LMFDB - Embedded newform 1134.2.k.b.647.4

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [1134,2,Mod(647,1134)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(1134, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([3, 1])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("1134.647"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 1134 = 2 \cdot 3^{4} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1134.k (of order $6$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [16,0,0,8,0,0,-4,0,0,0,12] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(11)] == traces)

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

Self dual:	no
Analytic conductor:	$9.05503558921$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$8$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 8 x^{15} + 23 x^{14} - 8 x^{13} - 131 x^{12} + 380 x^{11} - 289 x^{10} - 880 x^{9} + \cdots + 6561 $ x^16 - 8x^15 + 23x^14 - 8x^13 - 131x^12 + 380x^11 - 289x^10 - 880x^9 + 2785x^8 - 2640x^7 - 2601x^6 + 10260x^5 - 10611x^4 - 1944x^3 + 16767x^2 - 17496*x + 6561
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 3^{4} $
Twist minimal:	no (minimal twist has level 126)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			647.4
Root			$0.765614 + 1.55365i$ of defining polynomial
Character	$\chi$	$=$	1134.647
Dual form			1134.2.k.b.971.4

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.866025 + 0.500000i) q^{2} +(0.500000 - 0.866025i) q^{4} +(1.82207 + 3.15592i) q^{5} +(-1.04503 + 2.43062i) q^{7} +1.00000i q^{8} +(-3.15592 - 1.82207i) q^{10} +(4.38809 + 2.53346i) q^{11} +3.39934i q^{13} +(-0.310282 - 2.62749i) q^{14} +(-0.500000 - 0.866025i) q^{16} +(0.774696 - 1.34181i) q^{17} +(-0.707140 + 0.408267i) q^{19} +3.64414 q^{20} -5.06693 q^{22} +(1.47275 - 0.850294i) q^{23} +(-4.13989 + 7.17050i) q^{25} +(-1.69967 - 2.94391i) q^{26} +(1.58246 + 2.12034i) q^{28} -4.16492i q^{29} +(1.87924 + 1.08498i) q^{31} +(0.866025 + 0.500000i) q^{32} +1.54939i q^{34} +(-9.57497 + 1.13071i) q^{35} +(-3.39979 - 5.88860i) q^{37} +(0.408267 - 0.707140i) q^{38} +(-3.15592 + 1.82207i) q^{40} +2.03363 q^{41} -6.12378 q^{43} +(4.38809 - 2.53346i) q^{44} +(-0.850294 + 1.47275i) q^{46} +(-3.37127 - 5.83922i) q^{47} +(-4.81580 - 5.08016i) q^{49} -8.27979i q^{50} +(2.94391 + 1.69967i) q^{52} +(11.4961 + 6.63726i) q^{53} +18.4646i q^{55} +(-2.43062 - 1.04503i) q^{56} +(2.08246 + 3.60693i) q^{58} +(-1.08816 + 1.88475i) q^{59} +(6.28199 - 3.62691i) q^{61} -2.16996 q^{62} -1.00000 q^{64} +(-10.7280 + 6.19384i) q^{65} +(-1.22820 + 2.12731i) q^{67} +(-0.774696 - 1.34181i) q^{68} +(7.72681 - 5.76671i) q^{70} -6.74272i q^{71} +(3.76912 + 2.17610i) q^{73} +(5.88860 + 3.39979i) q^{74} +0.816535i q^{76} +(-10.7436 + 8.01820i) q^{77} +(-6.37651 - 11.0444i) q^{79} +(1.82207 - 3.15592i) q^{80} +(-1.76117 + 1.01681i) q^{82} +1.53608 q^{83} +5.64621 q^{85} +(5.30335 - 3.06189i) q^{86} +(-2.53346 + 4.38809i) q^{88} +(6.01679 + 10.4214i) q^{89} +(-8.26249 - 3.55243i) q^{91} -1.70059i q^{92} +(5.83922 + 3.37127i) q^{94} +(-2.57692 - 1.48778i) q^{95} +6.46065i q^{97} +(6.71069 + 1.99165i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 8 q^{4} - 4 q^{7} + 12 q^{11} - 8 q^{16} + 18 q^{17} - 6 q^{23} - 8 q^{25} - 12 q^{26} - 2 q^{28} - 6 q^{31} - 30 q^{35} - 2 q^{37} - 12 q^{41} + 4 q^{43} + 12 q^{44} + 6 q^{46} - 18 q^{47} - 2 q^{49}+ \cdots + 24 q^{98}+O(q^{100}) $ 16 * q + 8 * q^4 - 4 * q^7 + 12 * q^11 - 8 * q^16 + 18 * q^17 - 6 * q^23 - 8 * q^25 - 12 * q^26 - 2 * q^28 - 6 * q^31 - 30 * q^35 - 2 * q^37 - 12 * q^41 + 4 * q^43 + 12 * q^44 + 6 * q^46 - 18 * q^47 - 2 * q^49 + 6 * q^52 + 36 * q^53 + 6 * q^56 + 6 * q^58 + 30 * q^59 + 60 * q^61 - 36 * q^62 - 16 * q^64 - 42 * q^65 + 14 * q^67 - 18 * q^68 + 18 * q^70 + 18 * q^74 - 24 * q^77 - 16 * q^79 + 24 * q^85 + 24 * q^86 + 24 * q^89 - 12 * q^91 + 66 * q^95 + 24 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1134\mathbb{Z}\right)^\times$.

$n$	$325$	$407$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$-1$

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 $

$2$	−0.866025	+	0.500000i	−0.612372	+	0.353553i
$2$	−0.866025	+	0.500000i	−0.612372	+	0.353553i
$3$		0			0
$3$		0			0
$4$	0.500000	−	0.866025i	0.250000	−	0.433013i
$5$	1.82207	+	3.15592i	0.814855	+	1.41137i	0.909432	+	0.415853i	$0.136517\pi$
$5$	1.82207	+	3.15592i	0.814855	+	1.41137i	−0.0945763	+	0.995518i	$0.530150\pi$
$6$		0			0
$7$	−1.04503	+	2.43062i	−0.394986	+	0.918687i
$7$	−1.04503	+	2.43062i	−0.394986	+	0.918687i
$8$			1.00000i			0.353553i
$9$		0			0
$10$	−3.15592	−	1.82207i	−0.997990	−	0.576190i
$11$	4.38809	+	2.53346i	1.32306	+	0.763868i	0.984215	−	0.176975i	$-0.0566313\pi$
$11$	4.38809	+	2.53346i	1.32306	+	0.763868i	0.338843	+	0.940843i	$0.389965\pi$
$12$		0			0
$13$			3.39934i			0.942807i	0.881918	+	0.471404i	$0.156252\pi$
$13$			3.39934i			0.942807i	−0.881918	+	0.471404i	$0.843748\pi$
$14$	−0.310282	−	2.62749i	−0.0829264	−	0.702227i
$15$		0			0
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$	0.774696	−	1.34181i	0.187891	−	0.325438i	−0.756656	−	0.653814i	$-0.773168\pi$
$17$	0.774696	−	1.34181i	0.187891	−	0.325438i	0.944547	+	0.328376i	$0.106501\pi$
$18$		0			0
$19$	−0.707140	+	0.408267i	−0.162229	+	0.0936629i	−0.578916	−	0.815387i	$-0.696524\pi$
$19$	−0.707140	+	0.408267i	−0.162229	+	0.0936629i	0.416687	+	0.909050i	$0.363191\pi$
$20$	3.64414			0.814855
$21$		0			0
$22$	−5.06693			−1.08027
$23$	1.47275	−	0.850294i	0.307090	−	0.177299i	−0.338533	−	0.940954i	$-0.609931\pi$
$23$	1.47275	−	0.850294i	0.307090	−	0.177299i	0.645624	+	0.763656i	$0.276598\pi$
$24$		0			0
$25$	−4.13989	+	7.17050i	−0.827979	+	1.43410i
$26$	−1.69967	−	2.94391i	−0.333333	−	0.577349i
$27$		0			0
$28$	1.58246	+	2.12034i	0.299057	+	0.400706i
$29$		−	4.16492i		−	0.773406i	−0.922204	−	0.386703i	$-0.873614\pi$
$29$		−	4.16492i		−	0.773406i	0.922204	−	0.386703i	$-0.126386\pi$
$30$		0			0
$31$	1.87924	+	1.08498i	0.337521	+	0.194868i	0.659175	−	0.751989i	$-0.270906\pi$
$31$	1.87924	+	1.08498i	0.337521	+	0.194868i	−0.321654	+	0.946857i	$0.604239\pi$
$32$	0.866025	+	0.500000i	0.153093	+	0.0883883i
$33$		0			0
$34$			1.54939i			0.265719i
$35$	−9.57497	+	1.13071i	−1.61846	+	0.191125i
$36$		0			0
$37$	−3.39979	−	5.88860i	−0.558921	−	0.968080i	−0.997587	−	0.0694297i	$-0.977882\pi$
$37$	−3.39979	−	5.88860i	−0.558921	−	0.968080i	0.438666	−	0.898650i	$-0.355451\pi$
$38$	0.408267	−	0.707140i	0.0662297	−	0.114713i
$39$		0			0
$40$	−3.15592	+	1.82207i	−0.498995	+	0.288095i
$41$	2.03363			0.317599			0.158799	−	0.987311i	$-0.449238\pi$
$41$	2.03363			0.317599			0.158799	+	0.987311i	$0.449238\pi$
$42$		0			0
$43$	−6.12378			−0.933868			−0.466934	−	0.884292i	$-0.654641\pi$
$43$	−6.12378			−0.933868			−0.466934	+	0.884292i	$0.654641\pi$
$44$	4.38809	−	2.53346i	0.661529	−	0.381934i
$45$		0			0
$46$	−0.850294	+	1.47275i	−0.125369	+	0.217146i
$47$	−3.37127	−	5.83922i	−0.491751	−	0.851737i	0.508204	−	0.861237i	$-0.330310\pi$
$47$	−3.37127	−	5.83922i	−0.491751	−	0.851737i	−0.999955	+	0.00949933i	$0.996976\pi$
$48$		0			0
$49$	−4.81580	−	5.08016i	−0.687972	−	0.725737i
$50$		−	8.27979i		−	1.17094i
$51$		0			0
$52$	2.94391	+	1.69967i	0.408247	+	0.235702i
$53$	11.4961	+	6.63726i	1.57911	+	0.911698i	0.994984	+	0.100032i	$0.0318946\pi$
$53$	11.4961	+	6.63726i	1.57911	+	0.911698i	0.584123	+	0.811665i	$0.301439\pi$
$54$		0			0
$55$			18.4646i			2.48977i
$56$	−2.43062	−	1.04503i	−0.324805	−	0.139649i
$57$		0			0
$58$	2.08246	+	3.60693i	0.273440	+	0.473612i
$59$	−1.08816	+	1.88475i	−0.141666	+	0.245373i	−0.928124	−	0.372271i	$-0.878579\pi$
$59$	−1.08816	+	1.88475i	−0.141666	+	0.245373i	0.786458	+	0.617644i	$0.211913\pi$
$60$		0			0
$61$	6.28199	−	3.62691i	0.804326	−	0.464378i	−0.0406555	−	0.999173i	$-0.512945\pi$
$61$	6.28199	−	3.62691i	0.804326	−	0.464378i	0.844982	+	0.534795i	$0.179611\pi$
$62$	−2.16996			−0.275585
$63$		0			0
$64$	−1.00000			−0.125000
$65$	−10.7280	+	6.19384i	−1.33065	+	0.768251i
$66$		0			0
$67$	−1.22820	+	2.12731i	−0.150049	+	0.259892i	−0.931245	−	0.364393i	$-0.881276\pi$
$67$	−1.22820	+	2.12731i	−0.150049	+	0.259892i	0.781196	+	0.624285i	$0.214610\pi$
$68$	−0.774696	−	1.34181i	−0.0939457	−	0.162719i
$69$		0			0
$70$	7.72681	−	5.76671i	0.923530	−	0.689254i
$71$		−	6.74272i		−	0.800213i	−0.916469	−	0.400107i	$-0.868973\pi$
$71$		−	6.74272i		−	0.800213i	0.916469	−	0.400107i	$-0.131027\pi$
$72$		0			0
$73$	3.76912	+	2.17610i	0.441142	+	0.254694i	0.704082	−	0.710119i	$-0.251359\pi$
$73$	3.76912	+	2.17610i	0.441142	+	0.254694i	−0.262940	+	0.964812i	$0.584692\pi$
$74$	5.88860	+	3.39979i	0.684536	+	0.395217i
$75$		0			0
$76$			0.816535i			0.0936629i
$77$	−10.7436	+	8.01820i	−1.22434	+	0.913759i
$78$		0			0
$79$	−6.37651	−	11.0444i	−0.717414	−	1.24260i	−0.962021	−	0.272975i	$-0.911992\pi$
$79$	−6.37651	−	11.0444i	−0.717414	−	1.24260i	0.244607	−	0.969622i	$-0.421341\pi$
$80$	1.82207	−	3.15592i	0.203714	−	0.352843i
$81$		0			0
$82$	−1.76117	+	1.01681i	−0.194489	+	0.112288i
$83$	1.53608			0.168607			0.0843034	−	0.996440i	$-0.473134\pi$
$83$	1.53608			0.168607			0.0843034	+	0.996440i	$0.473134\pi$
$84$		0			0
$85$	5.64621			0.612417
$86$	5.30335	−	3.06189i	0.571875	−	0.330172i
$87$		0			0
$88$	−2.53346	+	4.38809i	−0.270068	+	0.467772i
$89$	6.01679	+	10.4214i	0.637778	+	1.10466i	0.985919	+	0.167222i	$0.0534798\pi$
$89$	6.01679	+	10.4214i	0.637778	+	1.10466i	−0.348141	+	0.937442i	$0.613187\pi$
$90$		0			0
$91$	−8.26249	−	3.55243i	−0.866145	−	0.372396i
$92$		−	1.70059i		−	0.177299i
$93$		0			0
$94$	5.83922	+	3.37127i	0.602269	+	0.347720i
$95$	−2.57692	−	1.48778i	−0.264386	−	0.152643i
$96$		0			0
$97$			6.46065i			0.655980i	0.944681	+	0.327990i	$0.106371\pi$
$97$			6.46065i			0.655980i	−0.944681	+	0.327990i	$0.893629\pi$
$98$	6.71069	+	1.99165i	0.677882	+	0.201187i
$99$		0			0
$100$	4.13989	+	7.17050i	0.413989	+	0.717050i
$101$	−5.95045	+	10.3065i	−0.592092	+	1.02553i	0.401858	+	0.915702i	$0.368364\pi$
$101$	−5.95045	+	10.3065i	−0.592092	+	1.02553i	−0.993950	+	0.109831i	$0.964969\pi$
$102$		0			0
$103$	−12.7174	+	7.34240i	−1.25308	+	0.723468i	−0.971721	−	0.236134i	$-0.924120\pi$
$103$	−12.7174	+	7.34240i	−1.25308	+	0.723468i	−0.281363	+	0.959601i	$0.590786\pi$
$104$	−3.39934			−0.333333
$105$		0			0
$106$	−13.2745			−1.28934
$107$	2.87453	−	1.65961i	0.277891	−	0.160440i	−0.354577	−	0.935027i	$-0.615375\pi$
$107$	2.87453	−	1.65961i	0.277891	−	0.160440i	0.632468	+	0.774586i	$0.282042\pi$
$108$		0			0
$109$	1.41837	−	2.45668i	0.135855	−	0.235308i	−0.790069	−	0.613018i	$-0.789955\pi$
$109$	1.41837	−	2.45668i	0.135855	−	0.235308i	0.925924	+	0.377711i	$0.123289\pi$
$110$	−9.23230	−	15.9908i	−0.880266	−	1.52466i
$111$		0			0
$112$	2.62749	−	0.310282i	0.248275	−	0.0293189i
$113$			7.85733i			0.739155i	0.929200	+	0.369578i	$0.120498\pi$
$113$			7.85733i			0.739155i	−0.929200	+	0.369578i	$0.879502\pi$
$114$		0			0
$115$	5.36692	+	3.09859i	0.500468	+	0.288945i
$116$	−3.60693	−	2.08246i	−0.334895	−	0.193351i
$117$		0			0
$118$		−	2.17632i		−	0.200346i
$119$	2.45185	+	3.28523i	0.224761	+	0.301157i
$120$		0			0
$121$	7.33687	+	12.7078i	0.666988	+	1.15526i
$122$	−3.62691	+	6.28199i	−0.328365	+	0.568744i
$123$		0			0
$124$	1.87924	−	1.08498i	0.168761	−	0.0974339i
$125$	−11.9520			−1.06902
$126$		0			0
$127$	−17.4279			−1.54647			−0.773237	−	0.634117i	$-0.781364\pi$
$127$	−17.4279			−1.54647			−0.773237	+	0.634117i	$0.781364\pi$
$128$	0.866025	−	0.500000i	0.0765466	−	0.0441942i
$129$		0			0
$130$	6.19384	−	10.7280i	0.543236	−	0.940912i
$131$	−1.61603	−	2.79904i	−0.141193	−	0.244554i	0.786753	−	0.617268i	$-0.211760\pi$
$131$	−1.61603	−	2.79904i	−0.141193	−	0.244554i	−0.927946	+	0.372714i	$0.878427\pi$
$132$		0			0
$133$	−0.253356	−	2.14544i	−0.0219687	−	0.186033i
$134$		−	2.45641i		−	0.212201i
$135$		0			0
$136$	1.34181	+	0.774696i	0.115060	+	0.0664297i
$137$	12.6284	+	7.29101i	1.07892	+	0.622913i	0.930604	−	0.366027i	$-0.119282\pi$
$137$	12.6284	+	7.29101i	1.07892	+	0.622913i	0.148313	+	0.988940i	$0.452616\pi$
$138$		0			0
$139$		−	5.74826i		−	0.487561i	−0.969830	−	0.243780i	$-0.921612\pi$
$139$		−	5.74826i		−	0.487561i	0.969830	−	0.243780i	$-0.0783876\pi$
$140$	−3.80826	+	8.85752i	−0.321857	+	0.748597i
$141$		0			0
$142$	3.37136	+	5.83936i	0.282918	+	0.490029i
$143$	−8.61210	+	14.9166i	−0.720180	+	1.24739i
$144$		0			0
$145$	13.1442	−	7.58878i	1.09156	−	0.630214i
$146$	−4.35220			−0.360191
$147$		0			0
$148$	−6.79957			−0.558921
$149$	4.95904	−	2.86310i	0.406261	−	0.234555i	−0.282921	−	0.959143i	$-0.591303\pi$
$149$	4.95904	−	2.86310i	0.406261	−	0.234555i	0.689182	+	0.724589i	$0.257970\pi$
$150$		0			0
$151$	6.38483	−	11.0589i	0.519590	−	0.899957i	−0.480151	−	0.877186i	$-0.659418\pi$
$151$	6.38483	−	11.0589i	0.519590	−	0.899957i	0.999741	−	0.0227705i	$-0.00724870\pi$
$152$	−0.408267	−	0.707140i	−0.0331148	−	0.0573566i
$153$		0			0
$154$	5.29511	−	12.3158i	0.426692	−	0.992432i
$155$			7.90763i			0.635156i
$156$		0			0
$157$	−11.0598	−	6.38536i	−0.882666	−	0.509607i	−0.0111295	−	0.999938i	$-0.503543\pi$
$157$	−11.0598	−	6.38536i	−0.882666	−	0.509607i	−0.871537	+	0.490331i	$0.836876\pi$
$158$	11.0444	+	6.37651i	0.878649	+	0.507288i
$159$		0			0
$160$			3.64414i			0.288095i
$161$	0.527662	+	4.46829i	0.0415856	+	0.352150i
$162$		0			0
$163$	−1.51018	−	2.61570i	−0.118286	−	0.204878i	0.800802	−	0.598929i	$-0.204407\pi$
$163$	−1.51018	−	2.61570i	−0.118286	−	0.204878i	−0.919089	+	0.394051i	$0.871073\pi$
$164$	1.01681	−	1.76117i	0.0793997	−	0.137524i
$165$		0			0
$166$	−1.33028	+	0.768040i	−0.103250	+	0.0596115i
$167$	−14.2953			−1.10621			−0.553103	−	0.833113i	$-0.686556\pi$
$167$	−14.2953			−1.10621			−0.553103	+	0.833113i	$0.686556\pi$
$168$		0			0
$169$	1.44449			0.111115
$170$	−4.88976	+	2.82310i	−0.375028	+	0.216522i
$171$		0			0
$172$	−3.06189	+	5.30335i	−0.233467	+	0.404377i
$173$	1.09953	+	1.90444i	0.0835954	+	0.144792i	0.904792	−	0.425854i	$-0.140026\pi$
$173$	1.09953	+	1.90444i	0.0835954	+	0.144792i	−0.821196	+	0.570646i	$0.806693\pi$
$174$		0			0
$175$	−13.1024	−	17.5559i	−0.990450	−	1.32710i
$176$		−	5.06693i		−	0.381934i
$177$		0			0
$178$	−10.4214	−	6.01679i	−0.781116	−	0.450977i
$179$	−9.30715	−	5.37349i	−0.695649	−	0.401633i	0.110076	−	0.993923i	$-0.464891\pi$
$179$	−9.30715	−	5.37349i	−0.695649	−	0.401633i	−0.805725	+	0.592290i	$0.798224\pi$
$180$		0			0
$181$		−	14.4710i		−	1.07562i	−0.843065	−	0.537811i	$-0.819251\pi$
$181$		−	14.4710i		−	1.07562i	0.843065	−	0.537811i	$-0.180749\pi$
$182$	8.93174	−	1.05475i	0.662065	−	0.0781835i
$183$		0			0
$184$	0.850294	+	1.47275i	0.0626845	+	0.108573i
$185$	12.3893	−	21.4589i	0.910880	−	1.57769i
$186$		0			0
$187$	6.79887	−	3.92533i	0.497183	−	0.287048i
$188$	−6.74255			−0.491751
$189$		0			0
$190$	2.97557			0.215871
$191$	−7.21567	+	4.16597i	−0.522108	+	0.301439i	−0.737797	−	0.675023i	$-0.764134\pi$
$191$	−7.21567	+	4.16597i	−0.522108	+	0.301439i	0.215689	+	0.976462i	$0.430800\pi$
$192$		0			0
$193$	4.78393	−	8.28601i	0.344355	−	0.596440i	−0.640881	−	0.767640i	$-0.721431\pi$
$193$	4.78393	−	8.28601i	0.344355	−	0.596440i	0.985236	+	0.171200i	$0.0547643\pi$
$194$	−3.23033	−	5.59509i	−0.231924	−	0.401704i
$195$		0			0
$196$	−6.80745	+	1.63053i	−0.486246	+	0.116466i
$197$		−	2.37228i		−	0.169018i	−0.996423	−	0.0845089i	$-0.973068\pi$
$197$		−	2.37228i		−	0.169018i	0.996423	−	0.0845089i	$-0.0269322\pi$
$198$		0			0
$199$	19.4983	+	11.2573i	1.38220	+	0.798011i	0.992419	−	0.122898i	$-0.0392188\pi$
$199$	19.4983	+	11.2573i	1.38220	+	0.798011i	0.389777	+	0.920909i	$0.372552\pi$
$200$	−7.17050	−	4.13989i	−0.507031	−	0.292735i
$201$		0			0
$202$		−	11.9009i		−	0.837344i
$203$	10.1233	+	4.35249i	0.710518	+	0.305485i
$204$		0			0
$205$	3.70541	+	6.41796i	0.258797	+	0.448250i
$206$	7.34240	−	12.7174i	0.511569	−	0.886064i
$207$		0			0
$208$	2.94391	−	1.69967i	0.204124	−	0.117851i
$209$	−4.13732			−0.286184
$210$		0			0
$211$	14.5442			1.00126			0.500632	−	0.865660i	$-0.333101\pi$
$211$	14.5442			1.00126			0.500632	+	0.865660i	$0.333101\pi$
$212$	11.4961	−	6.63726i	0.789553	−	0.455849i
$213$		0			0
$214$	−1.65961	+	2.87453i	−0.113449	+	0.196499i
$215$	−11.1580	−	19.3262i	−0.760967	−	1.31803i
$216$		0			0
$217$	−4.60104	+	3.43387i	−0.312339	+	0.233106i
$218$			2.83674i			0.192128i
$219$		0			0
$220$	15.9908	+	9.23230i	1.07810	+	0.622442i
$221$	4.56128	+	2.63346i	0.306825	+	0.177145i
$222$		0			0
$223$			26.0062i			1.74151i	0.491720	+	0.870753i	$0.336368\pi$
$223$			26.0062i			1.74151i	−0.491720	+	0.870753i	$0.663632\pi$
$224$	−2.12034	+	1.58246i	−0.141671	+	0.105732i
$225$		0			0
$226$	−3.92866	−	6.80465i	−0.261331	−	0.452638i
$227$	11.4390	−	19.8129i	0.759231	−	1.31503i	−0.184012	−	0.982924i	$-0.558909\pi$
$227$	11.4390	−	19.8129i	0.759231	−	1.31503i	0.943243	−	0.332103i	$-0.107758\pi$
$228$		0			0
$229$	23.3224	−	13.4652i	1.54118	−	0.889803i	0.542420	−	0.840107i	$-0.317508\pi$
$229$	23.3224	−	13.4652i	1.54118	−	0.889803i	0.998764	−	0.0496960i	$-0.0158252\pi$
$230$	−6.19719			−0.408630
$231$		0			0
$232$	4.16492			0.273440
$233$	3.82003	−	2.20550i	0.250259	−	0.144487i	−0.369624	−	0.929181i	$-0.620514\pi$
$233$	3.82003	−	2.20550i	0.250259	−	0.144487i	0.619883	+	0.784694i	$0.287180\pi$
$234$		0			0
$235$	12.2854	−	21.2789i	0.801412	−	1.38809i
$236$	1.08816	+	1.88475i	0.0708331	+	0.122687i
$237$		0			0
$238$	−3.76598	−	1.61917i	−0.244112	−	0.104955i
$239$		−	18.6669i		−	1.20746i	−0.797189	−	0.603729i	$-0.793681\pi$
$239$		−	18.6669i		−	1.20746i	0.797189	−	0.603729i	$-0.206319\pi$
$240$		0			0
$241$	−0.412458	−	0.238133i	−0.0265688	−	0.0153395i	0.486657	−	0.873593i	$-0.338216\pi$
$241$	−0.412458	−	0.238133i	−0.0265688	−	0.0153395i	−0.513226	+	0.858254i	$0.671550\pi$
$242$	−12.7078	−	7.33687i	−0.816890	−	0.471632i
$243$		0			0
$244$		−	7.25382i		−	0.464378i
$245$	7.25785	−	24.4547i	0.463687	−	1.56235i
$246$		0			0
$247$	−1.38784	−	2.40381i	−0.0883061	−	0.152951i
$248$	−1.08498	+	1.87924i	−0.0688962	+	0.119332i
$249$		0			0
$250$	10.3507	−	5.97601i	0.654639	−	0.377956i
$251$	17.6939			1.11683			0.558415	−	0.829562i	$-0.311410\pi$
$251$	17.6939			1.11683			0.558415	+	0.829562i	$0.311410\pi$
$252$		0			0
$253$	8.61675			0.541731
$254$	15.0930	−	8.71394i	0.947018	−	0.546761i
$255$		0			0
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	11.5971	+	20.0867i	0.723405	+	1.25297i	0.959627	+	0.281275i	$0.0907573\pi$
$257$	11.5971	+	20.0867i	0.723405	+	1.25297i	−0.236222	+	0.971699i	$0.575909\pi$
$258$		0			0
$259$	17.8658	−	2.10978i	1.11013	−	0.131096i
$260$			12.3877i			0.768251i
$261$		0			0
$262$	2.79904	+	1.61603i	0.172925	+	0.0998386i
$263$	2.98247	+	1.72193i	0.183907	+	0.106179i	0.589127	−	0.808040i	$-0.299472\pi$
$263$	2.98247	+	1.72193i	0.183907	+	0.106179i	−0.405220	+	0.914219i	$0.632805\pi$
$264$		0			0
$265$			48.3743i			2.97161i
$266$	1.29213	+	1.73133i	0.0792257	+	0.106154i
$267$		0			0
$268$	1.22820	+	2.12731i	0.0750245	+	0.129946i
$269$	4.00690	−	6.94015i	0.244305	−	0.423148i	−0.717631	−	0.696423i	$-0.754774\pi$
$269$	4.00690	−	6.94015i	0.244305	−	0.423148i	0.961936	+	0.273275i	$0.0881069\pi$
$270$		0			0
$271$	−1.55095	+	0.895442i	−0.0942136	+	0.0543942i	−0.546367	−	0.837546i	$-0.683989\pi$
$271$	−1.55095	+	0.895442i	−0.0942136	+	0.0543942i	0.452153	+	0.891940i	$0.350656\pi$
$272$	−1.54939			−0.0939457
$273$		0			0
$274$	−14.5820			−0.880932
$275$	−36.3324	+	20.9765i	−2.19093	+	1.26493i
$276$		0			0
$277$	12.2968	−	21.2986i	0.738841	−	1.27971i	−0.214176	−	0.976795i	$-0.568707\pi$
$277$	12.2968	−	21.2986i	0.738841	−	1.27971i	0.953017	−	0.302915i	$-0.0979599\pi$
$278$	2.87413	+	4.97814i	0.172379	+	0.298569i
$279$		0			0
$280$	−1.13071	−	9.57497i	−0.0675730	−	0.572214i
$281$			21.5077i			1.28304i	0.767105	+	0.641521i	$0.221696\pi$
$281$			21.5077i			1.28304i	−0.767105	+	0.641521i	$0.778304\pi$
$282$		0			0
$283$	17.2755	+	9.97402i	1.02692	+	0.592894i	0.916101	−	0.400947i	$-0.131319\pi$
$283$	17.2755	+	9.97402i	1.02692	+	0.592894i	0.110821	+	0.993840i	$0.464652\pi$
$284$	−5.83936	−	3.37136i	−0.346502	−	0.200053i
$285$		0			0
$286$		−	17.2242i		−	1.01849i
$287$	−2.12521	+	4.94297i	−0.125447	+	0.291774i
$288$		0			0
$289$	7.29969	+	12.6434i	0.429394	+	0.743732i
$290$	−7.58878	+	13.1442i	−0.445629	+	0.771851i
$291$		0			0
$292$	3.76912	−	2.17610i	0.220571	−	0.127347i
$293$	−2.49313			−0.145650			−0.0728251	−	0.997345i	$-0.523201\pi$
$293$	−2.49313			−0.145650			−0.0728251	+	0.997345i	$0.523201\pi$
$294$		0			0
$295$	−7.93082			−0.461750
$296$	5.88860	−	3.39979i	0.342268	−	0.197609i
$297$		0			0
$298$	−2.86310	+	4.95904i	−0.165855	+	0.287270i
$299$	2.89044	+	5.00639i	0.167158	+	0.289527i
$300$		0			0
$301$	6.39956	−	14.8846i	0.368865	−	0.857932i
$302$			12.7697i			0.734811i
$303$		0			0
$304$	0.707140	+	0.408267i	0.0405572	+	0.0234157i
$305$	22.8925	+	13.2170i	1.31082	+	0.756802i
$306$		0			0
$307$			9.23124i			0.526854i	0.964679	+	0.263427i	$0.0848529\pi$
$307$			9.23124i			0.526854i	−0.964679	+	0.263427i	$0.915147\pi$
$308$	1.57218	+	13.3133i	0.0895830	+	0.758597i
$309$		0			0
$310$	−3.95382	−	6.84821i	−0.224562	−	0.388952i
$311$	11.4857	−	19.8938i	0.651294	−	1.12807i	−0.331515	−	0.943450i	$-0.607560\pi$
$311$	11.4857	−	19.8938i	0.651294	−	1.12807i	0.982809	−	0.184624i	$-0.0591068\pi$
$312$		0			0
$313$	5.57145	−	3.21668i	0.314917	−	0.181818i	−0.334208	−	0.942500i	$-0.608469\pi$
$313$	5.57145	−	3.21668i	0.314917	−	0.181818i	0.649125	+	0.760682i	$0.275135\pi$
$314$	12.7707			0.720694
$315$		0			0
$316$	−12.7530			−0.717414
$317$	−7.56502	+	4.36767i	−0.424894	+	0.245313i	−0.697169	−	0.716907i	$-0.745557\pi$
$317$	−7.56502	+	4.36767i	−0.424894	+	0.245313i	0.272275	+	0.962219i	$0.412224\pi$
$318$		0			0
$319$	10.5517	−	18.2760i	0.590780	−	1.02326i
$320$	−1.82207	−	3.15592i	−0.101857	−	0.176421i
$321$		0			0
$322$	−2.69111	−	3.60582i	−0.149970	−	0.200944i
$323$			1.26513i			0.0703939i
$324$		0			0
$325$	−24.3750	−	14.0729i	−1.35208	−	0.780624i
$326$	2.61570	+	1.51018i	0.144870	+	0.0836410i
$327$		0			0
$328$			2.03363i			0.112288i
$329$	17.7160	−	2.09209i	0.976715	−	0.115341i
$330$		0			0
$331$	−15.8504	−	27.4537i	−0.871215	−	1.50899i	−0.860740	−	0.509044i	$-0.829999\pi$
$331$	−15.8504	−	27.4537i	−0.871215	−	1.50899i	−0.0104748	−	0.999945i	$-0.503334\pi$
$332$	0.768040	−	1.33028i	0.0421517	−	0.0730088i
$333$		0			0
$334$	12.3801	−	7.14766i	0.677410	−	0.391103i
$335$	−8.95150			−0.489073
$336$		0			0
$337$	−32.2616			−1.75740			−0.878700	−	0.477375i	$-0.841588\pi$
$337$	−32.2616			−1.75740			−0.878700	+	0.477375i	$0.841588\pi$
$338$	−1.25097	+	0.722247i	−0.0680437	+	0.0392851i
$339$		0			0
$340$	2.82310	−	4.88976i	0.153104	−	0.265185i
$341$	5.49750	+	9.52196i	0.297707	+	0.515643i
$342$		0			0
$343$	17.3806	−	6.39643i	0.938465	−	0.345375i
$344$		−	6.12378i		−	0.330172i
$345$		0			0
$346$	−1.90444	−	1.09953i	−0.102383	−	0.0591109i
$347$	−5.90994	−	3.41210i	−0.317262	−	0.183171i	0.332909	−	0.942959i	$-0.391970\pi$
$347$	−5.90994	−	3.41210i	−0.317262	−	0.183171i	−0.650172	+	0.759787i	$0.725303\pi$
$348$		0			0
$349$			4.83102i			0.258599i	0.991606	+	0.129299i	$0.0412728\pi$
$349$			4.83102i			0.258599i	−0.991606	+	0.129299i	$0.958727\pi$
$350$	20.1250	+	8.65267i	1.07573	+	0.462504i
$351$		0			0
$352$	2.53346	+	4.38809i	0.135034	+	0.233886i
$353$	17.2922	−	29.9510i	0.920371	−	1.59413i	0.121529	−	0.992588i	$-0.461220\pi$
$353$	17.2922	−	29.9510i	0.920371	−	1.59413i	0.798842	−	0.601541i	$-0.205446\pi$
$354$		0			0
$355$	21.2795	−	12.2857i	1.12940	−	0.652058i
$356$	12.0336			0.637778
$357$		0			0
$358$	10.7470			0.567995
$359$	−23.5112	+	13.5742i	−1.24087	+	0.716417i	−0.969272	−	0.245993i	$-0.920886\pi$
$359$	−23.5112	+	13.5742i	−1.24087	+	0.716417i	−0.271600	+	0.962410i	$0.587553\pi$
$360$		0			0
$361$	−9.16664	+	15.8771i	−0.482455	+	0.835636i
$362$	7.23551	+	12.5323i	0.380290	+	0.658682i
$363$		0			0
$364$	−7.20774	+	5.37932i	−0.377788	+	0.281953i
$365$			15.8601i			0.830153i
$366$		0			0
$367$	10.3307	+	5.96444i	0.539259	+	0.311341i	0.744778	−	0.667312i	$-0.232555\pi$
$367$	10.3307	+	5.96444i	0.539259	+	0.311341i	−0.205520	+	0.978653i	$0.565888\pi$
$368$	−1.47275	−	0.850294i	−0.0767725	−	0.0443246i
$369$		0			0
$370$			24.7786i			1.28818i
$371$	−28.1464	+	21.0064i	−1.46129	+	1.09060i
$372$		0			0
$373$	−4.81925	−	8.34718i	−0.249531	−	0.432201i	0.713865	−	0.700284i	$-0.246943\pi$
$373$	−4.81925	−	8.34718i	−0.249531	−	0.432201i	−0.963396	+	0.268083i	$0.913610\pi$
$374$	−3.92533	+	6.79887i	−0.202974	+	0.351561i
$375$		0			0
$376$	5.83922	−	3.37127i	0.301135	−	0.173860i
$377$	14.1580			0.729173
$378$		0			0
$379$	−16.0145			−0.822612			−0.411306	−	0.911497i	$-0.634927\pi$
$379$	−16.0145			−0.822612			−0.411306	+	0.911497i	$0.634927\pi$
$380$	−2.57692	+	1.48778i	−0.132193	+	0.0763217i
$381$		0			0
$382$	4.16597	−	7.21567i	0.213150	−	0.369186i
$383$	3.18472	+	5.51610i	0.162732	+	0.281860i	0.935847	−	0.352405i	$-0.114636\pi$
$383$	3.18472	+	5.51610i	0.162732	+	0.281860i	−0.773116	+	0.634265i	$0.781303\pi$
$384$		0			0
$385$	−44.8804	−	19.2962i	−2.28732	−	0.983423i
$386$			9.56786i			0.486991i
$387$		0			0
$388$	5.59509	+	3.23033i	0.284048	+	0.163995i
$389$	−15.2013	−	8.77645i	−0.770735	−	0.444984i	0.0624020	−	0.998051i	$-0.480124\pi$
$389$	−15.2013	−	8.77645i	−0.770735	−	0.444984i	−0.833137	+	0.553067i	$0.813457\pi$
$390$		0			0
$391$		−	2.63488i		−	0.133252i
$392$	5.08016	−	4.81580i	0.256587	−	0.243235i
$393$		0			0
$394$	1.18614	+	2.05445i	0.0597568	+	0.103502i
$395$	23.2369	−	40.2476i	1.16918	−	2.02507i
$396$		0			0
$397$	11.5693	−	6.67955i	0.580647	−	0.335237i	−0.180743	−	0.983530i	$-0.557850\pi$
$397$	11.5693	−	6.67955i	0.580647	−	0.335237i	0.761391	+	0.648293i	$0.224517\pi$
$398$	−22.5147			−1.12856
$399$		0			0
$400$	8.27979			0.413989
$401$	3.66182	−	2.11415i	0.182863	−	0.105576i	−0.405774	−	0.913973i	$-0.632998\pi$
$401$	3.66182	−	2.11415i	0.182863	−	0.105576i	0.588637	+	0.808398i	$0.299665\pi$
$402$		0			0
$403$	−3.68821	+	6.38817i	−0.183723	+	0.318217i
$404$	5.95045	+	10.3065i	0.296046	+	0.512767i
$405$		0			0
$406$	−10.9433	+	1.29230i	−0.543107	+	0.0641357i
$407$		−	34.4529i		−	1.70777i
$408$		0			0
$409$	−33.2687	−	19.2077i	−1.64503	−	0.949759i	−0.979006	−	0.203829i	$-0.934661\pi$
$409$	−33.2687	−	19.2077i	−1.64503	−	0.949759i	−0.666025	−	0.745930i	$-0.732005\pi$
$410$	−6.41796	−	3.70541i	−0.316961	−	0.182997i
$411$		0			0
$412$			14.6848i			0.723468i
$413$	−3.44394	−	4.61453i	−0.169465	−	0.227066i
$414$		0			0
$415$	2.79885	+	4.84775i	0.137390	+	0.237967i
$416$	−1.69967	+	2.94391i	−0.0833332	+	0.144337i
$417$		0			0
$418$	3.58302	−	2.06866i	0.175251	−	0.101181i
$419$	14.0660			0.687170			0.343585	−	0.939122i	$-0.388359\pi$
$419$	14.0660			0.687170			0.343585	+	0.939122i	$0.388359\pi$
$420$		0			0
$421$	−21.1008			−1.02839			−0.514195	−	0.857673i	$-0.671909\pi$
$421$	−21.1008			−1.02839			−0.514195	+	0.857673i	$0.671909\pi$
$422$	−12.5957	+	7.27211i	−0.613147	+	0.354001i
$423$		0			0
$424$	−6.63726	+	11.4961i	−0.322334	+	0.558299i
$425$	6.41432	+	11.1099i	0.311140	+	0.538911i
$426$		0			0
$427$	2.25073	+	19.0594i	0.108920	+	0.922347i
$428$		−	3.31922i		−	0.160440i
$429$		0			0
$430$	19.3262	+	11.1580i	0.931991	+	0.538085i
$431$	−10.0928	−	5.82709i	−0.486154	−	0.280681i	0.236824	−	0.971553i	$-0.423894\pi$
$431$	−10.0928	−	5.82709i	−0.486154	−	0.280681i	−0.722977	+	0.690872i	$0.757227\pi$
$432$		0			0
$433$			17.9149i			0.860936i	0.902606	+	0.430468i	$0.141652\pi$
$433$			17.9149i			0.860936i	−0.902606	+	0.430468i	$0.858348\pi$
$434$	2.26768	−	5.27433i	0.108852	−	0.253176i
$435$		0			0
$436$	−1.41837	−	2.45668i	−0.0679275	−	0.117654i
$437$	−0.694295	+	1.20255i	−0.0332126	+	0.0575259i
$438$		0			0
$439$	16.4783	−	9.51377i	0.786468	−	0.454068i	−0.0522494	−	0.998634i	$-0.516639\pi$
$439$	16.4783	−	9.51377i	0.786468	−	0.454068i	0.838718	+	0.544566i	$0.183306\pi$
$440$	−18.4646			−0.880266
$441$		0			0
$442$	−5.26691			−0.250521
$443$	6.64877	−	3.83867i	0.315893	−	0.182381i	−0.333668	−	0.942691i	$-0.608286\pi$
$443$	6.64877	−	3.83867i	0.315893	−	0.182381i	0.649560	+	0.760310i	$0.274953\pi$
$444$		0			0
$445$	−21.9260	+	37.9770i	−1.03939	+	1.80028i
$446$	−13.0031	−	22.5221i	−0.615716	−	1.06645i
$447$		0			0
$448$	1.04503	−	2.43062i	0.0493733	−	0.114836i
$449$		−	30.1018i		−	1.42059i	−0.703903	−	0.710296i	$-0.748561\pi$
$449$		−	30.1018i		−	1.42059i	0.703903	−	0.710296i	$-0.251439\pi$
$450$		0			0
$451$	8.92373	+	5.15212i	0.420202	+	0.242604i
$452$	6.80465	+	3.92866i	0.320064	+	0.184789i
$453$		0			0
$454$			22.8779i			1.07371i
$455$	−3.84367	−	32.5486i	−0.180194	−	1.52590i
$456$		0			0
$457$	19.7438	+	34.1973i	0.923576	+	1.59968i	0.793835	+	0.608133i	$0.208081\pi$
$457$	19.7438	+	34.1973i	0.923576	+	1.59968i	0.129741	+	0.991548i	$0.458586\pi$
$458$	−13.4652	+	23.3224i	−0.629186	+	1.08978i
$459$		0			0
$460$	5.36692	−	3.09859i	0.250234	−	0.144473i
$461$	22.7553			1.05982			0.529909	−	0.848054i	$-0.322226\pi$
$461$	22.7553			1.05982			0.529909	+	0.848054i	$0.322226\pi$
$462$		0			0
$463$	−13.2773			−0.617049			−0.308525	−	0.951216i	$-0.599835\pi$
$463$	−13.2773			−0.617049			−0.308525	+	0.951216i	$0.599835\pi$
$464$	−3.60693	+	2.08246i	−0.167447	+	0.0966757i
$465$		0			0
$466$	−2.20550	+	3.82003i	−0.102168	+	0.176960i
$467$	11.5873	+	20.0698i	0.536195	+	0.928717i	0.999104	+	0.0423116i	$0.0134722\pi$
$467$	11.5873	+	20.0698i	0.536195	+	0.928717i	−0.462909	+	0.886406i	$0.653194\pi$
$468$		0			0
$469$	−3.88716	−	5.20841i	−0.179493	−	0.240502i
$470$			24.5708i			1.13337i
$471$		0			0
$472$	−1.88475	−	1.08816i	−0.0867525	−	0.0500866i
$473$	−26.8717	−	15.5144i	−1.23556	−	0.713351i
$474$		0			0
$475$		−	6.76073i		−	0.310204i
$476$	4.07102	−	0.480749i	0.186595	−	0.0220351i
$477$		0			0
$478$	9.33343	+	16.1660i	0.426901	+	0.739414i
$479$	12.3567	−	21.4025i	0.564594	−	0.977905i	−0.432493	−	0.901637i	$-0.642366\pi$
$479$	12.3567	−	21.4025i	0.564594	−	0.977905i	0.997087	−	0.0762684i	$-0.0243006\pi$
$480$		0			0
$481$	20.0174	−	11.5570i	0.912713	−	0.526955i
$482$	0.476266			0.0216933
$483$		0			0
$484$	14.6737			0.666988
$485$	−20.3893	+	11.7718i	−0.925831	+	0.534529i
$486$		0			0
$487$	16.9877	−	29.4236i	0.769788	−	1.33331i	−0.167889	−	0.985806i	$-0.553695\pi$
$487$	16.9877	−	29.4236i	0.769788	−	1.33331i	0.937678	−	0.347506i	$-0.112971\pi$
$488$	3.62691	+	6.28199i	0.164182	+	0.284372i
$489$		0			0
$490$	5.94188	+	24.8073i	0.268427	+	1.12068i
$491$			29.5526i			1.33369i	0.745197	+	0.666845i	$0.232356\pi$
$491$			29.5526i			1.33369i	−0.745197	+	0.666845i	$0.767644\pi$
$492$		0			0
$493$	−5.58854	−	3.22655i	−0.251695	−	0.145316i
$494$	2.40381	+	1.38784i	0.108152	+	0.0624418i
$495$		0			0
$496$		−	2.16996i		−	0.0974339i
$497$	16.3890	+	7.04637i	0.735146	+	0.316073i
$498$		0			0
$499$	5.38644	+	9.32959i	0.241130	+	0.417650i	0.961037	−	0.276421i	$-0.0891486\pi$
$499$	5.38644	+	9.32959i	0.241130	+	0.417650i	−0.719906	+	0.694071i	$0.755815\pi$
$500$	−5.97601	+	10.3507i	−0.267255	+	0.462899i
$501$		0			0
$502$	−15.3234	+	8.84695i	−0.683916	+	0.394859i
$503$	−20.2016			−0.900743			−0.450372	−	0.892841i	$-0.648708\pi$
$503$	−20.2016			−0.900743			−0.450372	+	0.892841i	$0.648708\pi$
$504$		0			0
$505$	−43.3686			−1.92988
$506$	−7.46233	+	4.30838i	−0.331741	+	0.191531i
$507$		0			0
$508$	−8.71394	+	15.0930i	−0.386619	+	0.669643i
$509$	0.529272	+	0.916725i	0.0234595	+	0.0406331i	0.877517	−	0.479546i	$-0.159199\pi$
$509$	0.529272	+	0.916725i	0.0234595	+	0.0406331i	−0.854057	+	0.520179i	$0.825865\pi$
$510$		0			0
$511$	−9.22813	+	6.88719i	−0.408229	+	0.304671i
$512$		−	1.00000i		−	0.0441942i
$513$		0			0
$514$	−20.0867	−	11.5971i	−0.885987	−	0.511525i
$515$	−46.3441	−	26.7568i	−2.04216	−	1.17904i
$516$		0			0
$517$		−	34.1640i		−	1.50253i
$518$	−14.4174	+	10.7600i	−0.633463	+	0.472769i
$519$		0			0
$520$	−6.19384	−	10.7280i	−0.271618	−	0.470456i
$521$	−5.05068	+	8.74804i	−0.221275	+	0.383259i	−0.955195	−	0.295976i	$-0.904355\pi$
$521$	−5.05068	+	8.74804i	−0.221275	+	0.383259i	0.733921	+	0.679235i	$0.237688\pi$
$522$		0			0
$523$	−8.02992	+	4.63608i	−0.351124	+	0.202722i	−0.665180	−	0.746683i	$-0.731645\pi$
$523$	−8.02992	+	4.63608i	−0.351124	+	0.202722i	0.314056	+	0.949404i	$0.398312\pi$
$524$	−3.23206			−0.141193
$525$		0			0
$526$	−3.44386			−0.150159
$527$	2.91168	−	1.68106i	0.126835	−	0.0732280i
$528$		0			0
$529$	−10.0540	+	17.4140i	−0.437130	+	0.757132i
$530$	−24.1871	−	41.8933i	−1.05062	−	1.81973i
$531$		0			0
$532$	−1.98468	−	0.853307i	−0.0860469	−	0.0369956i
$533$			6.91298i			0.299435i
$534$		0			0
$535$	10.4752	+	6.04786i	0.452882	+	0.261472i
$536$	−2.12731	−	1.22820i	−0.0918858	−	0.0530503i
$537$		0			0
$538$			8.01379i			0.345499i
$539$	−8.26177	−	34.4928i	−0.355859	−	1.48571i
$540$		0			0
$541$	−2.87498	−	4.97960i	−0.123605	−	0.214090i	0.797582	−	0.603211i	$-0.206112\pi$
$541$	−2.87498	−	4.97960i	−0.123605	−	0.214090i	−0.921187	+	0.389121i	$0.872779\pi$
$542$	0.895442	−	1.55095i	0.0384625	−	0.0666191i
$543$		0			0
$544$	1.34181	−	0.774696i	0.0575298	−	0.0332148i
$545$	10.3375			0.442809
$546$		0			0
$547$	−36.6188			−1.56571			−0.782853	−	0.622207i	$-0.786236\pi$
$547$	−36.6188			−1.56571			−0.782853	+	0.622207i	$0.786236\pi$
$548$	12.6284	−	7.29101i	0.539459	−	0.311457i
$549$		0			0
$550$	20.9765	−	36.3324i	0.894442	−	1.54922i
$551$	1.70040	+	2.94518i	0.0724395	+	0.125469i
$552$		0			0
$553$	33.5085	−	3.95704i	1.42493	−	0.168270i
$554$			24.5935i			1.04488i
$555$		0			0
$556$	−4.97814	−	2.87413i	−0.211120	−	0.121890i
$557$	0.323902	+	0.187005i	0.0137242	+	0.00792365i	0.506846	−	0.862036i	$-0.330811\pi$
$557$	0.323902	+	0.187005i	0.0137242	+	0.00792365i	−0.493122	+	0.869960i	$0.664144\pi$
$558$		0			0
$559$		−	20.8168i		−	0.880457i
$560$	5.76671	+	7.72681i	0.243688	+	0.326517i
$561$		0			0
$562$	−10.7539	−	18.6262i	−0.453624	−	0.785700i
$563$	−2.18961	+	3.79252i	−0.0922812	+	0.159836i	−0.908471	−	0.417949i	$-0.862749\pi$
$563$	−2.18961	+	3.79252i	−0.0922812	+	0.159836i	0.816189	+	0.577784i	$0.196083\pi$
$564$		0			0
$565$	−24.7971	+	14.3166i	−1.04322	+	0.602305i
$566$	−19.9480			−0.838478
$567$		0			0
$568$	6.74272			0.282918
$569$	31.9253	−	18.4321i	1.33838	−	0.772712i	0.351810	−	0.936072i	$-0.385566\pi$
$569$	31.9253	−	18.4321i	1.33838	−	0.772712i	0.986567	+	0.163360i	$0.0522331\pi$
$570$		0			0
$571$	−15.8297	+	27.4179i	−0.662454	+	1.14740i	0.317515	+	0.948253i	$0.397152\pi$
$571$	−15.8297	+	27.4179i	−0.662454	+	1.14740i	−0.979969	+	0.199150i	$0.936182\pi$
$572$	8.61210	+	14.9166i	0.360090	+	0.623694i
$573$		0			0
$574$	−0.630997	−	5.34334i	−0.0263373	−	0.223027i
$575$			14.0805i			0.587198i
$576$		0			0
$577$	12.2923	+	7.09699i	0.511737	+	0.295452i	0.733547	−	0.679638i	$-0.237863\pi$
$577$	12.2923	+	7.09699i	0.511737	+	0.295452i	−0.221810	+	0.975090i	$0.571197\pi$
$578$	−12.6434	−	7.29969i	−0.525898	−	0.303627i
$579$		0			0
$580$		−	15.1776i		−	0.630214i
$581$	−1.60526	+	3.73362i	−0.0665973	+	0.154897i
$582$		0			0
$583$	33.6305	+	58.2497i	1.39283	+	2.41246i
$584$	−2.17610	+	3.76912i	−0.0900478	+	0.155967i
$585$		0			0
$586$	2.15911	−	1.24656i	0.0891921	−	0.0514951i
$587$	−4.64455			−0.191701			−0.0958505	−	0.995396i	$-0.530557\pi$
$587$	−4.64455			−0.191701			−0.0958505	+	0.995396i	$0.530557\pi$
$588$		0			0
$589$	−1.77184			−0.0730076
$590$	6.86829	−	3.96541i	0.282763	−	0.163253i
$591$		0			0
$592$	−3.39979	+	5.88860i	−0.139730	+	0.242020i
$593$	−11.5215	−	19.9558i	−0.473132	−	0.819488i	0.526395	−	0.850240i	$-0.323543\pi$
$593$	−11.5215	−	19.9558i	−0.473132	−	0.819488i	−0.999527	+	0.0307518i	$0.990210\pi$
$594$		0			0
$595$	−5.90049	+	13.7238i	−0.241896	+	0.562620i
$596$		−	5.72621i		−	0.234555i
$597$		0			0
$598$	−5.00639	−	2.89044i	−0.204726	−	0.118199i
$599$	25.0820	+	14.4811i	1.02482	+	0.591682i	0.915497	−	0.402324i	$-0.131797\pi$
$599$	25.0820	+	14.4811i	1.02482	+	0.591682i	0.109326	+	0.994006i	$0.465131\pi$
$600$		0			0
$601$		−	5.83116i		−	0.237858i	−0.992903	−	0.118929i	$-0.962054\pi$
$601$		−	5.83116i		−	0.237858i	0.992903	−	0.118929i	$-0.0379461\pi$
$602$	1.90010	+	16.0902i	0.0774422	+	0.655787i
$603$		0			0
$604$	−6.38483	−	11.0589i	−0.259795	−	0.449978i
$605$	−26.7366	+	46.3092i	−1.08700	+	1.88273i
$606$		0			0
$607$	−16.3750	+	9.45411i	−0.664641	+	0.383731i	−0.794043	−	0.607862i	$-0.792028\pi$
$607$	−16.3750	+	9.45411i	−0.664641	+	0.383731i	0.129402	+	0.991592i	$0.458694\pi$
$608$	−0.816535			−0.0331148
$609$		0			0
$610$	−26.4339			−1.07028
$611$	19.8495	−	11.4601i	0.803024	−	0.463626i
$612$		0			0
$613$	−16.5880	+	28.7313i	−0.669984	+	1.16045i	0.307924	+	0.951411i	$0.400366\pi$
$613$	−16.5880	+	28.7313i	−0.669984	+	1.16045i	−0.977908	+	0.209036i	$0.932967\pi$
$614$	−4.61562	−	7.99448i	−0.186271	−	0.322631i
$615$		0			0
$616$	−8.01820	−	10.7436i	−0.323063	−	0.432871i
$617$		−	39.2854i		−	1.58157i	−0.612093	−	0.790786i	$-0.709672\pi$
$617$		−	39.2854i		−	1.58157i	0.612093	−	0.790786i	$-0.290328\pi$
$618$		0			0
$619$	8.46727	+	4.88858i	0.340329	+	0.196489i	0.660417	−	0.750899i	$-0.270379\pi$
$619$	8.46727	+	4.88858i	0.340329	+	0.196489i	−0.320089	+	0.947388i	$0.603713\pi$
$620$	6.84821	+	3.95382i	0.275031	+	0.158789i
$621$		0			0
$622$			22.9714i			0.921069i
$623$	−31.6182	+	3.73380i	−1.26675	+	0.149592i
$624$		0			0
$625$	−1.07796	−	1.86708i	−0.0431185	−	0.0746834i
$626$	−3.21668	+	5.57145i	−0.128564	+	0.222680i
$627$		0			0
$628$	−11.0598	+	6.38536i	−0.441333	+	0.254804i
$629$	−10.5352			−0.420066
$630$		0			0
$631$	11.6364			0.463237			0.231618	−	0.972807i	$-0.425598\pi$
$631$	11.6364			0.463237			0.231618	+	0.972807i	$0.425598\pi$
$632$	11.0444	−	6.37651i	0.439325	−	0.253644i
$633$		0			0
$634$	4.36767	−	7.56502i	0.173462	−	0.300445i
$635$	−31.7549	−	55.0010i	−1.26015	−	2.18265i
$636$		0			0
$637$	17.2692	−	16.3706i	0.684230	−	0.648625i
$638$			21.1033i			0.835489i
$639$		0			0
$640$	3.15592	+	1.82207i	0.124749	+	0.0720237i
$641$	25.2233	+	14.5627i	0.996262	+	0.575192i	0.907140	−	0.420828i	$-0.138261\pi$
$641$	25.2233	+	14.5627i	0.996262	+	0.575192i	0.0891220	+	0.996021i	$0.471594\pi$
$642$		0			0
$643$			39.1917i			1.54557i	0.634667	+	0.772785i	$0.281137\pi$
$643$			39.1917i			1.54557i	−0.634667	+	0.772785i	$0.718863\pi$
$644$	4.13348	+	1.77717i	0.162882	+	0.0700305i
$645$		0			0
$646$	−0.632566	−	1.09564i	−0.0248880	−	0.0431073i
$647$	−10.1800	+	17.6323i	−0.400218	+	0.693199i	−0.993752	−	0.111610i	$-0.964399\pi$
$647$	−10.1800	+	17.6323i	−0.400218	+	0.693199i	0.593534	+	0.804809i	$0.297732\pi$
$648$		0			0
$649$	−9.54988	+	5.51362i	−0.374865	+	0.216429i
$650$	28.1458			1.10397
$651$		0			0
$652$	−3.02035			−0.118286
$653$	−13.1105	+	7.56933i	−0.513052	+	0.296211i	−0.734087	−	0.679055i	$-0.762390\pi$
$653$	−13.1105	+	7.56933i	−0.513052	+	0.296211i	0.221035	+	0.975266i	$0.429056\pi$
$654$		0			0
$655$	5.88904	−	10.2001i	0.230104	−	0.398552i
$656$	−1.01681	−	1.76117i	−0.0396999	−	0.0687622i
$657$		0			0
$658$	−14.2965	+	10.6698i	−0.557334	+	0.415952i
$659$		−	10.5934i		−	0.412659i	−0.978483	−	0.206330i	$-0.933848\pi$
$659$		−	10.5934i		−	0.412659i	0.978483	−	0.206330i	$-0.0661519\pi$
$660$		0			0
$661$	14.7583	+	8.52074i	0.574033	+	0.331418i	0.758759	−	0.651372i	$-0.225806\pi$
$661$	14.7583	+	8.52074i	0.574033	+	0.331418i	−0.184725	+	0.982790i	$0.559140\pi$
$662$	27.4537	+	15.8504i	1.06702	+	0.616042i
$663$		0			0
$664$			1.53608i			0.0596115i
$665$	6.30921	−	4.70872i	0.244661	−	0.182596i
$666$		0			0
$667$	−3.54141	−	6.13389i	−0.137124	−	0.237505i
$668$	−7.14766	+	12.3801i	−0.276551	+	0.479001i
$669$		0			0
$670$	7.75223	−	4.47575i	0.299495	−	0.172913i
$671$	36.7545			1.41889
$672$		0			0
$673$	25.0096			0.964050			0.482025	−	0.876158i	$-0.339902\pi$
$673$	25.0096			0.964050			0.482025	+	0.876158i	$0.339902\pi$
$674$	27.9393	−	16.1308i	1.07618	−	0.621335i
$675$		0			0
$676$	0.722247	−	1.25097i	0.0277787	−	0.0481142i
$677$	19.8534	+	34.3871i	0.763028	+	1.32160i	0.941283	+	0.337619i	$0.109622\pi$
$677$	19.8534	+	34.3871i	0.763028	+	1.32160i	−0.178255	+	0.983984i	$0.557045\pi$
$678$		0			0
$679$	−15.7034	−	6.75161i	−0.602640	−	0.259103i
$680$			5.64621i			0.216522i
$681$		0			0
$682$	−9.52196	−	5.49750i	−0.364615	−	0.210510i
$683$	−2.31868	−	1.33869i	−0.0887218	−	0.0512236i	0.454983	−	0.890500i	$-0.349645\pi$
$683$	−2.31868	−	1.33869i	−0.0887218	−	0.0512236i	−0.543705	+	0.839277i	$0.682979\pi$
$684$		0			0
$685$			53.1390i			2.03034i
$686$	−11.8538	+	14.2298i	−0.452582	+	0.543295i
$687$		0			0
$688$	3.06189	+	5.30335i	0.116733	+	0.202188i
$689$	−22.5623	+	39.0790i	−0.859555	+	1.48879i
$690$		0			0
$691$	−16.6346	+	9.60399i	−0.632810	+	0.365353i	−0.781839	−	0.623480i	$-0.785718\pi$
$691$	−16.6346	+	9.60399i	−0.632810	+	0.365353i	0.149030	+	0.988833i	$0.452385\pi$
$692$	2.19905			0.0835954
$693$		0			0
$694$	6.82421			0.259043
$695$	18.1410	−	10.4737i	0.688129	−	0.397291i
$696$		0			0
$697$	1.57544	−	2.72875i	0.0596741	−	0.103359i
$698$	−2.41551	−	4.18379i	−0.0914284	−	0.158359i
$699$		0			0
$700$	−21.7551	+	2.56907i	−0.822265	+	0.0971017i
$701$			34.1916i			1.29140i	0.763591	+	0.645700i	$0.223434\pi$
$701$			34.1916i			1.29140i	−0.763591	+	0.645700i	$0.776566\pi$
$702$		0			0
$703$	4.80825	+	2.77604i	0.181346	+	0.104700i
$704$	−4.38809	−	2.53346i	−0.165382	−	0.0954835i
$705$		0			0
$706$			34.5844i			1.30160i
$707$	−18.8327	−	25.2339i	−0.708276	−	0.949018i
$708$		0			0
$709$	11.7284	+	20.3141i	0.440468	+	0.762914i	0.997724	−	0.0674271i	$-0.0214790\pi$
$709$	11.7284	+	20.3141i	0.440468	+	0.762914i	−0.557256	+	0.830341i	$0.688146\pi$
$710$	−12.2857	+	21.2795i	−0.461075	+	0.798605i
$711$		0			0
$712$	−10.4214	+	6.01679i	−0.390558	+	0.225489i
$713$	3.69020			0.138199
$714$		0			0
$715$	−62.7675			−2.34737
$716$	−9.30715	+	5.37349i	−0.347825	+	0.200817i
$717$		0			0
$718$	13.5742	−	23.5112i	0.506584	−	0.877429i
$719$	7.98801	+	13.8356i	0.297902	+	0.515982i	0.975656	−	0.219307i	$-0.0703796\pi$
$719$	7.98801	+	13.8356i	0.297902	+	0.515982i	−0.677753	+	0.735289i	$0.737046\pi$
$720$		0			0
$721$	−4.55643	−	38.5842i	−0.169690	−	1.43695i
$722$		−	18.3333i		−	0.682294i
$723$		0			0
$724$	−12.5323	−	7.23551i	−0.465758	−	0.268906i
$725$	29.8646	+	17.2423i	1.10914	+	0.640364i
$726$		0			0
$727$		−	25.0324i		−	0.928401i	−0.885730	−	0.464201i	$-0.846342\pi$
$727$		−	25.0324i		−	0.928401i	0.885730	−	0.464201i	$-0.153658\pi$
$728$	3.55243	−	8.26249i	0.131662	−	0.306228i
$729$		0			0
$730$	−7.93003	−	13.7352i	−0.293504	−	0.508363i
$731$	−4.74407	+	8.21697i	−0.175466	+	0.303916i
$732$		0			0
$733$	−10.1433	+	5.85625i	−0.374652	+	0.216305i	−0.675489	−	0.737370i	$-0.736067\pi$
$733$	−10.1433	+	5.85625i	−0.374652	+	0.216305i	0.300837	+	0.953676i	$0.402734\pi$
$734$	−11.9289			−0.440303
$735$		0			0
$736$	1.70059			0.0626845
$737$	−10.7789	+	6.22322i	−0.397047	+	0.229235i
$738$		0			0
$739$	−8.20255	+	14.2072i	−0.301736	+	0.522622i	−0.976529	−	0.215385i	$-0.930899\pi$
$739$	−8.20255	+	14.2072i	−0.301736	+	0.522622i	0.674793	+	0.738007i	$0.264233\pi$
$740$	−12.3893	−	21.4589i	−0.455440	−	0.788845i
$741$		0			0
$742$	13.8723	−	32.2653i	0.509269	−	1.18450i
$743$		−	9.27063i		−	0.340106i	−0.985435	−	0.170053i	$-0.945606\pi$
$743$		−	9.27063i		−	0.340106i	0.985435	−	0.170053i	$-0.0543940\pi$
$744$		0			0
$745$	18.0715	+	10.4336i	0.662087	+	0.382256i
$746$	8.34718	+	4.81925i	0.305612	+	0.176445i
$747$		0			0
$748$		−	7.85066i		−	0.287048i
$749$	1.02989	+	8.72123i	0.0376315	+	0.318667i
$750$		0			0
$751$	−10.0756	−	17.4515i	−0.367665	−	0.636815i	0.621535	−	0.783386i	$-0.286509\pi$
$751$	−10.0756	−	17.4515i	−0.367665	−	0.636815i	−0.989200	+	0.146572i	$0.953176\pi$
$752$	−3.37127	+	5.83922i	−0.122938	+	0.212934i
$753$		0			0
$754$	−12.2612	+	7.07898i	−0.446525	+	0.257801i
$755$	46.5345			1.69356
$756$		0			0
$757$	47.4297			1.72386			0.861932	−	0.507024i	$-0.169255\pi$
$757$	47.4297			1.72386			0.861932	+	0.507024i	$0.169255\pi$
$758$	13.8690	−	8.00727i	0.503745	−	0.290837i
$759$		0			0
$760$	1.48778	−	2.57692i	0.0539676	−	0.0934747i
$761$	24.0809	+	41.7094i	0.872933	+	1.51196i	0.858948	+	0.512063i	$0.171118\pi$
$761$	24.0809	+	41.7094i	0.872933	+	1.51196i	0.0139853	+	0.999902i	$0.495548\pi$
$762$		0			0
$763$	4.48902	+	6.01483i	0.162513	+	0.217751i
$764$			8.33194i			0.301439i
$765$		0			0
$766$	−5.51610	−	3.18472i	−0.199305	−	0.115069i
$767$	−6.40690	−	3.69902i	−0.231340	−	0.133564i
$768$		0			0
$769$			11.3736i			0.410143i	0.978747	+	0.205071i	$0.0657427\pi$
$769$			11.3736i			0.410143i	−0.978747	+	0.205071i	$0.934257\pi$
$770$	48.5156	−	5.72924i	1.74838	−	0.206467i
$771$		0			0
$772$	−4.78393	−	8.28601i	−0.172177	−	0.298220i
$773$	−2.13778	+	3.70275i	−0.0768906	+	0.133179i	−0.901907	−	0.431931i	$-0.857833\pi$
$773$	−2.13778	+	3.70275i	−0.0768906	+	0.133179i	0.825016	+	0.565109i	$0.191166\pi$
$774$		0			0
$775$	−15.5597	+	8.98339i	−0.558920	+	0.322693i
$776$	−6.46065			−0.231924
$777$		0			0
$778$	17.5529			0.629302
$779$	−1.43806	+	0.830263i	−0.0515238	+	0.0297473i
$780$		0			0
$781$	17.0824	−	29.5876i	0.611257	−	1.05873i
$782$	1.31744	+	2.28187i	0.0471115	+	0.0815996i
$783$		0			0
$784$	−1.99165	+	6.71069i	−0.0711302	+	0.239667i
$785$		−	46.5384i		−	1.66103i
$786$		0			0
$787$	22.8644	+	13.2008i	0.815029	+	0.470557i	0.848699	−	0.528876i	$-0.177386\pi$
$787$	22.8644	+	13.2008i	0.815029	+	0.470557i	−0.0336701	+	0.999433i	$0.510720\pi$
$788$	−2.05445	−	1.18614i	−0.0731869	−	0.0422545i
$789$		0			0
$790$			46.4739i			1.65347i
$791$	−19.0982	−	8.21118i	−0.679053	−	0.291956i
$792$		0			0
$793$	12.3291	+	21.3546i	0.437819	+	0.758324i
$794$	−6.67955	+	11.5693i	−0.237048	+	0.410580i
$795$		0			0
$796$	19.4983	−	11.2573i	0.691098	−	0.399006i
$797$	−53.4507			−1.89332			−0.946660	−	0.322234i	$-0.895566\pi$
$797$	−53.4507			−1.89332			−0.946660	+	0.322234i	$0.895566\pi$
$798$		0			0
$799$	−10.4469			−0.369583
$800$	−7.17050	+	4.13989i	−0.253516	+	0.146367i
$801$		0			0
$802$	−2.11415	+	3.66182i	−0.0746533	+	0.129303i
$803$	11.0261	+	19.0978i	0.389104	+	0.673948i
$804$		0			0
$805$	−13.1401	+	9.80680i	−0.463128	+	0.345644i
$806$		−	7.37642i		−	0.259823i
$807$		0			0
$808$	−10.3065	−	5.95045i	−0.362581	−	0.209336i
$809$	−8.76550	−	5.06076i	−0.308179	−	0.177927i	0.337933	−	0.941170i	$-0.390272\pi$
$809$	−8.76550	−	5.06076i	−0.308179	−	0.177927i	−0.646111	+	0.763243i	$0.723606\pi$
$810$		0			0
$811$		−	44.8854i		−	1.57614i	−0.615586	−	0.788070i	$-0.711080\pi$
$811$		−	44.8854i		−	1.57614i	0.615586	−	0.788070i	$-0.288920\pi$
$812$	8.83102	−	6.59081i	0.309908	−	0.231292i
$813$		0			0
$814$	17.2265	+	29.8371i	0.603787	+	1.04579i
$815$	5.50330	−	9.53200i	0.192772	−	0.333891i
$816$		0			0
$817$	4.33037	−	2.50014i	0.151500	−	0.0874688i
$818$	38.4154			1.34316
$819$		0			0
$820$	7.41083			0.258797
$821$	−29.8527	+	17.2354i	−1.04187	+	0.601521i	−0.920361	−	0.391070i	$-0.872105\pi$
$821$	−29.8527	+	17.2354i	−1.04187	+	0.601521i	−0.121504	+	0.992591i	$0.538772\pi$
$822$		0			0
$823$	14.4561	−	25.0386i	0.503906	−	0.872792i	−0.496083	−	0.868275i	$-0.665229\pi$
$823$	14.4561	−	25.0386i	0.503906	−	0.872792i	0.999990	−	0.00451663i	$-0.00143769\pi$
$824$	−7.34240	−	12.7174i	−0.255785	−	0.443032i
$825$		0			0
$826$	5.28980	+	2.27433i	0.184056	+	0.0791340i
$827$		−	18.8795i		−	0.656506i	−0.944590	−	0.328253i	$-0.893540\pi$
$827$		−	18.8795i		−	0.656506i	0.944590	−	0.328253i	$-0.106460\pi$
$828$		0			0
$829$	15.6663	+	9.04494i	0.544113	+	0.314144i	0.746744	−	0.665111i	$-0.231616\pi$
$829$	15.6663	+	9.04494i	0.544113	+	0.314144i	−0.202631	+	0.979255i	$0.564949\pi$
$830$	−4.84775	−	2.79885i	−0.168268	−	0.0971495i
$831$		0			0
$832$		−	3.39934i		−	0.117851i
$833$	−10.5474	+	2.52633i	−0.365446	+	0.0875321i
$834$		0			0
$835$	−26.0471	−	45.1149i	−0.901397	−	1.56127i
$836$	−2.06866	+	3.58302i	−0.0715461	+	0.123921i
$837$		0			0
$838$	−12.1815	+	7.03301i	−0.420804	+	0.242951i
$839$	5.06098			0.174725			0.0873623	−	0.996177i	$-0.472156\pi$
$839$	5.06098			0.174725			0.0873623	+	0.996177i	$0.472156\pi$
$840$		0			0
$841$	11.6535			0.401843
$842$	18.2738	−	10.5504i	0.629758	−	0.363591i
$843$		0			0
$844$	7.27211	−	12.5957i	0.250316	−	0.433560i
$845$	2.63197	+	4.55871i	0.0905426	+	0.156824i
$846$		0			0
$847$	−38.5552	+	4.55300i	−1.32477	+	0.156443i
$848$		−	13.2745i		−	0.455849i
$849$		0			0
$850$	−11.1099	−	6.41432i	−0.381067	−	0.220009i
$851$	−10.0141	−	5.78163i	−0.343278	−	0.198192i
$852$		0			0
$853$		−	42.7427i		−	1.46348i	−0.681582	−	0.731742i	$-0.738708\pi$
$853$		−	42.7427i		−	1.46348i	0.681582	−	0.731742i	$-0.261292\pi$
$854$	−11.4789	−	15.3805i	−0.392799	−	0.526311i
$855$		0			0
$856$	1.65961	+	2.87453i	0.0567243	+	0.0982493i
$857$	−0.537523	+	0.931017i	−0.0183614	+	0.0318030i	−0.875060	−	0.484014i	$-0.839178\pi$
$857$	−0.537523	+	0.931017i	−0.0183614	+	0.0318030i	0.856699	+	0.515817i	$0.172512\pi$
$858$		0			0
$859$	20.9983	−	12.1234i	0.716452	−	0.413644i	−0.0969931	−	0.995285i	$-0.530922\pi$
$859$	20.9983	−	12.1234i	0.716452	−	0.413644i	0.813446	+	0.581641i	$0.197589\pi$
$860$	−22.3159			−0.760967
$861$		0			0
$862$	11.6542			0.396943
$863$	38.7211	−	22.3556i	1.31808	−	0.760994i	0.334661	−	0.942339i	$-0.391378\pi$
$863$	38.7211	−	22.3556i	1.31808	−	0.760994i	0.983420	+	0.181344i	$0.0580449\pi$
$864$		0			0
$865$	−4.00683	+	6.94004i	−0.136236	+	0.235968i
$866$	−8.95746	−	15.5148i	−0.304387	−	0.527214i
$867$		0			0
$868$	0.673298	+	5.70155i	0.0228532	+	0.193523i
$869$		−	64.6186i		−	2.19204i
$870$		0			0
$871$	−7.23145	−	4.17508i	−0.245028	−	0.141467i
$872$	2.45668	+	1.41837i	0.0831938	+	0.0480320i
$873$		0			0
$874$		−	1.38859i		−	0.0469697i
$875$	12.4903	−	29.0508i	0.422248	−	0.982095i
$876$		0			0
$877$	2.08435	+	3.61020i	0.0703835	+	0.121908i	0.899069	−	0.437806i	$-0.144244\pi$
$877$	2.08435	+	3.61020i	0.0703835	+	0.121908i	−0.828686	+	0.559714i	$0.810911\pi$
$878$	−9.51377	+	16.4783i	−0.321074	+	0.556117i
$879$		0			0
$880$	15.9908	−	9.23230i	0.539050	−	0.311221i
$881$	32.0880			1.08107			0.540536	−	0.841321i	$-0.318221\pi$
$881$	32.0880			1.08107			0.540536	+	0.841321i	$0.318221\pi$
$882$		0			0
$883$	−29.5080			−0.993022			−0.496511	−	0.868031i	$-0.665386\pi$
$883$	−29.5080			−0.993022			−0.496511	+	0.868031i	$0.665386\pi$
$884$	4.56128	−	2.63346i	0.153412	−	0.0885727i
$885$		0			0
$886$	−3.83867	+	6.64877i	−0.128963	+	0.223370i
$887$	−12.4214	−	21.5145i	−0.417071	−	0.722387i	0.578573	−	0.815631i	$-0.303610\pi$
$887$	−12.4214	−	21.5145i	−0.417071	−	0.722387i	−0.995643	+	0.0932433i	$0.970277\pi$
$888$		0			0
$889$	18.2127	−	42.3605i	0.610836	−	1.42073i
$890$		−	43.8521i		−	1.46993i
$891$		0			0
$892$	22.5221	+	13.0031i	0.754095	+	0.435377i
$893$	4.76792	+	2.75276i	0.159552	+	0.0921176i
$894$		0			0
$895$		−	39.1635i		−	1.30909i
$896$	0.310282	+	2.62749i	0.0103658	+	0.0877784i
$897$		0			0
$898$	15.0509	+	26.0689i	0.502255	+	0.869932i
$899$	4.51885	−	7.82687i	0.150712	−	0.261041i
$900$		0			0
$901$	17.8119	−	10.2837i	0.593401	−	0.342600i
$902$	−10.3042			−0.343093
$903$		0			0
$904$	−7.85733			−0.261331
$905$	45.6694	−	26.3673i	1.51810	−	0.876477i
$906$		0			0
$907$	−20.4561	+	35.4311i	−0.679235	+	1.17647i	0.295977	+	0.955195i	$0.404355\pi$
$907$	−20.4561	+	35.4311i	−0.679235	+	1.17647i	−0.975212	+	0.221274i	$0.928979\pi$
$908$	−11.4390	−	19.8129i	−0.379616	−	0.657513i
$909$		0			0
$910$	19.6030	+	26.2660i	0.649833	+	0.870711i
$911$			2.55972i			0.0848072i	0.999101	+	0.0424036i	$0.0135015\pi$
$911$			2.55972i			0.0848072i	−0.999101	+	0.0424036i	$0.986498\pi$
$912$		0			0
$913$	6.74045	+	3.89160i	0.223076	+	0.128793i
$914$	−34.1973	−	19.7438i	−1.13115	−	0.653067i
$915$		0			0
$916$		−	26.9303i		−	0.889803i
$917$	8.49221	−	1.00285i	0.280438	−	0.0331170i
$918$		0			0
$919$	5.12246	+	8.87236i	0.168974	+	0.292672i	0.938060	−	0.346474i	$-0.112621\pi$
$919$	5.12246	+	8.87236i	0.168974	+	0.292672i	−0.769085	+	0.639146i	$0.779288\pi$
$920$	−3.09859	+	5.36692i	−0.102158	+	0.176942i
$921$		0			0
$922$	−19.7066	+	11.3776i	−0.649004	+	0.374703i
$923$	22.9208			0.754447
$924$		0			0
$925$	56.2990			1.85110
$926$	11.4985	−	6.63866i	0.377864	−	0.218160i
$927$		0			0
$928$	2.08246	−	3.60693i	0.0683601	−	0.118403i
$929$	−14.7852	−	25.6087i	−0.485087	−	0.840195i	0.514767	−	0.857330i	$-0.327879\pi$
$929$	−14.7852	−	25.6087i	−0.485087	−	0.840195i	−0.999853	+	0.0171358i	$0.994545\pi$
$930$		0			0
$931$	5.47951	+	1.62625i	0.179584	+	0.0532981i
$932$		−	4.41099i		−	0.144487i
$933$		0			0
$934$	−20.0698	−	11.5873i	−0.656702	−	0.379147i
$935$	24.7761	+	14.3045i	0.810264	+	0.467806i
$936$		0			0
$937$		−	17.9991i		−	0.588005i	−0.955805	−	0.294002i	$-0.905013\pi$
$937$		−	17.9991i		−	0.588005i	0.955805	−	0.294002i	$-0.0949874\pi$
$938$	5.97059	+	2.56703i	0.194947	+	0.0838166i
$939$		0			0
$940$	−12.2854	−	21.2789i	−0.400706	−	0.694043i
$941$	14.8619	−	25.7415i	0.484483	−	0.839148i	−0.515359	−	0.856975i	$-0.672341\pi$
$941$	14.8619	−	25.7415i	0.484483	−	0.839148i	0.999841	+	0.0178263i	$0.00567457\pi$
$942$		0			0
$943$	2.99503	−	1.72918i	0.0975315	−	0.0563098i
$944$	2.17632			0.0708331
$945$		0			0
$946$	31.0287			1.00883
$947$	−19.2222	+	11.0980i	−0.624639	+	0.360635i	−0.778673	−	0.627430i	$-0.784107\pi$
$947$	−19.2222	+	11.0980i	−0.624639	+	0.360635i	0.154034	+	0.988066i	$0.450773\pi$
$948$		0			0
$949$	−7.39731	+	12.8125i	−0.240127	+	0.415912i
$950$	3.38037	+	5.85497i	0.109674	+	0.189960i
$951$		0			0
$952$	−3.28523	+	2.45185i	−0.106475	+	0.0794649i
$953$		−	2.12319i		−	0.0687769i	−0.999409	−	0.0343884i	$-0.989052\pi$
$953$		−	2.12319i		−	0.0687769i	0.999409	−	0.0343884i	$-0.0109483\pi$
$954$		0			0
$955$	−26.2950	−	15.1814i	−0.850885	−	0.491258i
$956$	−16.1660	−	9.33343i	−0.522845	−	0.301865i
$957$		0			0
$958$			24.7135i			0.798456i
$959$	−30.9188	+	23.0755i	−0.998419	+	0.745145i
$960$		0			0
$961$	−13.1456	−	22.7689i	−0.424053	−	0.734481i
$962$	−11.5570	+	20.0174i	−0.372613	+	0.645385i
$963$		0			0
$964$	−0.412458	+	0.238133i	−0.0132844	+	0.00766974i
$965$	34.8667			1.12240
$966$		0			0
$967$	4.46817			0.143687			0.0718434	−	0.997416i	$-0.477112\pi$
$967$	4.46817			0.143687			0.0718434	+	0.997416i	$0.477112\pi$
$968$	−12.7078	+	7.33687i	−0.408445	+	0.235816i
$969$		0			0
$970$	11.7718	−	20.3893i	0.377969	−	0.654661i
$971$	0.916026	+	1.58660i	0.0293967	+	0.0509165i	0.880349	−	0.474326i	$-0.157308\pi$
$971$	0.916026	+	1.58660i	0.0293967	+	0.0509165i	−0.850953	+	0.525242i	$0.823975\pi$
$972$		0			0
$973$	13.9718	+	6.00713i	0.447916	+	0.192580i
$974$			33.9755i			1.08864i
$975$		0			0
$976$	−6.28199	−	3.62691i	−0.201082	−	0.116094i
$977$	26.8034	+	15.4749i	0.857515	+	0.495087i	0.863179	−	0.504897i	$-0.168470\pi$
$977$	26.8034	+	15.4749i	0.857515	+	0.495087i	−0.00566423	+	0.999984i	$0.501803\pi$
$978$		0			0
$979$			60.9733i			1.94871i
$980$	−17.5495	−	18.5128i	−0.560598	−	0.591371i
$981$		0			0
$982$	−14.7763	−	25.5933i	−0.471531	−	0.816715i
$983$	−16.2825	+	28.2020i	−0.519330	+	0.899505i	0.480418	+	0.877040i	$0.340485\pi$
$983$	−16.2825	+	28.2020i	−0.519330	+	0.899505i	−0.999748	+	0.0224656i	$0.992848\pi$
$984$		0			0
$985$	7.48673	−	4.32246i	0.238547	−	0.137725i
$986$	6.45309			0.205508
$987$		0			0
$988$	−2.77568			−0.0883061
$989$	−9.01881	+	5.20701i	−0.286782	+	0.165573i
$990$		0			0
$991$	1.45730	−	2.52411i	0.0462926	−	0.0801811i	−0.841951	−	0.539555i	$-0.818593\pi$
$991$	1.45730	−	2.52411i	0.0462926	−	0.0801811i	0.888243	+	0.459373i	$0.151926\pi$
$992$	1.08498	+	1.87924i	0.0344481	+	0.0596659i
$993$		0			0
$994$	−17.7164	+	2.09214i	−0.561932	+	0.0663588i
$995$			82.0467i			2.60106i
$996$		0			0
$997$	−39.9943	−	23.0907i	−1.26663	−	0.731290i	−0.292282	−	0.956332i	$-0.594415\pi$
$997$	−39.9943	−	23.0907i	−1.26663	−	0.731290i	−0.974349	+	0.225042i	$0.927748\pi$
$998$	−9.32959	−	5.38644i	−0.295323	−	0.170505i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1134.2.k.b.647.4		16
3.2	odd	2		1134.2.k.a.647.5		16
7.5	odd	6		1134.2.k.a.971.5		16
9.2	odd	6		378.2.t.a.17.4		16
9.4	even	3		378.2.l.a.143.4		16
9.5	odd	6		126.2.l.a.101.8	yes	16
9.7	even	3		126.2.t.a.59.8	yes	16
21.5	even	6	inner	1134.2.k.b.971.4		16
36.7	odd	6		1008.2.df.c.689.1		16
36.11	even	6		3024.2.df.c.17.8		16
36.23	even	6		1008.2.ca.c.353.2		16
36.31	odd	6		3024.2.ca.c.2033.8		16
63.2	odd	6		2646.2.l.a.1097.5		16
63.4	even	3		2646.2.m.b.1763.8		16
63.5	even	6		126.2.t.a.47.8	yes	16
63.11	odd	6		2646.2.m.a.881.5		16
63.13	odd	6		2646.2.l.a.521.1		16
63.16	even	3		882.2.l.b.509.1		16
63.20	even	6		2646.2.t.b.2285.1		16
63.23	odd	6		882.2.t.a.803.5		16
63.25	even	3		882.2.m.a.293.2		16
63.31	odd	6		2646.2.m.a.1763.5		16
63.32	odd	6		882.2.m.b.587.3		16
63.34	odd	6		882.2.t.a.815.5		16
63.38	even	6		2646.2.m.b.881.8		16
63.40	odd	6		378.2.t.a.89.4		16
63.41	even	6		882.2.l.b.227.5		16
63.47	even	6		378.2.l.a.341.8		16
63.52	odd	6		882.2.m.b.293.3		16
63.58	even	3		2646.2.t.b.1979.1		16
63.59	even	6		882.2.m.a.587.2		16
63.61	odd	6		126.2.l.a.5.4	✓	16
252.47	odd	6		3024.2.ca.c.2609.8		16
252.103	even	6		3024.2.df.c.1601.8		16
252.131	odd	6		1008.2.df.c.929.1		16
252.187	even	6		1008.2.ca.c.257.2		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
126.2.l.a.5.4	✓	16	63.61	odd	6
126.2.l.a.101.8	yes	16	9.5	odd	6
126.2.t.a.47.8	yes	16	63.5	even	6
126.2.t.a.59.8	yes	16	9.7	even	3
378.2.l.a.143.4		16	9.4	even	3
378.2.l.a.341.8		16	63.47	even	6
378.2.t.a.17.4		16	9.2	odd	6
378.2.t.a.89.4		16	63.40	odd	6
882.2.l.b.227.5		16	63.41	even	6
882.2.l.b.509.1		16	63.16	even	3
882.2.m.a.293.2		16	63.25	even	3
882.2.m.a.587.2		16	63.59	even	6
882.2.m.b.293.3		16	63.52	odd	6
882.2.m.b.587.3		16	63.32	odd	6
882.2.t.a.803.5		16	63.23	odd	6
882.2.t.a.815.5		16	63.34	odd	6
1008.2.ca.c.257.2		16	252.187	even	6
1008.2.ca.c.353.2		16	36.23	even	6
1008.2.df.c.689.1		16	36.7	odd	6
1008.2.df.c.929.1		16	252.131	odd	6
1134.2.k.a.647.5		16	3.2	odd	2
1134.2.k.a.971.5		16	7.5	odd	6
1134.2.k.b.647.4		16	1.1	even	1	trivial
1134.2.k.b.971.4		16	21.5	even	6	inner
2646.2.l.a.521.1		16	63.13	odd	6
2646.2.l.a.1097.5		16	63.2	odd	6
2646.2.m.a.881.5		16	63.11	odd	6
2646.2.m.a.1763.5		16	63.31	odd	6
2646.2.m.b.881.8		16	63.38	even	6
2646.2.m.b.1763.8		16	63.4	even	3
2646.2.t.b.1979.1		16	63.58	even	3
2646.2.t.b.2285.1		16	63.20	even	6
3024.2.ca.c.2033.8		16	36.31	odd	6
3024.2.ca.c.2609.8		16	252.47	odd	6
3024.2.df.c.17.8		16	36.11	even	6
3024.2.df.c.1601.8		16	252.103	even	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 1134 = 2 \cdot 3^{4} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1134.k (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.866025 + 0.500000i) q^{2} +(0.500000 - 0.866025i) q^{4} +(1.82207 + 3.15592i) q^{5} +(-1.04503 + 2.43062i) q^{7} +1.00000i q^{8} +(-3.15592 - 1.82207i) q^{10} +(4.38809 + 2.53346i) q^{11} +3.39934i q^{13} +(-0.310282 - 2.62749i) q^{14} +(-0.500000 - 0.866025i) q^{16} +(0.774696 - 1.34181i) q^{17} +(-0.707140 + 0.408267i) q^{19} +3.64414 q^{20} -5.06693 q^{22} +(1.47275 - 0.850294i) q^{23} +(-4.13989 + 7.17050i) q^{25} +(-1.69967 - 2.94391i) q^{26} +(1.58246 + 2.12034i) q^{28} -4.16492i q^{29} +(1.87924 + 1.08498i) q^{31} +(0.866025 + 0.500000i) q^{32} +1.54939i q^{34} +(-9.57497 + 1.13071i) q^{35} +(-3.39979 - 5.88860i) q^{37} +(0.408267 - 0.707140i) q^{38} +(-3.15592 + 1.82207i) q^{40} +2.03363 q^{41} -6.12378 q^{43} +(4.38809 - 2.53346i) q^{44} +(-0.850294 + 1.47275i) q^{46} +(-3.37127 - 5.83922i) q^{47} +(-4.81580 - 5.08016i) q^{49} -8.27979i q^{50} +(2.94391 + 1.69967i) q^{52} +(11.4961 + 6.63726i) q^{53} +18.4646i q^{55} +(-2.43062 - 1.04503i) q^{56} +(2.08246 + 3.60693i) q^{58} +(-1.08816 + 1.88475i) q^{59} +(6.28199 - 3.62691i) q^{61} -2.16996 q^{62} -1.00000 q^{64} +(-10.7280 + 6.19384i) q^{65} +(-1.22820 + 2.12731i) q^{67} +(-0.774696 - 1.34181i) q^{68} +(7.72681 - 5.76671i) q^{70} -6.74272i q^{71} +(3.76912 + 2.17610i) q^{73} +(5.88860 + 3.39979i) q^{74} +0.816535i q^{76} +(-10.7436 + 8.01820i) q^{77} +(-6.37651 - 11.0444i) q^{79} +(1.82207 - 3.15592i) q^{80} +(-1.76117 + 1.01681i) q^{82} +1.53608 q^{83} +5.64621 q^{85} +(5.30335 - 3.06189i) q^{86} +(-2.53346 + 4.38809i) q^{88} +(6.01679 + 10.4214i) q^{89} +(-8.26249 - 3.55243i) q^{91} -1.70059i q^{92} +(5.83922 + 3.37127i) q^{94} +(-2.57692 - 1.48778i) q^{95} +6.46065i q^{97} +(6.71069 + 1.99165i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 8 q^{4} - 4 q^{7} + 12 q^{11} - 8 q^{16} + 18 q^{17} - 6 q^{23} - 8 q^{25} - 12 q^{26} - 2 q^{28} - 6 q^{31} - 30 q^{35} - 2 q^{37} - 12 q^{41} + 4 q^{43} + 12 q^{44} + 6 q^{46} - 18 q^{47} - 2 q^{49}+ \cdots + 24 q^{98}+O(q^{100}) \) 16 * q + 8 * q^4 - 4 * q^7 + 12 * q^11 - 8 * q^16 + 18 * q^17 - 6 * q^23 - 8 * q^25 - 12 * q^26 - 2 * q^28 - 6 * q^31 - 30 * q^35 - 2 * q^37 - 12 * q^41 + 4 * q^43 + 12 * q^44 + 6 * q^46 - 18 * q^47 - 2 * q^49 + 6 * q^52 + 36 * q^53 + 6 * q^56 + 6 * q^58 + 30 * q^59 + 60 * q^61 - 36 * q^62 - 16 * q^64 - 42 * q^65 + 14 * q^67 - 18 * q^68 + 18 * q^70 + 18 * q^74 - 24 * q^77 - 16 * q^79 + 24 * q^85 + 24 * q^86 + 24 * q^89 - 12 * q^91 + 66 * q^95 + 24 * q^98

Introduction

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