LMFDB - Embedded newform 1134.2.k.a.647.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1134,2,Mod(647,1134)]

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

lf = mfeigenbasis(mf)

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")

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

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			647.5
Root			$0.765614 + 1.55365i$ of defining polynomial
Character	$\chi$	$=$	1134.647
Dual form			1134.2.k.a.971.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

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

Display 100 coefficients 10 coefficients

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	$-0.863483\pi$
$5$	−1.82207	−	3.15592i	−0.814855	−	1.41137i	0.0945763	−	0.995518i	$-0.469850\pi$
$6$		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	−0.338843	−	0.940843i	$-0.610035\pi$
$11$	−4.38809	−	2.53346i	−1.32306	−	0.763868i	−0.984215	+	0.176975i	$0.943369\pi$
$12$		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	−0.944547	−	0.328376i	$-0.893499\pi$
$17$	−0.774696	+	1.34181i	−0.187891	+	0.325438i	0.756656	+	0.653814i	$0.226832\pi$
$18$		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	−0.645624	−	0.763656i	$-0.723402\pi$
$23$	−1.47275	+	0.850294i	−0.307090	+	0.177299i	0.338533	+	0.940954i	$0.390069\pi$
$24$		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	$0.126386\pi$
$29$			4.16492i			0.773406i	−0.922204	+	0.386703i	$0.873614\pi$
$30$		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	$-0.550762\pi$
$41$	−2.03363			−0.317599			−0.158799	+	0.987311i	$0.550762\pi$
$42$		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	0.999955	−	0.00949933i	$-0.00302378\pi$
$47$	3.37127	+	5.83922i	0.491751	+	0.851737i	−0.508204	+	0.861237i	$0.669690\pi$
$48$		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	$-0.968105\pi$
$53$	−11.4961	−	6.63726i	−1.57911	−	0.911698i	−0.584123	−	0.811665i	$-0.698561\pi$
$54$		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	−0.786458	−	0.617644i	$-0.788087\pi$
$59$	1.08816	−	1.88475i	0.141666	−	0.245373i	0.928124	+	0.372271i	$0.121421\pi$
$60$		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	$0.131027\pi$
$71$			6.74272i			0.800213i	−0.916469	+	0.400107i	$0.868973\pi$
$72$		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	$-0.526866\pi$
$83$	−1.53608			−0.168607			−0.0843034	+	0.996440i	$0.526866\pi$
$84$		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	$-0.946520\pi$
$89$	−6.01679	−	10.4214i	−0.637778	−	1.10466i	0.348141	−	0.937442i	$-0.386813\pi$
$90$		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	$-0.631636\pi$
$101$	5.95045	−	10.3065i	0.592092	−	1.02553i	0.993950	−	0.109831i	$-0.0350311\pi$
$102$		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	−0.632468	−	0.774586i	$-0.717958\pi$
$107$	−2.87453	+	1.65961i	−0.277891	+	0.160440i	0.354577	+	0.935027i	$0.384625\pi$
$108$		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	$-0.879502\pi$
$113$		−	7.85733i		−	0.739155i	0.929200	−	0.369578i	$-0.120498\pi$
$114$		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	0.927946	−	0.372714i	$-0.121573\pi$
$131$	1.61603	+	2.79904i	0.141193	+	0.244554i	−0.786753	+	0.617268i	$0.788240\pi$
$132$		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	−0.148313	−	0.988940i	$-0.547384\pi$
$137$	−12.6284	−	7.29101i	−1.07892	−	0.622913i	−0.930604	+	0.366027i	$0.880718\pi$
$138$		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	−0.689182	−	0.724589i	$-0.742030\pi$
$149$	−4.95904	+	2.86310i	−0.406261	+	0.234555i	0.282921	+	0.959143i	$0.408697\pi$
$150$		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	$-0.313444\pi$
$167$	14.2953			1.10621			0.553103	+	0.833113i	$0.313444\pi$
$168$		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	0.821196	−	0.570646i	$-0.193307\pi$
$173$	−1.09953	−	1.90444i	−0.0835954	−	0.144792i	−0.904792	+	0.425854i	$0.859974\pi$
$174$		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	0.805725	−	0.592290i	$-0.201776\pi$
$179$	9.30715	+	5.37349i	0.695649	+	0.401633i	−0.110076	+	0.993923i	$0.535109\pi$
$180$		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	−0.215689	−	0.976462i	$-0.569200\pi$
$191$	7.21567	−	4.16597i	0.522108	−	0.301439i	0.737797	+	0.675023i	$0.235866\pi$
$192$		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	$0.0269322\pi$
$197$			2.37228i			0.169018i	−0.996423	+	0.0845089i	$0.973068\pi$
$198$		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	$0.441091\pi$
$227$	−11.4390	+	19.8129i	−0.759231	+	1.31503i	−0.943243	+	0.332103i	$0.892242\pi$
$228$		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	−0.619883	−	0.784694i	$-0.712820\pi$
$233$	−3.82003	+	2.20550i	−0.250259	+	0.144487i	0.369624	+	0.929181i	$0.379486\pi$
$234$		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	$0.206319\pi$
$239$			18.6669i			1.20746i	−0.797189	+	0.603729i	$0.793681\pi$
$240$		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	$-0.688590\pi$
$251$	−17.6939			−1.11683			−0.558415	+	0.829562i	$0.688590\pi$
$252$		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	$-0.909243\pi$
$257$	−11.5971	−	20.0867i	−0.723405	−	1.25297i	0.236222	−	0.971699i	$-0.424091\pi$
$258$		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	0.405220	−	0.914219i	$-0.367195\pi$
$263$	−2.98247	−	1.72193i	−0.183907	−	0.106179i	−0.589127	+	0.808040i	$0.700528\pi$
$264$		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	−0.961936	−	0.273275i	$-0.911893\pi$
$269$	−4.00690	+	6.94015i	−0.244305	+	0.423148i	0.717631	+	0.696423i	$0.245226\pi$
$270$		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	$-0.778304\pi$
$281$		−	21.5077i		−	1.28304i	0.767105	−	0.641521i	$-0.221696\pi$
$282$		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	$-0.476799\pi$
$293$	2.49313			0.145650			0.0728251	+	0.997345i	$0.476799\pi$
$294$		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	$0.392440\pi$
$311$	−11.4857	+	19.8938i	−0.651294	+	1.12807i	−0.982809	+	0.184624i	$0.940893\pi$
$312$		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	−0.272275	−	0.962219i	$-0.587776\pi$
$317$	7.56502	−	4.36767i	0.424894	−	0.245313i	0.697169	+	0.716907i	$0.254443\pi$
$318$		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	0.650172	−	0.759787i	$-0.274697\pi$
$347$	5.90994	+	3.41210i	0.317262	+	0.183171i	−0.332909	+	0.942959i	$0.608030\pi$
$348$		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	$0.538780\pi$
$353$	−17.2922	+	29.9510i	−0.920371	+	1.59413i	−0.798842	+	0.601541i	$0.794554\pi$
$354$		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	0.271600	−	0.962410i	$-0.412447\pi$
$359$	23.5112	−	13.5742i	1.24087	−	0.716417i	0.969272	+	0.245993i	$0.0791140\pi$
$360$		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	0.773116	−	0.634265i	$-0.218697\pi$
$383$	−3.18472	−	5.51610i	−0.162732	−	0.281860i	−0.935847	+	0.352405i	$0.885364\pi$
$384$		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	0.833137	−	0.553067i	$-0.186543\pi$
$389$	15.2013	+	8.77645i	0.770735	+	0.444984i	−0.0624020	+	0.998051i	$0.519876\pi$
$390$		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	−0.588637	−	0.808398i	$-0.700335\pi$
$401$	−3.66182	+	2.11415i	−0.182863	+	0.105576i	0.405774	+	0.913973i	$0.367002\pi$
$402$		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	$-0.611641\pi$
$419$	−14.0660			−0.687170			−0.343585	+	0.939122i	$0.611641\pi$
$420$		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	0.722977	−	0.690872i	$-0.242773\pi$
$431$	10.0928	+	5.82709i	0.486154	+	0.280681i	−0.236824	+	0.971553i	$0.576106\pi$
$432$		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	−0.649560	−	0.760310i	$-0.725047\pi$
$443$	−6.64877	+	3.83867i	−0.315893	+	0.182381i	0.333668	+	0.942691i	$0.391714\pi$
$444$		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	$0.251439\pi$
$449$			30.1018i			1.42059i	−0.703903	+	0.710296i	$0.748561\pi$
$450$		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	$-0.677774\pi$
$461$	−22.7553			−1.05982			−0.529909	+	0.848054i	$0.677774\pi$
$462$		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	$-0.986528\pi$
$467$	−11.5873	−	20.0698i	−0.536195	−	0.928717i	0.462909	−	0.886406i	$-0.346806\pi$
$468$		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	$0.357634\pi$
$479$	−12.3567	+	21.4025i	−0.564594	+	0.977905i	−0.997087	+	0.0762684i	$0.975699\pi$
$480$		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	$-0.767644\pi$
$491$		−	29.5526i		−	1.33369i	0.745197	−	0.666845i	$-0.232356\pi$
$492$		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	$-0.351292\pi$
$503$	20.2016			0.900743			0.450372	+	0.892841i	$0.351292\pi$
$504$		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	0.854057	−	0.520179i	$-0.174135\pi$
$509$	−0.529272	−	0.916725i	−0.0234595	−	0.0406331i	−0.877517	+	0.479546i	$0.840801\pi$
$510$		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	−0.733921	−	0.679235i	$-0.762312\pi$
$521$	5.05068	−	8.74804i	0.221275	−	0.383259i	0.955195	+	0.295976i	$0.0956450\pi$
$522$		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	0.493122	−	0.869960i	$-0.335856\pi$
$557$	−0.323902	−	0.187005i	−0.0137242	−	0.00792365i	−0.506846	+	0.862036i	$0.669189\pi$
$558$		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	−0.816189	−	0.577784i	$-0.803917\pi$
$563$	2.18961	−	3.79252i	0.0922812	−	0.159836i	0.908471	+	0.417949i	$0.137251\pi$
$564$		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	−0.986567	−	0.163360i	$-0.947767\pi$
$569$	−31.9253	+	18.4321i	−1.33838	+	0.772712i	−0.351810	+	0.936072i	$0.614434\pi$
$570$		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	$-0.469443\pi$
$587$	4.64455			0.191701			0.0958505	+	0.995396i	$0.469443\pi$
$588$		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	0.999527	−	0.0307518i	$-0.00979014\pi$
$593$	11.5215	+	19.9558i	0.473132	+	0.819488i	−0.526395	+	0.850240i	$0.676457\pi$
$594$		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	−0.109326	−	0.994006i	$-0.534869\pi$
$599$	−25.0820	−	14.4811i	−1.02482	−	0.591682i	−0.915497	+	0.402324i	$0.868203\pi$
$600$		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	$0.290328\pi$
$617$			39.2854i			1.58157i	−0.612093	+	0.790786i	$0.709672\pi$
$618$		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	−0.0891220	−	0.996021i	$-0.528406\pi$
$641$	−25.2233	−	14.5627i	−0.996262	−	0.575192i	−0.907140	+	0.420828i	$0.861739\pi$
$642$		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	−0.593534	−	0.804809i	$-0.702268\pi$
$647$	10.1800	−	17.6323i	0.400218	−	0.693199i	0.993752	+	0.111610i	$0.0356009\pi$
$648$		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	−0.221035	−	0.975266i	$-0.570944\pi$
$653$	13.1105	−	7.56933i	0.513052	−	0.296211i	0.734087	+	0.679055i	$0.237610\pi$
$654$		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	$0.0661519\pi$
$659$			10.5934i			0.412659i	−0.978483	+	0.206330i	$0.933848\pi$
$660$		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	$-0.890378\pi$
$677$	−19.8534	−	34.3871i	−0.763028	−	1.32160i	0.178255	−	0.983984i	$-0.442955\pi$
$678$		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	0.543705	−	0.839277i	$-0.317021\pi$
$683$	2.31868	+	1.33869i	0.0887218	+	0.0512236i	−0.454983	+	0.890500i	$0.650355\pi$
$684$		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	$-0.776566\pi$
$701$		−	34.1916i		−	1.29140i	0.763591	−	0.645700i	$-0.223434\pi$
$702$		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	0.677753	−	0.735289i	$-0.262954\pi$
$719$	−7.98801	−	13.8356i	−0.297902	−	0.515982i	−0.975656	+	0.219307i	$0.929620\pi$
$720$		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	$0.0543940\pi$
$743$			9.27063i			0.340106i	−0.985435	+	0.170053i	$0.945606\pi$
$744$		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	$-0.828882\pi$
$761$	−24.0809	−	41.7094i	−0.872933	−	1.51196i	−0.0139853	−	0.999902i	$-0.504452\pi$
$762$		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	−0.825016	−	0.565109i	$-0.808834\pi$
$773$	2.13778	−	3.70275i	0.0768906	−	0.133179i	0.901907	+	0.431931i	$0.142167\pi$
$774$		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	$-0.104434\pi$
$797$	53.4507			1.89332			0.946660	+	0.322234i	$0.104434\pi$
$798$		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	0.646111	−	0.763243i	$-0.276394\pi$
$809$	8.76550	+	5.06076i	0.308179	+	0.177927i	−0.337933	+	0.941170i	$0.609728\pi$
$810$		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	0.121504	−	0.992591i	$-0.461228\pi$
$821$	29.8527	−	17.2354i	1.04187	−	0.601521i	0.920361	+	0.391070i	$0.127895\pi$
$822$		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	$0.106460\pi$
$827$			18.8795i			0.656506i	−0.944590	+	0.328253i	$0.893540\pi$
$828$		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	$-0.527844\pi$
$839$	−5.06098			−0.174725			−0.0873623	+	0.996177i	$0.527844\pi$
$840$		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	−0.856699	−	0.515817i	$-0.827488\pi$
$857$	0.537523	−	0.931017i	0.0183614	−	0.0318030i	0.875060	+	0.484014i	$0.160822\pi$
$858$		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	−0.983420	−	0.181344i	$-0.941955\pi$
$863$	−38.7211	+	22.3556i	−1.31808	+	0.760994i	−0.334661	+	0.942339i	$0.608622\pi$
$864$		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	$-0.681779\pi$
$881$	−32.0880			−1.08107			−0.540536	+	0.841321i	$0.681779\pi$
$882$		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	0.995643	−	0.0932433i	$-0.0297234\pi$
$887$	12.4214	+	21.5145i	0.417071	+	0.722387i	−0.578573	+	0.815631i	$0.696390\pi$
$888$		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	$-0.986498\pi$
$911$		−	2.55972i		−	0.0848072i	0.999101	−	0.0424036i	$-0.0135015\pi$
$912$		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	0.999853	−	0.0171358i	$-0.00545475\pi$
$929$	14.7852	+	25.6087i	0.485087	+	0.840195i	−0.514767	+	0.857330i	$0.672121\pi$
$930$		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	−0.999841	−	0.0178263i	$-0.994325\pi$
$941$	−14.8619	+	25.7415i	−0.484483	+	0.839148i	0.515359	+	0.856975i	$0.327659\pi$
$942$		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	−0.154034	−	0.988066i	$-0.549227\pi$
$947$	19.2222	−	11.0980i	0.624639	−	0.360635i	0.778673	+	0.627430i	$0.215893\pi$
$948$		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	$0.0109483\pi$
$953$			2.12319i			0.0687769i	−0.999409	+	0.0343884i	$0.989052\pi$
$954$		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	0.850953	−	0.525242i	$-0.176025\pi$
$971$	−0.916026	−	1.58660i	−0.0293967	−	0.0509165i	−0.880349	+	0.474326i	$0.842692\pi$
$972$		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	0.00566423	−	0.999984i	$-0.498197\pi$
$977$	−26.8034	−	15.4749i	−0.857515	−	0.495087i	−0.863179	+	0.504897i	$0.831530\pi$
$978$		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	$-0.659515\pi$
$983$	16.2825	−	28.2020i	0.519330	−	0.899505i	0.999748	−	0.0224656i	$-0.00715163\pi$
$984$		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.a.647.5		16
3.2	odd	2		1134.2.k.b.647.4		16
7.5	odd	6		1134.2.k.b.971.4		16
9.2	odd	6		126.2.t.a.59.8	yes	16
9.4	even	3		126.2.l.a.101.8	yes	16
9.5	odd	6		378.2.l.a.143.4		16
9.7	even	3		378.2.t.a.17.4		16
21.5	even	6	inner	1134.2.k.a.971.5		16
36.7	odd	6		3024.2.df.c.17.8		16
36.11	even	6		1008.2.df.c.689.1		16
36.23	even	6		3024.2.ca.c.2033.8		16
36.31	odd	6		1008.2.ca.c.353.2		16
63.2	odd	6		882.2.l.b.509.1		16
63.4	even	3		882.2.m.b.587.3		16
63.5	even	6		378.2.t.a.89.4		16
63.11	odd	6		882.2.m.a.293.2		16
63.13	odd	6		882.2.l.b.227.5		16
63.16	even	3		2646.2.l.a.1097.5		16
63.20	even	6		882.2.t.a.815.5		16
63.23	odd	6		2646.2.t.b.1979.1		16
63.25	even	3		2646.2.m.a.881.5		16
63.31	odd	6		882.2.m.a.587.2		16
63.32	odd	6		2646.2.m.b.1763.8		16
63.34	odd	6		2646.2.t.b.2285.1		16
63.38	even	6		882.2.m.b.293.3		16
63.40	odd	6		126.2.t.a.47.8	yes	16
63.41	even	6		2646.2.l.a.521.1		16
63.47	even	6		126.2.l.a.5.4	✓	16
63.52	odd	6		2646.2.m.b.881.8		16
63.58	even	3		882.2.t.a.803.5		16
63.59	even	6		2646.2.m.a.1763.5		16
63.61	odd	6		378.2.l.a.341.8		16
252.47	odd	6		1008.2.ca.c.257.2		16
252.103	even	6		1008.2.df.c.929.1		16
252.131	odd	6		3024.2.df.c.1601.8		16
252.187	even	6		3024.2.ca.c.2609.8		16

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

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

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

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