936	−	0.222936i
$604$	−0.575221	−	3.10070i	−0.0234054	−	0.126166i
$605$	−7.01799	−	7.01799i	−0.285322	−	0.285322i
$606$	−5.03926	+	0.463471i	−0.204706	+	0.0188272i
$607$	−22.2575			−0.903404			−0.451702	−	0.892169i	$-0.649183\pi$
$607$	−22.2575			−0.903404			−0.451702	+	0.892169i	$0.649183\pi$
$608$	−25.8466	−	8.76160i	−1.04822	−	0.355330i
$609$	3.63637			0.147353
$610$	−7.41912	+	0.682351i	−0.300391	+	0.0276276i
$611$	0.0152256	+	0.0152256i	0.000615960	+	0.000615960i
$612$	−0.364802	−	1.96645i	−0.0147463	−	0.0794890i
$613$	−8.05316	+	8.05316i	−0.325264	+	0.325264i	−0.850782	−	0.525518i	$-0.823871\pi$
$613$	−8.05316	+	8.05316i	−0.325264	+	0.325264i	0.525518	+	0.850782i	$0.323871\pi$
$614$	18.7293	+	15.5743i	0.755852	+	0.628528i
$615$		−	6.09954i		−	0.245957i
$616$	−1.04833	−	0.586745i	−0.0422384	−	0.0236406i
$617$			19.7436i			0.794847i	0.917635	+	0.397424i	$0.130096\pi$
$617$			19.7436i			0.794847i	−0.917635	+	0.397424i	$0.869904\pi$
$618$	−3.44504	+	4.14292i	−0.138580	+	0.166653i
$619$	1.83104	−	1.83104i	0.0735957	−	0.0735957i	−0.669351	−	0.742946i	$-0.733428\pi$
$619$	1.83104	−	1.83104i	0.0735957	−	0.0735957i	0.742946	+	0.669351i	$0.233428\pi$
$620$	−2.14219	+	3.11804i	−0.0860326	+	0.125223i
$621$	−4.27101	−	4.27101i	−0.171390	−	0.171390i
$622$	−2.49777	−	27.1579i	−0.100151	−	1.08893i
$623$	7.41928			0.297247
$624$	−0.0711861	−	0.185260i	−0.00284972	−	0.00741632i
$625$	−13.2320			−0.529281
$626$	−1.77419	−	19.2905i	−0.0709107	−	0.771003i
$627$	−1.12808	−	1.12808i	−0.0450511	−	0.0450511i
$628$	1.40570	+	0.965761i	0.0560935	+	0.0385381i
$629$	−5.06780	+	5.06780i	−0.202066	+	0.202066i
$630$	1.05844	−	1.27285i	0.0421693	−	0.0507117i
$631$			41.6144i			1.65664i	0.560252	+	0.828322i	$0.310704\pi$
$631$			41.6144i			1.65664i	−0.560252	+	0.828322i	$0.689296\pi$
$632$	14.0164	−	3.95685i	0.557541	−	0.157395i
$633$			8.99848i			0.357657i
$634$	19.7294	+	16.4060i	0.783556	+	0.651565i
$635$	4.55708	−	4.55708i	0.180842	−	0.180842i
$636$	−0.329616	+	0.0611481i	−0.0130701	+	0.00242468i
$637$	−0.187705	−	0.187705i	−0.00743715	−	0.00743715i
$638$	1.31837	−	0.121253i	0.0521948	−	0.00480046i
$639$	−3.98814			−0.157768
$640$	1.47346	−	10.2047i	0.0582437	−	0.403374i
$641$	14.1354			0.558317			0.279158	−	0.960245i	$-0.409945\pi$
$641$	14.1354			0.558317			0.279158	+	0.960245i	$0.409945\pi$
$642$	7.59964	−	0.698954i	0.299934	−	0.0275855i
$643$	−10.1071	−	10.1071i	−0.398586	−	0.398586i	0.479148	−	0.877734i	$-0.340946\pi$
$643$	−10.1071	−	10.1071i	−0.398586	−	0.398586i	−0.877734	+	0.479148i	$0.840946\pi$
$644$	15.2563	−	2.83025i	0.601184	−	0.111528i
$645$	4.69541	−	4.69541i	0.184882	−	0.184882i
$646$	5.24603	+	4.36233i	0.206402	+	0.171634i
$647$			30.1934i			1.18702i	0.804825	+	0.593512i	$0.202259\pi$
$647$			30.1934i			1.18702i	−0.804825	+	0.593512i	$0.797741\pi$
$648$	2.72204	−	0.768437i	0.106932	−	0.0301871i
$649$		−	0.101393i		−	0.00398004i
$650$	−0.187059	+	0.224952i	−0.00733704	+	0.00882334i
$651$	1.88513	−	1.88513i	0.0738839	−	0.0738839i
$652$	−22.4663	−	15.4351i	−0.879847	−	0.604484i
$653$	7.04734	+	7.04734i	0.275784	+	0.275784i	0.831423	−	0.555640i	$-0.187527\pi$
$653$	7.04734	+	7.04734i	0.275784	+	0.275784i	−0.555640	+	0.831423i	$0.687527\pi$
$654$	−2.29759	−	24.9814i	−0.0898428	−	0.976850i
$655$	3.17016			0.123868
$656$	9.60269	+	24.9907i	0.374922	+	0.975723i
$657$	−13.1366			−0.512508
$658$	−0.0721983	−	0.785003i	−0.00281458	−	0.0306026i
$659$	−12.3885	−	12.3885i	−0.482586	−	0.482586i	0.423371	−	0.905957i	$-0.360847\pi$
$659$	−12.3885	−	12.3885i	−0.482586	−	0.482586i	−0.905957	+	0.423371i	$0.860847\pi$
$660$	0.341296	−	0.496768i	0.0132849	−	0.0193367i
$661$	25.3403	−	25.3403i	0.985625	−	0.985625i	−0.0142732	−	0.999898i	$-0.504543\pi$
$661$	25.3403	−	25.3403i	0.985625	−	0.985625i	0.999898	+	0.0142732i	$0.00454344\pi$
$662$	3.08329	−	3.70789i	0.119835	−	0.144111i
$663$			0.0496164i			0.00192694i
$664$	−8.92723	−	4.99653i	−0.346444	−	0.193903i
$665$			5.64735i			0.218995i
$666$	−7.79321	−	6.48044i	−0.301981	−	0.251112i
$667$	−12.0914	+	12.0914i	−0.468181	+	0.468181i
$668$	−3.23011	−	17.4117i	−0.124977	−	0.673680i
$669$	−14.8907	−	14.8907i	−0.575708	−	0.575708i
$670$	−9.93603	+	0.913837i	−0.383862	+	0.0353046i
$671$	1.91160			0.0737967
$672$	−2.33269	+	6.88140i	−0.0899855	+	0.265456i
$673$	−6.33283			−0.244113			−0.122056	−	0.992523i	$-0.538949\pi$
$673$	−6.33283			−0.244113			−0.122056	+	0.992523i	$0.538949\pi$
$674$	5.00188	−	0.460033i	0.192665	−	0.0177198i
$675$	−2.94827	−	2.94827i	−0.113479	−	0.113479i
$676$	−4.74153	−	25.5590i	−0.182367	−	0.983038i
$677$	−11.4371	+	11.4371i	−0.439564	+	0.439564i	−0.891865	−	0.452301i	$-0.850603\pi$
$677$	−11.4371	+	11.4371i	−0.439564	+	0.439564i	0.452301	+	0.891865i	$0.350603\pi$
$678$	−10.0701	−	8.37380i	−0.386741	−	0.321594i
$679$		−	9.86473i		−	0.378574i
$680$	−1.25891	+	2.24928i	−0.0482771	+	0.0862560i
$681$			1.54999i			0.0593957i
$682$	0.620596	−	0.746313i	0.0237638	−	0.0285778i
$683$	17.4679	−	17.4679i	0.668392	−	0.668392i	−0.288952	−	0.957344i	$-0.593307\pi$
$683$	17.4679	−	17.4679i	0.668392	−	0.668392i	0.957344	+	0.288952i	$0.0933068\pi$
$684$	−5.46387	+	7.95285i	−0.208916	+	0.304085i
$685$	8.46139	+	8.46139i	0.323293	+	0.323293i
$686$	2.05464	+	22.3399i	0.0784466	+	0.852940i
$687$	14.5413			0.554784
$688$	−11.8457	+	26.6299i	−0.451611	+	1.01526i
$689$	0.00831669			0.000316841
$690$	0.712953	+	7.75185i	0.0271417	+	0.295108i
$691$	−12.5054	−	12.5054i	−0.475728	−	0.475728i	0.428034	−	0.903762i	$-0.359206\pi$
$691$	−12.5054	−	12.5054i	−0.475728	−	0.475728i	−0.903762	+	0.428034i	$0.859206\pi$
$692$	−35.6831	−	24.5154i	−1.35647	−	0.931937i
$693$	−0.300340	+	0.300340i	−0.0114090	+	0.0114090i
$694$	17.9481	−	21.5839i	0.681299	−	0.819314i
$695$		−	15.4319i		−	0.585367i
$696$	−2.17548	−	7.70620i	−0.0824612	−	0.292103i
$697$		−	6.69303i		−	0.253517i
$698$	1.83777	+	1.52819i	0.0695605	+	0.0578429i
$699$	−5.00230	+	5.00230i	−0.189204	+	0.189204i
$700$	10.5314	−	1.95372i	0.398050	−	0.0738436i
$701$	−20.5410	−	20.5410i	−0.775825	−	0.775825i	0.203293	−	0.979118i	$-0.434836\pi$
$701$	−20.5410	−	20.5410i	−0.775825	−	0.775825i	−0.979118	+	0.203293i	$0.934836\pi$
$702$	−0.0698733	+	0.00642638i	−0.00263720	+	0.000242548i
$703$	34.5766			1.30408
$704$	−0.616263	+	2.57264i	−0.0232263	+	0.0969602i
$705$	0.395492			0.0148951
$706$	−4.66487	+	0.429038i	−0.175565	+	0.0161470i
$707$	−3.25004	−	3.25004i	−0.122230	−	0.122230i
$708$	−0.602958	+	0.111857i	−0.0226605	+	0.00420383i
$709$	−9.21025	+	9.21025i	−0.345898	+	0.345898i	−0.858579	−	0.512681i	$-0.828652\pi$
$709$	−9.21025	+	9.21025i	−0.345898	+	0.345898i	0.512681	+	0.858579i	$0.328652\pi$
$710$	3.95209	+	3.28636i	0.148319	+	0.123335i
$711$		−	5.14921i		−	0.193111i
$712$	−4.43862	−	15.7230i	−0.166344	−	0.589242i
$713$			12.5366i			0.469498i
$714$	1.16143	−	1.39670i	0.0434653	−	0.0522704i
$715$	−0.0105728	+	0.0105728i	−0.000395400	+	0.000395400i
$716$	−26.8705	−	18.4609i	−1.00420	−	0.689917i
$717$	4.50803	+	4.50803i	0.168355	+	0.168355i
$718$	−1.82567	−	19.8503i	−0.0681335	−	0.740807i
$719$	18.1177			0.675677			0.337839	−	0.941204i	$-0.390304\pi$
$719$	18.1177			0.675677			0.337839	+	0.941204i	$0.390304\pi$
$720$	−3.33065	−	1.48156i	−0.124126	−	0.0552144i
$721$	−4.89380			−0.182255
$722$	−0.553756	−	6.02092i	−0.0206087	−	0.224075i
$723$	4.90654	+	4.90654i	0.182476	+	0.182476i
$724$	21.3957	−	31.1422i	0.795167	−	1.15739i
$725$	−8.34667	+	8.34667i	−0.309987	+	0.309987i
$726$	9.84746	−	11.8423i	0.365473	−	0.439509i
$727$		−	49.0069i		−	1.81757i	−0.417269	−	0.908783i	$-0.637013\pi$
$727$		−	49.0069i		−	1.81757i	0.417269	−	0.908783i	$-0.362987\pi$
$728$	0.0880377	−	0.157296i	0.00326289	−	0.00582977i
$729$		−	1.00000i		−	0.0370370i
$730$	13.0179	+	10.8250i	0.481813	+	0.400651i
$731$	5.15228	−	5.15228i	0.190564	−	0.190564i
$732$	−2.10887	−	11.3678i	−0.0779461	−	0.420164i
$733$	31.4573	+	31.4573i	1.16190	+	1.16190i	0.984059	+	0.177842i	$0.0569115\pi$
$733$	31.4573	+	31.4573i	1.16190	+	1.16190i	0.177842	+	0.984059i	$0.443088\pi$
$734$	14.2115	−	1.30706i	0.524558	−	0.0482446i
$735$	−4.87574			−0.179844
$736$	−15.1251	−	30.6380i	−0.557517	−	1.12933i
$737$	2.56011			0.0943029
$738$	9.42559	−	0.866891i	0.346961	−	0.0319107i
$739$	−5.58496	−	5.58496i	−0.205446	−	0.205446i	0.596883	−	0.802329i	$-0.296406\pi$
$739$	−5.58496	−	5.58496i	−0.205446	−	0.205446i	−0.802329	+	0.596883i	$0.796406\pi$
$740$	2.38268	+	12.8437i	0.0875891	+	0.472144i
$741$	0.169262	−	0.169262i	0.00621798	−	0.00621798i
$742$	−0.234115	−	0.194678i	−0.00859465	−	0.00714687i
$743$			37.3446i			1.37004i	0.728523	+	0.685021i	$0.240207\pi$
$743$			37.3446i			1.37004i	−0.728523	+	0.685021i	$0.759793\pi$
$744$	−5.12275	−	2.86718i	−0.187809	−	0.105116i
$745$			12.6909i			0.464958i
$746$	19.1574	−	23.0383i	0.701404	−	0.843491i
$747$	−2.55760	+	2.55760i	−0.0935776	+	0.0935776i
$748$	0.374505	−	0.545104i	0.0136932	−	0.0199310i
$749$	4.90133	+	4.90133i	0.179091	+	0.179091i
$750$	1.08233	+	11.7681i	0.0395212	+	0.429709i
$751$	21.3988			0.780853			0.390427	−	0.920634i	$-0.372328\pi$
$751$	21.3988			0.780853			0.390427	+	0.920634i	$0.372328\pi$
$752$	−1.62039	+	0.622635i	−0.0590894	+	0.0227051i
$753$	15.0043			0.546787
$754$	0.0181933	+	0.197814i	0.000662563	+	0.00720396i
$755$	1.01610	+	1.01610i	0.0369796	+	0.0369796i
$756$	2.11737	+	1.45470i	0.0770079	+	0.0529070i
$757$	−27.7031	+	27.7031i	−1.00689	+	1.00689i	−0.00690987	+	0.999976i	$0.502199\pi$
$757$	−27.7031	+	27.7031i	−1.00689	+	1.00689i	−0.999976	+	0.00690987i	$0.997801\pi$
$758$	23.0795	−	27.7549i	0.838286	−	1.00810i
$759$		−	1.99734i		−	0.0724987i
$760$	11.9679	−	3.37856i	0.434121	−	0.122553i
$761$		−	3.33464i		−	0.120881i	−0.998172	−	0.0604404i	$-0.980749\pi$
$761$		−	3.33464i		−	0.120881i	0.998172	−	0.0604404i	$-0.0192505\pi$
$762$	7.68972	+	6.39438i	0.278569	+	0.231644i
$763$	16.1116	−	16.1116i	0.583278	−	0.583278i
$764$	21.8199	−	4.04787i	0.789415	−	0.146447i
$765$	0.644405	+	0.644405i	0.0232985	+	0.0232985i
$766$	−36.4424	+	3.35168i	−1.31672	+	0.121101i
$767$	0.0152135			0.000549328
$768$	15.9786	+	0.826609i	0.576579	+	0.0298277i
$769$	24.7825			0.893681			0.446840	−	0.894614i	$-0.352549\pi$
$769$	24.7825			0.893681			0.446840	+	0.894614i	$0.352549\pi$
$770$	0.545115	−	0.0501353i	0.0196446	−	0.00180675i
$771$	10.7114	+	10.7114i	0.385760	+	0.385760i
$772$	24.0838	−	4.46787i	0.866796	−	0.160802i
$773$	1.14601	−	1.14601i	0.0412190	−	0.0412190i	−0.686197	−	0.727416i	$-0.740721\pi$
$773$	1.14601	−	1.14601i	0.0412190	−	0.0412190i	0.727416	+	0.686197i	$0.240721\pi$
$774$	7.92313	+	6.58847i	0.284791	+	0.236818i
$775$			8.65397i			0.310860i
$776$	−20.9054	+	5.90163i	−0.750459	+	0.211856i
$777$		−	9.20569i		−	0.330252i
$778$	12.7844	−	15.3742i	0.458344	−	0.551193i
$779$	−22.8326	+	22.8326i	−0.818065	+	0.818065i
$780$	0.0745372	+	0.0512095i	0.00266886	+	0.00183359i
$781$	−0.932527	−	0.932527i	−0.0333684	−	0.0333684i
$782$	0.782325	+	8.50612i	0.0279759	+	0.304178i
$783$	−2.83104			−0.101173
$784$	19.9766	−	7.67602i	0.713450	−	0.274144i
$785$	−0.777127			−0.0277369
$786$	0.450556	+	4.89884i	0.0160708	+	0.174736i
$787$	20.8106	+	20.8106i	0.741816	+	0.741816i	0.972927	−	0.231111i	$-0.0742361\pi$
$787$	20.8106	+	20.8106i	0.741816	+	0.741816i	−0.231111	+	0.972927i	$0.574236\pi$
$788$	27.7239	−	40.3531i	0.987623	−	1.43752i
$789$	7.22319	−	7.22319i	0.257153	−	0.257153i
$790$	−4.24312	+	5.10267i	−0.150963	+	0.181545i
$791$		−	11.8953i		−	0.422947i
$792$	0.816161	+	0.456801i	0.0290010	+	0.0162317i
$793$			0.286825i			0.0101855i
$794$	−8.05532	−	6.69839i	−0.285872	−	0.237717i
$795$	0.108015	−	0.108015i	0.00383090	−	0.00383090i
$796$	−2.14240	−	11.5485i	−0.0759355	−	0.409326i
$797$	−23.5168	−	23.5168i	−0.833008	−	0.833008i	0.154919	−	0.987927i	$-0.450488\pi$
$797$	−23.5168	−	23.5168i	−0.833008	−	0.833008i	−0.987927	+	0.154919i	$0.950488\pi$
$798$	−8.72683	+	0.802624i	−0.308927	+	0.0284126i
$799$	0.433973			0.0153529
$800$	−10.4408	−	21.1494i	−0.369138	−	0.747744i
$801$	−5.77616			−0.204091
$802$	−36.3754	+	3.34552i	−1.28446	+	0.118134i
$803$	−3.07166	−	3.07166i	−0.108397	−	0.108397i
$804$	−2.82430	−	15.2242i	−0.0996053	−	0.536917i
$805$	−4.99950	+	4.99950i	−0.176209	+	0.176209i
$806$	0.111980	+	0.0931168i	0.00394433	+	0.00327990i
$807$		−	9.98991i		−	0.351662i
$808$	−4.94314	+	8.83184i	−0.173899	+	0.310703i
$809$		−	52.4182i		−	1.84292i	−0.388468	−	0.921462i	$-0.626996\pi$
$809$		−	52.4182i		−	1.84292i	0.388468	−	0.921462i	$-0.373004\pi$
$810$	−0.824032	+	0.990961i	−0.0289535	+	0.0348188i
$811$	31.9720	−	31.9720i	1.12269	−	1.12269i	0.131355	−	0.991335i	$-0.458067\pi$
$811$	31.9720	−	31.9720i	1.12269	−	1.12269i	0.991335	−	0.131355i	$-0.0419328\pi$
$812$	4.11832	−	5.99435i	0.144525	−	0.210360i
$813$	13.4166	+	13.4166i	0.470540	+	0.470540i
$814$	−0.306960	−	3.33753i	−0.0107589	−	0.116981i
$815$	12.4203			0.435063
$816$	−3.65473	−	1.62572i	−0.127941	−	0.0569114i
$817$	−35.1531			−1.22985
$818$	−4.88096	−	53.0700i	−0.170659	−	1.85555i
$819$	−0.0450643	−	0.0450643i	−0.00157467	−	0.00157467i
$820$	−10.0547	−	6.90794i	−0.351127	−	0.241236i
$821$	−34.0234	+	34.0234i	−1.18742	+	1.18742i	−0.209647	+	0.977777i	$0.567232\pi$
$821$	−34.0234	+	34.0234i	−1.18742	+	1.18742i	−0.977777	+	0.209647i	$0.932768\pi$
$822$	−11.8728	+	14.2779i	−0.414111	+	0.498000i
$823$			21.4346i			0.747163i	0.927597	+	0.373582i	$0.121870\pi$
$823$			21.4346i			0.747163i	−0.927597	+	0.373582i	$0.878130\pi$
$824$	2.92774	+	10.3710i	0.101993	+	0.361289i
$825$		−	1.37876i		−	0.0480022i
$826$	−0.428261	−	0.356120i	−0.0149011	−	0.0123910i
$827$	−33.3300	+	33.3300i	−1.15900	+	1.15900i	−0.174308	+	0.984691i	$0.555769\pi$
$827$	−33.3300	+	33.3300i	−1.15900	+	1.15900i	−0.984691	+	0.174308i	$0.944231\pi$
$828$	−11.8776	+	2.20345i	−0.412774	+	0.0765751i
$829$	−6.88817	−	6.88817i	−0.239236	−	0.239236i	0.577298	−	0.816534i	$-0.304107\pi$
$829$	−6.88817	−	6.88817i	−0.239236	−	0.239236i	−0.816534	+	0.577298i	$0.804107\pi$
$830$	4.64202	−	0.426936i	0.161127	−	0.0148192i
$831$	−25.6906			−0.891197
$832$	−0.386011	−	0.0924666i	−0.0133825	−	0.00320570i
$833$	−5.35015			−0.185372
$834$	23.8469	−	2.19325i	0.825751	−	0.0759460i
$835$	5.70583	+	5.70583i	0.197458	+	0.197458i
$836$	−3.13716	+	0.581985i	−0.108501	+	0.0201284i
$837$	−1.46763	+	1.46763i	−0.0507289	+	0.0507289i
$838$	4.74389	+	3.94477i	0.163875	+	0.136270i
$839$			10.2069i			0.352382i	0.984356	+	0.176191i	$0.0563776\pi$
$839$			10.2069i			0.352382i	−0.984356	+	0.176191i	$0.943622\pi$
$840$	−0.899507	−	3.18633i	−0.0310360	−	0.109939i
$841$		−	20.9852i		−	0.723628i
$842$	−20.6251	+	24.8033i	−0.710789	+	0.854777i
$843$	12.6996	−	12.6996i	0.437398	−	0.437398i
$844$	14.8335	+	10.1911i	0.510589	+	0.350792i
$845$	8.37568	+	8.37568i	0.288132	+	0.288132i
$846$	0.0562089	+	0.611152i	0.00193250	+	0.0210118i
$847$	13.9887			0.480656
$848$	−0.272502	+	0.612605i	−0.00935777	+	0.0210370i
$849$	−8.63153			−0.296233
$850$	0.540038	+	5.87176i	0.0185231	+	0.201400i
$851$	30.6101	+	30.6101i	1.04930	+	1.04930i
$852$	−4.51671	+	6.57423i	−0.154740	+	0.225229i
$853$	13.4780	−	13.4780i	0.461477	−	0.461477i	−0.437662	−	0.899139i	$-0.644194\pi$
$853$	13.4780	−	13.4780i	0.461477	−	0.461477i	0.899139	+	0.437662i	$0.144194\pi$
$854$	6.71405	−	8.07415i	0.229750	−	0.276292i
$855$		−	4.39666i		−	0.150363i
$856$	7.45467	−	13.3192i	0.254795	−	0.455239i
$857$			46.3030i			1.58168i	0.612022	+	0.790840i	$0.290356\pi$
$857$			46.3030i			1.58168i	−0.612022	+	0.790840i	$0.709644\pi$
$858$	−0.0178408	−	0.0148355i	−0.000609073	−	0.000506474i
$859$	24.0961	−	24.0961i	0.822148	−	0.822148i	−0.164267	−	0.986416i	$-0.552526\pi$
$859$	24.0961	−	24.0961i	0.822148	−	0.822148i	0.986416	+	0.164267i	$0.0525260\pi$
$860$	−2.42240	−	13.0578i	−0.0826032	−	0.445268i
$861$	6.07897	+	6.07897i	0.207171	+	0.207171i
$862$	−8.70158	+	0.800302i	−0.296377	+	0.0272584i
$863$	−19.4093			−0.660699			−0.330350	−	0.943859i	$-0.607167\pi$
$863$	−19.4093			−0.660699			−0.330350	+	0.943859i	$0.607167\pi$
$864$	1.81608	−	5.35741i	0.0617843	−	0.182263i
$865$	19.7271			0.670740
$866$	−4.03634	+	0.371231i	−0.137160	+	0.0126149i
$867$	0.707107	+	0.707107i	0.0240146	+	0.0240146i
$868$	−0.972552	−	5.24249i	−0.0330106	−	0.177942i
$869$	1.20401	−	1.20401i	0.0408434	−	0.0408434i
$870$	2.80545	+	2.33287i	0.0951136	+	0.0790916i
$871$			0.384130i			0.0130157i
$872$	−43.7825	−	24.5048i	−1.48266	−	0.829839i
$873$			7.68003i			0.259930i
$874$	26.3490	−	31.6867i	0.891268	−	1.07182i
$875$	−7.58973	+	7.58973i	−0.256580	+	0.256580i
$876$	−14.8777	+	21.6549i	−0.502670	+	0.731653i
$877$	29.1399	+	29.1399i	0.983985	+	0.983985i	0.999874	−	0.0158889i	$-0.00505780\pi$
$877$	29.1399	+	29.1399i	0.983985	+	0.983985i	−0.0158889	+	0.999874i	$0.505058\pi$
$878$	3.13785	+	34.1174i	0.105897	+	1.15141i
$879$	15.7260			0.530424
$880$	−0.432364	−	1.12521i	−0.0145750	−	0.0379310i
$881$	−8.55581			−0.288252			−0.144126	−	0.989559i	$-0.546037\pi$
$881$	−8.55581			−0.288252			−0.144126	+	0.989559i	$0.546037\pi$
$882$	−0.692959	−	7.53446i	−0.0233332	−	0.253698i
$883$	21.9839	+	21.9839i	0.739818	+	0.739818i	0.972543	−	0.232725i	$-0.0747642\pi$
$883$	21.9839	+	21.9839i	0.739818	+	0.739818i	−0.232725	+	0.972543i	$0.574764\pi$
$884$	0.0817898	+	0.0561923i	0.00275089	+	0.00188995i
$885$	0.197589	−	0.197589i	0.00664189	−	0.00664189i
$886$	−22.5276	+	27.0911i	−0.756829	+	0.910144i
$887$			7.16225i			0.240485i	0.992745	+	0.120242i	$0.0383672\pi$
$887$			7.16225i			0.240485i	−0.992745	+	0.120242i	$0.961633\pi$
$888$	−19.5087	+	5.50735i	−0.654670	+	0.184815i
$889$			9.08344i			0.304649i
$890$	5.72395	+	4.75975i	0.191867	+	0.159547i
$891$	0.233825	−	0.233825i	0.00783343	−	0.00783343i
$892$	−41.4107	+	7.68224i	−1.38653	+	0.257221i
$893$	−1.48046	−	1.48046i	−0.0495417	−	0.0495417i
$894$	−19.6112	+	1.80368i	−0.655896	+	0.0603241i
$895$	14.8551			0.496552
$896$	8.70175	+	11.6387i	0.290705	+	0.388823i
$897$	0.299689			0.0100063
$898$	−15.9930	+	1.47091i	−0.533694	+	0.0490849i
$899$	4.15493	+	4.15493i	0.138575	+	0.138575i
$900$	−8.19907	+	1.52104i	−0.273302	+	0.0507012i
$901$	0.118525	−	0.118525i	0.00394865	−	0.00394865i
$902$	2.40664	+	2.00124i	0.0801323	+	0.0666339i
$903$			9.35915i			0.311453i
$904$	−25.2085	+	7.11641i	−0.838422	+	0.236688i
$905$			17.2167i			0.572302i
$906$	−1.42576	+	1.71459i	−0.0473678	+	0.0569633i
$907$	−16.9438	+	16.9438i	−0.562611	+	0.562611i	−0.930048	−	0.367437i	$-0.880235\pi$
$907$	−16.9438	+	16.9438i	−0.562611	+	0.562611i	0.367437	+	0.930048i	$0.380235\pi$
$908$	2.55507	+	1.75542i	0.0847929	+	0.0582555i
$909$	2.53027	+	2.53027i	0.0839236	+	0.0839236i
$910$	0.00752251	+	0.0817913i	0.000249369	+	0.00271136i
$911$	4.87780			0.161609			0.0808044	−	0.996730i	$-0.474251\pi$
$911$	4.87780			0.161609			0.0808044	+	0.996730i	$0.474251\pi$
$912$	6.92179	+	18.0137i	0.229204	+	0.596495i
$913$	−1.19606			−0.0395838
$914$	0.0976378	+	1.06160i	0.00322957	+	0.0351147i
$915$	3.72521	+	3.72521i	0.123152	+	0.123152i
$916$	16.4685	−	23.9705i	0.544134	−	0.792006i
$917$	−3.15947	+	3.15947i	−0.104335	+	0.104335i
$918$	−0.904212	+	1.08738i	−0.0298434	+	0.0358890i
$919$			12.3795i			0.408362i	0.978933	+	0.204181i	$0.0654530\pi$
$919$			12.3795i			0.408362i	−0.978933	+	0.204181i	$0.934547\pi$
$920$	13.5859	+	7.60398i	0.447915	+	0.250696i
$921$		−	17.2242i		−	0.567556i
$922$	4.10273	+	3.41162i	0.135116	+	0.112356i
$923$	0.139920	−	0.139920i	0.00460553	−	0.00460553i
$924$	0.154948	+	0.835238i	0.00509741	+	0.0274773i
$925$	21.1301	+	21.1301i	0.694753	+	0.694753i
$926$	−17.0752	+	1.57044i	−0.561126	+	0.0516079i
$927$	3.80999			0.125137
$928$	−15.1670	−	5.14139i	−0.497883	−	0.168775i
$929$	11.3776			0.373287			0.186643	−	0.982428i	$-0.440239\pi$
$929$	11.3776			0.373287			0.186643	+	0.982428i	$0.440239\pi$
$930$	2.66375	−	0.244990i	0.0873477	−	0.00803355i
$931$	18.2515	+	18.2515i	0.598170	+	0.598170i
$932$	2.58073	+	13.9113i	0.0845346	+	0.455679i
$933$	−13.6363	+	13.6363i	−0.446431	+	0.446431i
$934$	17.9184	+	14.9000i	0.586308	+	0.487544i
$935$			0.301356i			0.00985539i
$936$	−0.0685404	+	0.122460i	−0.00224031	+	0.00400274i
$937$		−	50.7637i		−	1.65838i	−0.558968	−	0.829189i	$-0.688803\pi$
$937$		−	50.7637i		−	1.65838i	0.558968	−	0.829189i	$-0.311197\pi$
$938$	8.99177	−	10.8133i	0.293592	−	0.353066i
$939$	−9.68596	+	9.68596i	−0.316089	+	0.316089i
$940$	0.447908	−	0.651945i	0.0146091	−	0.0212641i
$941$	11.3707	+	11.3707i	0.370674	+	0.370674i	0.867723	−	0.497049i	$-0.165583\pi$
$941$	11.3707	+	11.3707i	0.370674	+	0.370674i	−0.497049	+	0.867723i	$0.665583\pi$
$942$	−0.110448	−	1.20089i	−0.00359861	−	0.0391272i
$943$	−40.4267			−1.31647
$944$	−0.498481	+	1.12062i	−0.0162242	+	0.0364732i
$945$	−1.17057			−0.0380785
$946$	0.312077	+	3.39317i	0.0101465	+	0.110322i
$947$	18.8691	+	18.8691i	0.613165	+	0.613165i	0.943769	−	0.330604i	$-0.107253\pi$
$947$	18.8691	+	18.8691i	0.613165	+	0.613165i	−0.330604	+	0.943769i	$0.607253\pi$
$948$	−8.48818	−	5.83166i	−0.275683	−	0.189404i
$949$	0.460886	−	0.460886i	0.0149610	−	0.0149610i
$950$	18.1887	−	21.8732i	0.590118	−	0.709662i
$951$		−	18.1440i		−	0.588359i
$952$	−0.987031	−	3.49636i	−0.0319898	−	0.113318i
$953$			40.9834i			1.32758i	0.747917	+	0.663792i	$0.231054\pi$
$953$			40.9834i			1.32758i	−0.747917	+	0.663792i	$0.768946\pi$
$954$	0.182267	+	0.151564i	0.00590111	+	0.00490706i
$955$	−7.15037	+	7.15037i	−0.231381	+	0.231381i
$956$	12.5367	−	2.32573i	0.405467	−	0.0752194i
$957$	−0.661967	−	0.661967i	−0.0213984	−	0.0213984i
$958$	11.0342	−	1.01484i	0.356499	−	0.0327879i
$959$	−16.8657			−0.544622
$960$	−6.21434	+	3.81248i	−0.200567	+	0.123047i
$961$	−26.6921			−0.861035
$962$	0.500778	−	0.0460575i	0.0161457	−	0.00148495i
$963$	−3.81586	−	3.81586i	−0.122964	−	0.122964i
$964$	13.6450	−	2.53132i	0.439475	−	0.0815284i
$965$	−7.89227	+	7.89227i	−0.254061	+	0.254061i
$966$	−8.43626	−	7.01516i	−0.271432	−	0.225709i
$967$		−	47.0303i		−	1.51239i	−0.654345	−	0.756196i	$-0.727055\pi$
$967$		−	47.0303i		−	1.51239i	0.654345	−	0.756196i	$-0.272945\pi$
$968$	−8.36878	−	29.6448i	−0.268983	−	0.952820i
$969$		−	4.82446i		−	0.154984i
$970$	6.32860	−	7.61061i	0.203199	−	0.244362i
$971$	−0.687125	+	0.687125i	−0.0220509	+	0.0220509i	−0.718046	−	0.695995i	$-0.754963\pi$
$971$	−0.687125	+	0.687125i	−0.0220509	+	0.0220509i	0.695995	+	0.718046i	$0.254963\pi$
$972$	−1.64844	−	1.13253i	−0.0528738	−	0.0363261i
$973$	15.3799	+	15.3799i	0.493057	+	0.493057i
$974$	−0.245954	−	2.67423i	−0.00788089	−	0.0856879i
$975$	0.206875			0.00662529
$976$	−21.1275	−	9.39803i	−0.676274	−	0.300824i
$977$	30.5732			0.978124			0.489062	−	0.872249i	$-0.337339\pi$
$977$	30.5732			0.978124			0.489062	+	0.872249i	$0.337339\pi$
$978$	1.76522	+	19.1930i	0.0564455	+	0.613725i
$979$	−1.35061	−	1.35061i	−0.0431657	−	0.0431657i
$980$	−5.52194	+	8.03737i	−0.176392	+	0.256744i
$981$	−12.5434	+	12.5434i	−0.400480	+	0.400480i
$982$	−33.4924	+	40.2771i	−1.06878	+	1.28529i
$983$			48.3485i			1.54208i	0.636788	+	0.771039i	$0.280263\pi$
$983$			48.3485i			1.54208i	−0.636788	+	0.771039i	$0.719737\pi$
$984$	9.24579	−	16.5193i	0.294745	−	0.526617i
$985$			22.3088i			0.710819i
$986$	3.07842	+	2.55986i	0.0980370	+	0.0815225i
$987$	−0.394158	+	0.394158i	−0.0125462	+	0.0125462i
$988$	−0.0873235	−	0.470713i	−0.00277813	−	0.0149754i
$989$	−31.1204	−	31.1204i	−0.989570	−	0.989570i
$990$	−0.424391	+	0.0390321i	−0.0134880	+	0.00124052i
$991$	34.2827			1.08903			0.544513	−	0.838752i	$-0.316714\pi$
$991$	34.2827			1.08903			0.544513	+	0.838752i	$0.316714\pi$
$992$	−10.5281	+	5.19738i	−0.334266	+	0.165017i
$993$	−3.40992			−0.108210
$994$	−7.21404	+	0.663490i	−0.228816	+	0.0210446i
$995$	3.78445	+	3.78445i	0.119975	+	0.119975i
$996$	1.31949	+	7.11262i	0.0418095	+	0.225372i
$997$	26.6497	−	26.6497i	0.844004	−	0.844004i	−0.145373	−	0.989377i	$-0.546438\pi$
$997$	26.6497	−	26.6497i	0.844004	−	0.844004i	0.989377	+	0.145373i	$0.0464383\pi$
$998$	−23.2700	−	19.3501i	−0.736599	−	0.612518i
$999$			7.16695i			0.226752i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	816.2.u.a.205.2	✓	64
16.5	even	4	inner	816.2.u.a.613.2	yes	64

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
816.2.u.a.205.2	✓	64	1.1	even	1	trivial
816.2.u.a.613.2	yes	64	16.5	even	4	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:	\( N \)	\(=\)	\( 816 = 2^{4} \cdot 3 \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	816.u (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.40827 + 0.129521i) q^{2} +(0.707107 + 0.707107i) q^{3} +(1.96645 - 0.364802i) q^{4} +(-0.644405 + 0.644405i) q^{5} +(-1.08738 - 0.904212i) q^{6} -1.28446i q^{7} +(-2.72204 + 0.768437i) q^{8} +1.00000i q^{9} +(0.824032 - 0.990961i) q^{10} +(-0.233825 + 0.233825i) q^{11} +(1.64844 + 1.13253i) q^{12} +(-0.0350841 - 0.0350841i) q^{13} +(0.166366 + 1.80887i) q^{14} -0.911327 q^{15} +(3.73384 - 1.43473i) q^{16} -1.00000 q^{17} +(-0.129521 - 1.40827i) q^{18} +(3.41141 + 3.41141i) q^{19} +(-1.03211 + 1.50227i) q^{20} +(0.908254 - 0.908254i) q^{21} +(0.299003 - 0.359574i) q^{22} +6.04012i q^{23} +(-2.46814 - 1.38141i) q^{24} +4.16948i q^{25} +(0.0539520 + 0.0448637i) q^{26} +(-0.707107 + 0.707107i) q^{27} +(-0.468576 - 2.52583i) q^{28} +(2.00185 + 2.00185i) q^{29} +(1.28339 - 0.118036i) q^{30} +2.07555 q^{31} +(-5.07242 + 2.50410i) q^{32} -0.330678 q^{33} +(1.40827 - 0.129521i) q^{34} +(0.827716 + 0.827716i) q^{35} +(0.364802 + 1.96645i) q^{36} +(5.06780 - 5.06780i) q^{37} +(-5.24603 - 4.36233i) q^{38} -0.0496164i q^{39} +(1.25891 - 2.24928i) q^{40} +6.69303i q^{41} +(-1.16143 + 1.39670i) q^{42} +(-5.15228 + 5.15228i) q^{43} +(-0.374505 + 0.545104i) q^{44} +(-0.644405 - 0.644405i) q^{45} +(-0.782325 - 8.50612i) q^{46} -0.433973 q^{47} +(3.65473 + 1.62572i) q^{48} +5.35015 q^{49} +(-0.540038 - 5.87176i) q^{50} +(-0.707107 - 0.707107i) q^{51} +(-0.0817898 - 0.0561923i) q^{52} +(-0.118525 + 0.118525i) q^{53} +(0.904212 - 1.08738i) q^{54} -0.301356i q^{55} +(0.987031 + 3.49636i) q^{56} +4.82446i q^{57} +(-3.07842 - 2.55986i) q^{58} +(-0.216815 + 0.216815i) q^{59} +(-1.79208 + 0.332454i) q^{60} +(-4.08768 - 4.08768i) q^{61} +(-2.92293 + 0.268828i) q^{62} +1.28446 q^{63} +(6.81901 - 4.18344i) q^{64} +0.0452167 q^{65} +(0.465684 - 0.0428299i) q^{66} +(-5.47442 - 5.47442i) q^{67} +(-1.96645 + 0.364802i) q^{68} +(-4.27101 + 4.27101i) q^{69} +(-1.27285 - 1.05844i) q^{70} +3.98814i q^{71} +(-0.768437 - 2.72204i) q^{72} +13.1366i q^{73} +(-6.48044 + 7.79321i) q^{74} +(-2.94827 + 2.94827i) q^{75} +(7.95285 + 5.46387i) q^{76} +(0.300340 + 0.300340i) q^{77} +(0.00642638 + 0.0698733i) q^{78} -5.14921 q^{79} +(-1.48156 + 3.33065i) q^{80} -1.00000 q^{81} +(-0.866891 - 9.42559i) q^{82} +(2.55760 + 2.55760i) q^{83} +(1.45470 - 2.11737i) q^{84} +(0.644405 - 0.644405i) q^{85} +(6.58847 - 7.92313i) q^{86} +2.83104i q^{87} +(0.456801 - 0.816161i) q^{88} +5.77616i q^{89} +(0.990961 + 0.824032i) q^{90} +(-0.0450643 + 0.0450643i) q^{91} +(2.20345 + 11.8776i) q^{92} +(1.46763 + 1.46763i) q^{93} +(0.611152 - 0.0562089i) q^{94} -4.39666 q^{95} +(-5.35741 - 1.81608i) q^{96} +7.68003 q^{97} +(-7.53446 + 0.692959i) q^{98} +(-0.233825 - 0.233825i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 64 q + 4 q^{4} + 12 q^{10} + 8 q^{11} - 8 q^{12} + 20 q^{14} + 24 q^{15} + 28 q^{16} - 64 q^{17} - 4 q^{18} - 48 q^{22} - 20 q^{26} + 16 q^{29} + 8 q^{30} - 24 q^{31} + 40 q^{32} - 24 q^{35} + 16 q^{37}+ \cdots + 8 q^{99}+O(q^{100}) \) 64 * q + 4 * q^4 + 12 * q^10 + 8 * q^11 - 8 * q^12 + 20 * q^14 + 24 * q^15 + 28 * q^16 - 64 * q^17 - 4 * q^18 - 48 * q^22 - 20 * q^26 + 16 * q^29 + 8 * q^30 - 24 * q^31 + 40 * q^32 - 24 * q^35 + 16 * q^37 - 12 * q^38 - 56 * q^40 + 8 * q^42 + 8 * q^43 + 24 * q^44 + 52 * q^46 + 64 * q^47 - 64 * q^49 + 68 * q^50 + 44 * q^52 - 16 * q^53 - 56 * q^56 + 4 * q^58 + 4 * q^60 + 76 * q^62 - 8 * q^63 + 52 * q^64 + 8 * q^66 + 16 * q^67 - 4 * q^68 - 136 * q^70 + 4 * q^72 - 84 * q^74 - 16 * q^75 - 20 * q^76 + 32 * q^77 + 24 * q^78 + 40 * q^79 + 56 * q^80 - 64 * q^81 + 64 * q^83 - 52 * q^84 - 44 * q^86 - 96 * q^88 - 20 * q^90 - 56 * q^91 + 32 * q^92 + 88 * q^94 - 48 * q^95 + 72 * q^98 + 8 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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