LMFDB - Embedded newform 192.2.k.a.47.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [192,2,Mod(47,192)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(192, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([2, 3, 2]))

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

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

chi := DirichletCharacter("192.47");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 192 = 2^{6} \cdot 3 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	192.k (of order $4$, degree $2$, not minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$1.53312771881$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$6$ over $\Q(i)$
Coefficient field:	12.0.163368480538624.2
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 2x^{10} - 2x^{8} + 16x^{6} - 8x^{4} - 32x^{2} + 64 $ x^12 - 2x^10 - 2x^8 + 16x^6 - 8x^4 - 32*x^2 + 64
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{7} $
Twist minimal:	no (minimal twist has level 48)
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			47.4
Root			$0.204810 + 1.39930i$ of defining polynomial
Character	$\chi$	$=$	192.47
Dual form			192.2.k.a.143.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.814141 - 1.52878i) q^{3} +(2.08397 + 2.08397i) q^{5} +1.14637 q^{7} +(-1.67435 - 2.48929i) q^{9} +O(q^{10})$	\(q+(0.814141 - 1.52878i) q^{3} +(2.08397 + 2.08397i) q^{5} +1.14637 q^{7} +(-1.67435 - 2.48929i) q^{9} +(-1.67435 + 1.67435i) q^{11} +(0.146365 + 0.146365i) q^{13} +(4.88258 - 1.48929i) q^{15} -5.59722i q^{17} +(-1.48929 + 1.48929i) q^{19} +(0.933303 - 1.75254i) q^{21} -3.34870i q^{23} +3.68585i q^{25} +(-5.16874 + 0.533081i) q^{27} +(-3.51325 + 3.51325i) q^{29} +5.83221i q^{31} +(1.19656 + 3.92287i) q^{33} +(2.38899 + 2.38899i) q^{35} +(-4.83221 + 4.83221i) q^{37} +(0.342923 - 0.104599i) q^{39} +0.610042 q^{41} +(1.48929 + 1.48929i) q^{43} +(1.69831 - 8.67689i) q^{45} -6.41646 q^{47} -5.68585 q^{49} +(-8.55693 - 4.55693i) q^{51} +(0.164553 + 0.164553i) q^{53} -6.97858 q^{55} +(1.06431 + 3.48929i) q^{57} +(9.05051 - 9.05051i) q^{59} +(4.53948 + 4.53948i) q^{61} +(-1.91942 - 2.85363i) q^{63} +0.610042i q^{65} +(0.635654 - 0.635654i) q^{67} +(-5.11943 - 2.72631i) q^{69} +6.90659i q^{71} -7.07896i q^{73} +(5.63485 + 3.00080i) q^{75} +(-1.91942 + 1.91942i) q^{77} -9.83221i q^{79} +(-3.39312 + 8.33587i) q^{81} +(8.09081 + 8.09081i) q^{83} +(11.6644 - 11.6644i) q^{85} +(2.51071 + 8.23127i) q^{87} +0.490134 q^{89} +(0.167788 + 0.167788i) q^{91} +(8.91618 + 4.74824i) q^{93} -6.20726 q^{95} +12.3503 q^{97} +(6.97138 + 1.36449i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + 2 q^{3} + 8 q^{7}+O(q^{10}) $ 12 * q + 2 * q^3 + 8 * q^7	$ 12 q + 2 q^{3} + 8 q^{7} - 4 q^{13} + 12 q^{19} - 8 q^{21} - 10 q^{27} - 4 q^{33} - 4 q^{37} - 20 q^{39} - 12 q^{43} - 12 q^{45} - 20 q^{49} - 24 q^{51} - 24 q^{55} + 12 q^{61} - 28 q^{67} + 4 q^{69} + 34 q^{75} - 4 q^{81} + 32 q^{85} + 60 q^{87} + 56 q^{91} + 28 q^{93} - 8 q^{97} + 52 q^{99}+O(q^{100}) $ 12 * q + 2 * q^3 + 8 * q^7 - 4 * q^13 + 12 * q^19 - 8 * q^21 - 10 * q^27 - 4 * q^33 - 4 * q^37 - 20 * q^39 - 12 * q^43 - 12 * q^45 - 20 * q^49 - 24 * q^51 - 24 * q^55 + 12 * q^61 - 28 * q^67 + 4 * q^69 + 34 * q^75 - 4 * q^81 + 32 * q^85 + 60 * q^87 + 56 * q^91 + 28 * q^93 - 8 * q^97 + 52 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/192\mathbb{Z}\right)^\times$.

$n$	$65$	$127$	$133$
$\chi(n)$	$-1$	$-1$	$e\left(\frac{3}{4}\right)$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	0.814141	−	1.52878i	0.470045	−	0.882643i
$3$	0.814141	−	1.52878i	0.470045	−	0.882643i
$4$		0			0
$5$	2.08397	+	2.08397i	0.931979	+	0.931979i	0.997829	−	0.0658506i	$-0.0209761\pi$
$5$	2.08397	+	2.08397i	0.931979	+	0.931979i	−0.0658506	+	0.997829i	$0.520976\pi$
$6$		0			0
$7$	1.14637			0.433285			0.216643	−	0.976251i	$-0.430489\pi$
$7$	1.14637			0.433285			0.216643	+	0.976251i	$0.430489\pi$
$8$		0			0
$9$	−1.67435	−	2.48929i	−0.558116	−	0.829763i
$10$		0			0
$11$	−1.67435	+	1.67435i	−0.504835	+	0.504835i	−0.912937	−	0.408102i	$-0.866191\pi$
$11$	−1.67435	+	1.67435i	−0.504835	+	0.504835i	0.408102	+	0.912937i	$0.366191\pi$
$12$		0			0
$13$	0.146365	+	0.146365i	0.0405945	+	0.0405945i	0.727113	−	0.686518i	$-0.240862\pi$
$13$	0.146365	+	0.146365i	0.0405945	+	0.0405945i	−0.686518	+	0.727113i	$0.740862\pi$
$14$		0			0
$15$	4.88258	−	1.48929i	1.26068	−	0.384533i
$16$		0			0
$17$		−	5.59722i		−	1.35752i	−0.734358	−	0.678762i	$-0.762517\pi$
$17$		−	5.59722i		−	1.35752i	0.734358	−	0.678762i	$-0.237483\pi$
$18$		0			0
$19$	−1.48929	+	1.48929i	−0.341666	+	0.341666i	−0.856993	−	0.515327i	$-0.827670\pi$
$19$	−1.48929	+	1.48929i	−0.341666	+	0.341666i	0.515327	+	0.856993i	$0.327670\pi$
$20$		0			0
$21$	0.933303	−	1.75254i	0.203663	−	0.382436i
$22$		0			0
$23$		−	3.34870i		−	0.698252i	−0.937076	−	0.349126i	$-0.886479\pi$
$23$		−	3.34870i		−	0.698252i	0.937076	−	0.349126i	$-0.113521\pi$
$24$		0			0
$25$			3.68585i			0.737169i
$26$		0			0
$27$	−5.16874	+	0.533081i	−0.994724	+	0.102592i
$28$		0			0
$29$	−3.51325	+	3.51325i	−0.652394	+	0.652394i	−0.953569	−	0.301175i	$-0.902621\pi$
$29$	−3.51325	+	3.51325i	−0.652394	+	0.652394i	0.301175	+	0.953569i	$0.402621\pi$
$30$		0			0
$31$			5.83221i			1.04750i	0.851873	+	0.523748i	$0.175467\pi$
$31$			5.83221i			1.04750i	−0.851873	+	0.523748i	$0.824533\pi$
$32$		0			0
$33$	1.19656	+	3.92287i	0.208294	+	0.682884i
$34$		0			0
$35$	2.38899	+	2.38899i	0.403813	+	0.403813i
$36$		0			0
$37$	−4.83221	+	4.83221i	−0.794411	+	0.794411i	−0.982208	−	0.187797i	$-0.939865\pi$
$37$	−4.83221	+	4.83221i	−0.794411	+	0.794411i	0.187797	+	0.982208i	$0.439865\pi$
$38$		0			0
$39$	0.342923	−	0.104599i	0.0549116	−	0.0167492i
$40$		0			0
$41$	0.610042			0.0952726			0.0476363	−	0.998865i	$-0.484831\pi$
$41$	0.610042			0.0952726			0.0476363	+	0.998865i	$0.484831\pi$
$42$		0			0
$43$	1.48929	+	1.48929i	0.227114	+	0.227114i	0.811486	−	0.584372i	$-0.198659\pi$
$43$	1.48929	+	1.48929i	0.227114	+	0.227114i	−0.584372	+	0.811486i	$0.698659\pi$
$44$		0			0
$45$	1.69831	−	8.67689i	0.253169	−	1.29347i
$46$		0			0
$47$	−6.41646			−0.935936			−0.467968	−	0.883745i	$-0.655014\pi$
$47$	−6.41646			−0.935936			−0.467968	+	0.883745i	$0.655014\pi$
$48$		0			0
$49$	−5.68585			−0.812264
$50$		0			0
$51$	−8.55693	−	4.55693i	−1.19821	−	0.638097i
$52$		0			0
$53$	0.164553	+	0.164553i	0.0226031	+	0.0226031i	0.718318	−	0.695715i	$-0.244912\pi$
$53$	0.164553	+	0.164553i	0.0226031	+	0.0226031i	−0.695715	+	0.718318i	$0.744912\pi$
$54$		0			0
$55$	−6.97858			−0.940991
$56$		0			0
$57$	1.06431	+	3.48929i	0.140971	+	0.462168i
$58$		0			0
$59$	9.05051	−	9.05051i	1.17828	−	1.17828i	0.198093	−	0.980183i	$-0.436525\pi$
$59$	9.05051	−	9.05051i	1.17828	−	1.17828i	0.980183	−	0.198093i	$-0.0634749\pi$
$60$		0			0
$61$	4.53948	+	4.53948i	0.581221	+	0.581221i	0.935239	−	0.354018i	$-0.115185\pi$
$61$	4.53948	+	4.53948i	0.581221	+	0.581221i	−0.354018	+	0.935239i	$0.615185\pi$
$62$		0			0
$63$	−1.91942	−	2.85363i	−0.241824	−	0.359524i
$64$		0			0
$65$			0.610042i			0.0756664i
$66$		0			0
$67$	0.635654	−	0.635654i	0.0776575	−	0.0776575i	−0.667211	−	0.744869i	$-0.732512\pi$
$67$	0.635654	−	0.635654i	0.0776575	−	0.0776575i	0.744869	+	0.667211i	$0.232512\pi$
$68$		0			0
$69$	−5.11943	−	2.72631i	−0.616307	−	0.328209i
$70$		0			0
$71$			6.90659i			0.819662i	0.912162	+	0.409831i	$0.134412\pi$
$71$			6.90659i			0.819662i	−0.912162	+	0.409831i	$0.865588\pi$
$72$		0			0
$73$		−	7.07896i		−	0.828530i	−0.910156	−	0.414265i	$-0.864039\pi$
$73$		−	7.07896i		−	0.828530i	0.910156	−	0.414265i	$-0.135961\pi$
$74$		0			0
$75$	5.63485	+	3.00080i	0.650657	+	0.346502i
$76$		0			0
$77$	−1.91942	+	1.91942i	−0.218738	+	0.218738i
$78$		0			0
$79$		−	9.83221i		−	1.10621i	−0.833111	−	0.553105i	$-0.813443\pi$
$79$		−	9.83221i		−	1.10621i	0.833111	−	0.553105i	$-0.186557\pi$
$80$		0			0
$81$	−3.39312	+	8.33587i	−0.377013	+	0.926208i
$82$		0			0
$83$	8.09081	+	8.09081i	0.888081	+	0.888081i	0.994339	−	0.106257i	$-0.0338867\pi$
$83$	8.09081	+	8.09081i	0.888081	+	0.888081i	−0.106257	+	0.994339i	$0.533887\pi$
$84$		0			0
$85$	11.6644	−	11.6644i	1.26518	−	1.26518i
$86$		0			0
$87$	2.51071	+	8.23127i	0.269177	+	0.882485i
$88$		0			0
$89$	0.490134			0.0519541			0.0259770	−	0.999663i	$-0.491730\pi$
$89$	0.490134			0.0519541			0.0259770	+	0.999663i	$0.491730\pi$
$90$		0			0
$91$	0.167788	+	0.167788i	0.0175890	+	0.0175890i
$92$		0			0
$93$	8.91618	+	4.74824i	0.924565	+	0.492370i
$94$		0			0
$95$	−6.20726			−0.636851
$96$		0			0
$97$	12.3503			1.25398			0.626990	−	0.779027i	$-0.284287\pi$
$97$	12.3503			1.25398			0.626990	+	0.779027i	$0.284287\pi$
$98$		0			0
$99$	6.97138	+	1.36449i	0.700650	+	0.137137i
$100$		0			0
$101$	−8.29123	−	8.29123i	−0.825008	−	0.825008i	0.161813	−	0.986821i	$-0.448266\pi$
$101$	−8.29123	−	8.29123i	−0.825008	−	0.825008i	−0.986821	+	0.161813i	$0.948266\pi$
$102$		0			0
$103$	12.2253			1.20460			0.602299	−	0.798271i	$-0.294252\pi$
$103$	12.2253			1.20460			0.602299	+	0.798271i	$0.294252\pi$
$104$		0			0
$105$	5.59722	−	1.70727i	0.546233	−	0.166612i
$106$		0			0
$107$	0.714641	−	0.714641i	0.0690869	−	0.0690869i	−0.671719	−	0.740806i	$-0.734444\pi$
$107$	0.714641	−	0.714641i	0.0690869	−	0.0690869i	0.740806	+	0.671719i	$0.234444\pi$
$108$		0			0
$109$	−12.4966	−	12.4966i	−1.19696	−	1.19696i	−0.975072	−	0.221888i	$-0.928778\pi$
$109$	−12.4966	−	12.4966i	−1.19696	−	1.19696i	−0.221888	−	0.975072i	$-0.571222\pi$
$110$		0			0
$111$	3.45330	+	11.3215i	0.327772	+	1.07459i
$112$		0			0
$113$			5.47731i			0.515262i	0.966243	+	0.257631i	$0.0829419\pi$
$113$			5.47731i			0.515262i	−0.966243	+	0.257631i	$0.917058\pi$
$114$		0			0
$115$	6.97858	−	6.97858i	0.650756	−	0.650756i
$116$		0			0
$117$	0.119279	−	0.609413i	0.0110274	−	0.0563402i
$118$		0			0
$119$		−	6.41646i		−	0.588196i
$120$		0			0
$121$			5.39312i			0.490283i
$122$		0			0
$123$	0.496660	−	0.932621i	0.0447824	−	0.0840916i
$124$		0			0
$125$	2.73865	−	2.73865i	0.244953	−	0.244953i
$126$		0			0
$127$		−	7.20390i		−	0.639243i	−0.947545	−	0.319622i	$-0.896444\pi$
$127$		−	7.20390i		−	0.639243i	0.947545	−	0.319622i	$-0.103556\pi$
$128$		0			0
$129$	3.48929	−	1.06431i	0.307215	−	0.0937069i
$130$		0			0
$131$	−9.05051	−	9.05051i	−0.790747	−	0.790747i	0.190869	−	0.981616i	$-0.438870\pi$
$131$	−9.05051	−	9.05051i	−0.790747	−	0.790747i	−0.981616	+	0.190869i	$0.938870\pi$
$132$		0			0
$133$	−1.70727	+	1.70727i	−0.148039	+	0.148039i
$134$		0			0
$135$	−11.8824	−	9.66056i	−1.02267	−	0.831448i
$136$		0			0
$137$	13.4430			1.14851			0.574255	−	0.818677i	$-0.305292\pi$
$137$	13.4430			1.14851			0.574255	+	0.818677i	$0.305292\pi$
$138$		0			0
$139$	−8.63565	−	8.63565i	−0.732467	−	0.732467i	0.238641	−	0.971108i	$-0.423298\pi$
$139$	−8.63565	−	8.63565i	−0.732467	−	0.732467i	−0.971108	+	0.238641i	$0.923298\pi$
$140$		0			0
$141$	−5.22390	+	9.80936i	−0.439932	+	0.826097i
$142$		0			0
$143$	−0.490134			−0.0409870
$144$		0			0
$145$	−14.6430			−1.21603
$146$		0			0
$147$	−4.62908	+	8.69242i	−0.381800	+	0.716939i
$148$		0			0
$149$	11.6399	+	11.6399i	0.953580	+	0.953580i	0.998969	−	0.0453896i	$-0.0144529\pi$
$149$	11.6399	+	11.6399i	0.953580	+	0.953580i	−0.0453896	+	0.998969i	$0.514453\pi$
$150$		0			0
$151$	0.810789			0.0659811			0.0329905	−	0.999456i	$-0.489497\pi$
$151$	0.810789			0.0659811			0.0329905	+	0.999456i	$0.489497\pi$
$152$		0			0
$153$	−13.9331	+	9.37169i	−1.12642	+	0.757656i
$154$		0			0
$155$	−12.1541	+	12.1541i	−0.976244	+	0.976244i
$156$		0			0
$157$	5.51806	+	5.51806i	0.440389	+	0.440389i	0.892143	−	0.451754i	$-0.149201\pi$
$157$	5.51806	+	5.51806i	0.440389	+	0.440389i	−0.451754	+	0.892143i	$0.649201\pi$
$158$		0			0
$159$	0.385535	−	0.117596i	0.0305749	−	0.00932599i
$160$		0			0
$161$		−	3.83883i		−	0.302542i
$162$		0			0
$163$	−10.0748	+	10.0748i	−0.789115	+	0.789115i	−0.981349	−	0.192234i	$-0.938427\pi$
$163$	−10.0748	+	10.0748i	−0.789115	+	0.789115i	0.192234	+	0.981349i	$0.438427\pi$
$164$		0			0
$165$	−5.68155	+	10.6687i	−0.442308	+	0.830559i
$166$		0			0
$167$			2.36843i			0.183275i	0.995792	+	0.0916373i	$0.0292100\pi$
$167$			2.36843i			0.183275i	−0.995792	+	0.0916373i	$0.970790\pi$
$168$		0			0
$169$		−	12.9572i		−	0.996704i
$170$		0			0
$171$	6.20086	+	1.21368i	0.474191	+	0.0928125i
$172$		0			0
$173$	5.22347	−	5.22347i	0.397133	−	0.397133i	−0.480088	−	0.877221i	$-0.659395\pi$
$173$	5.22347	−	5.22347i	0.397133	−	0.397133i	0.877221	+	0.480088i	$0.159395\pi$
$174$		0			0
$175$			4.22533i			0.319405i
$176$		0			0
$177$	−6.46787	−	21.2047i	−0.486155	−	1.59384i
$178$		0			0
$179$	−7.13110	−	7.13110i	−0.533003	−	0.533003i	0.388462	−	0.921465i	$-0.373007\pi$
$179$	−7.13110	−	7.13110i	−0.533003	−	0.533003i	−0.921465	+	0.388462i	$0.873007\pi$
$180$		0			0
$181$	−6.73183	+	6.73183i	−0.500373	+	0.500373i	−0.911554	−	0.411181i	$-0.865116\pi$
$181$	−6.73183	+	6.73183i	−0.500373	+	0.500373i	0.411181	+	0.911554i	$0.365116\pi$
$182$		0			0
$183$	10.6357	−	3.24410i	0.786210	−	0.239811i
$184$		0			0
$185$	−20.1403			−1.48075
$186$		0			0
$187$	9.37169	+	9.37169i	0.685326	+	0.685326i
$188$		0			0
$189$	−5.92526	+	0.611106i	−0.430999	+	0.0444514i
$190$		0			0
$191$	25.5284			1.84717			0.923584	−	0.383396i	$-0.125246\pi$
$191$	25.5284			1.84717			0.923584	+	0.383396i	$0.125246\pi$
$192$		0			0
$193$	9.07896			0.653518			0.326759	−	0.945108i	$-0.394043\pi$
$193$	9.07896			0.653518			0.326759	+	0.945108i	$0.394043\pi$
$194$		0			0
$195$	0.932621	+	0.496660i	0.0667864	+	0.0355666i
$196$		0			0
$197$	3.18414	+	3.18414i	0.226861	+	0.226861i	0.811380	−	0.584519i	$-0.198717\pi$
$197$	3.18414	+	3.18414i	0.226861	+	0.226861i	−0.584519	+	0.811380i	$0.698717\pi$
$198$		0			0
$199$	−19.5542			−1.38616			−0.693079	−	0.720861i	$-0.743746\pi$
$199$	−19.5542			−1.38616			−0.693079	+	0.720861i	$0.743746\pi$
$200$		0			0
$201$	−0.454264	−	1.48929i	−0.0320413	−	0.105046i
$202$		0			0
$203$	−4.02747	+	4.02747i	−0.282673	+	0.282673i
$204$		0			0
$205$	1.27131	+	1.27131i	0.0887920	+	0.0887920i
$206$		0			0
$207$	−8.33587	+	5.60688i	−0.579383	+	0.389705i
$208$		0			0
$209$		−	4.98718i		−	0.344970i
$210$		0			0
$211$	10.3429	−	10.3429i	0.712036	−	0.712036i	−0.254925	−	0.966961i	$-0.582051\pi$
$211$	10.3429	−	10.3429i	0.712036	−	0.712036i	0.966961	+	0.254925i	$0.0820507\pi$
$212$		0			0
$213$	10.5587	+	5.62294i	0.723468	+	0.385277i
$214$		0			0
$215$			6.20726i			0.423332i
$216$		0			0
$217$			6.68585i			0.453865i
$218$		0			0
$219$	−10.8222	−	5.76327i	−0.731296	−	0.389446i
$220$		0			0
$221$	0.819240	−	0.819240i	0.0551080	−	0.0551080i
$222$		0			0
$223$			22.6184i			1.51464i	0.653042	+	0.757321i	$0.273492\pi$
$223$			22.6184i			1.51464i	−0.653042	+	0.757321i	$0.726508\pi$
$224$		0			0
$225$	9.17513	−	6.17139i	0.611676	−	0.411426i
$226$		0			0
$227$	−1.46515	−	1.46515i	−0.0972455	−	0.0972455i	0.656810	−	0.754056i	$-0.271905\pi$
$227$	−1.46515	−	1.46515i	−0.0972455	−	0.0972455i	−0.754056	+	0.656810i	$0.771905\pi$
$228$		0			0
$229$	−7.51806	+	7.51806i	−0.496807	+	0.496807i	−0.910443	−	0.413635i	$-0.864259\pi$
$229$	−7.51806	+	7.51806i	−0.496807	+	0.496807i	0.413635	+	0.910443i	$0.364259\pi$
$230$		0			0
$231$	1.37169	+	4.49704i	0.0902507	+	0.295884i
$232$		0			0
$233$	−18.3820			−1.20424			−0.602121	−	0.798405i	$-0.705678\pi$
$233$	−18.3820			−1.20424			−0.602121	+	0.798405i	$0.705678\pi$
$234$		0			0
$235$	−13.3717	−	13.3717i	−0.872273	−	0.872273i
$236$		0			0
$237$	−15.0313	−	8.00481i	−0.976388	−	0.519968i
$238$		0			0
$239$	13.5322			0.875328			0.437664	−	0.899139i	$-0.355806\pi$
$239$	13.5322			0.875328			0.437664	+	0.899139i	$0.355806\pi$
$240$		0			0
$241$	4.87819			0.314232			0.157116	−	0.987580i	$-0.449780\pi$
$241$	4.87819			0.314232			0.157116	+	0.987580i	$0.449780\pi$
$242$		0			0
$243$	9.98126	+	11.9739i	0.640298	+	0.768127i
$244$		0			0
$245$	−11.8491	−	11.8491i	−0.757013	−	0.757013i
$246$		0			0
$247$	−0.435961			−0.0277395
$248$		0			0
$249$	18.9561	−	5.78202i	1.20130	−	0.366421i
$250$		0			0
$251$	−5.23224	+	5.23224i	−0.330256	+	0.330256i	−0.852684	−	0.522427i	$-0.825027\pi$
$251$	−5.23224	+	5.23224i	−0.330256	+	0.330256i	0.522427	+	0.852684i	$0.325027\pi$
$252$		0			0
$253$	5.60688	+	5.60688i	0.352502	+	0.352502i
$254$		0			0
$255$	−8.33587	−	27.3288i	−0.522013	−	1.71140i
$256$		0			0
$257$			12.8329i			0.800495i	0.916407	+	0.400248i	$0.131076\pi$
$257$			12.8329i			0.800495i	−0.916407	+	0.400248i	$0.868924\pi$
$258$		0			0
$259$	−5.53948	+	5.53948i	−0.344207	+	0.344207i
$260$		0			0
$261$	14.6279	+	2.86309i	0.905444	+	0.177221i
$262$		0			0
$263$		−	28.3152i		−	1.74599i	−0.487729	−	0.872995i	$-0.662175\pi$
$263$		−	28.3152i		−	1.74599i	0.487729	−	0.872995i	$-0.337825\pi$
$264$		0			0
$265$			0.685846i			0.0421312i
$266$		0			0
$267$	0.399038	−	0.749307i	0.0244207	−	0.0458569i
$268$		0			0
$269$	6.58101	−	6.58101i	0.401251	−	0.401251i	−0.477423	−	0.878674i	$-0.658429\pi$
$269$	6.58101	−	6.58101i	0.401251	−	0.401251i	0.878674	+	0.477423i	$0.158429\pi$
$270$		0			0
$271$		−	8.66129i		−	0.526136i	−0.964777	−	0.263068i	$-0.915266\pi$
$271$		−	8.66129i		−	0.526136i	0.964777	−	0.263068i	$-0.0847343\pi$
$272$		0			0
$273$	0.393115	−	0.119908i	0.0237924	−	0.00725719i
$274$		0			0
$275$	−6.17139	−	6.17139i	−0.372149	−	0.372149i
$276$		0			0
$277$	13.1249	−	13.1249i	0.788601	−	0.788601i	−0.192664	−	0.981265i	$-0.561713\pi$
$277$	13.1249	−	13.1249i	0.788601	−	0.788601i	0.981265	+	0.192664i	$0.0617126\pi$
$278$		0			0
$279$	14.5181	−	9.76515i	0.869173	−	0.584624i
$280$		0			0
$281$	26.1560			1.56033			0.780167	−	0.625571i	$-0.215134\pi$
$281$	26.1560			1.56033			0.780167	+	0.625571i	$0.215134\pi$
$282$		0			0
$283$	17.9070	+	17.9070i	1.06446	+	1.06446i	0.997774	+	0.0666843i	$0.0212420\pi$
$283$	17.9070	+	17.9070i	1.06446	+	1.06446i	0.0666843	+	0.997774i	$0.478758\pi$
$284$		0			0
$285$	−5.05359	+	9.48955i	−0.299349	+	0.562112i
$286$		0			0
$287$	0.699331			0.0412802
$288$		0			0
$289$	−14.3288			−0.842873
$290$		0			0
$291$	10.0549	−	18.8809i	0.589426	−	1.10682i
$292$		0			0
$293$	−0.654687	−	0.654687i	−0.0382472	−	0.0382472i	0.687725	−	0.725972i	$-0.258610\pi$
$293$	−0.654687	−	0.654687i	−0.0382472	−	0.0382472i	−0.725972	+	0.687725i	$0.758610\pi$
$294$		0			0
$295$	37.7220			2.19626
$296$		0			0
$297$	7.76170	−	9.54683i	0.450379	−	0.553963i
$298$		0			0
$299$	0.490134	−	0.490134i	0.0283452	−	0.0283452i
$300$		0			0
$301$	1.70727	+	1.70727i	0.0984054	+	0.0984054i
$302$		0			0
$303$	−19.4257	+	5.92525i	−1.11598	+	0.340397i
$304$		0			0
$305$			18.9203i			1.08337i
$306$		0			0
$307$	0.971231	−	0.971231i	0.0554311	−	0.0554311i	−0.678848	−	0.734279i	$-0.737520\pi$
$307$	0.971231	−	0.971231i	0.0554311	−	0.0554311i	0.734279	+	0.678848i	$0.237520\pi$
$308$		0			0
$309$	9.95314	−	18.6899i	0.566214	−	1.06323i
$310$		0			0
$311$			33.1343i			1.87887i	0.342723	+	0.939437i	$0.388651\pi$
$311$			33.1343i			1.87887i	−0.342723	+	0.939437i	$0.611349\pi$
$312$		0			0
$313$			13.2285i			0.747717i	0.927486	+	0.373858i	$0.121965\pi$
$313$			13.2285i			0.747717i	−0.927486	+	0.373858i	$0.878035\pi$
$314$		0			0
$315$	1.94688	−	9.94688i	0.109694	−	0.560443i
$316$		0			0
$317$	−7.89038	+	7.89038i	−0.443168	+	0.443168i	−0.893075	−	0.449907i	$-0.851457\pi$
$317$	−7.89038	+	7.89038i	−0.443168	+	0.443168i	0.449907	+	0.893075i	$0.351457\pi$
$318$		0			0
$319$		−	11.7648i		−	0.658703i
$320$		0			0
$321$	−0.510711	−	1.67435i	−0.0285051	−	0.0934530i
$322$		0			0
$323$	8.33587	+	8.33587i	0.463820	+	0.463820i
$324$		0			0
$325$	−0.539481	+	0.539481i	−0.0299250	+	0.0299250i
$326$		0			0
$327$	−29.2787	+	8.93060i	−1.61911	+	0.493864i
$328$		0			0
$329$	−7.35561			−0.405528
$330$		0			0
$331$	3.02877	+	3.02877i	0.166476	+	0.166476i	0.785429	−	0.618952i	$-0.212443\pi$
$331$	3.02877	+	3.02877i	0.166476	+	0.166476i	−0.618952	+	0.785429i	$0.712443\pi$
$332$		0			0
$333$	20.1196	+	3.93796i	1.10255	+	0.215799i
$334$		0			0
$335$	2.64937			0.144750
$336$		0			0
$337$	15.2285			0.829547			0.414774	−	0.909925i	$-0.363861\pi$
$337$	15.2285			0.829547			0.414774	+	0.909925i	$0.363861\pi$
$338$		0			0
$339$	8.37361	+	4.45930i	0.454792	+	0.242196i
$340$		0			0
$341$	−9.76515	−	9.76515i	−0.528813	−	0.528813i
$342$		0			0
$343$	−14.5426			−0.785227
$344$		0			0
$345$	−4.98718	−	16.3503i	−0.268501	−	0.880269i
$346$		0			0
$347$	16.2175	−	16.2175i	0.870600	−	0.870600i	−0.121938	−	0.992538i	$-0.538911\pi$
$347$	16.2175	−	16.2175i	0.870600	−	0.870600i	0.992538	+	0.121938i	$0.0389108\pi$
$348$		0			0
$349$	−6.14637	−	6.14637i	−0.329007	−	0.329007i	0.523202	−	0.852209i	$-0.324737\pi$
$349$	−6.14637	−	6.14637i	−0.329007	−	0.329007i	−0.852209	+	0.523202i	$0.824737\pi$
$350$		0			0
$351$	−0.834549	−	0.678500i	−0.0445449	−	0.0362156i
$352$		0			0
$353$			22.9507i			1.22154i	0.791806	+	0.610772i	$0.209141\pi$
$353$			22.9507i			1.22154i	−0.791806	+	0.610772i	$0.790859\pi$
$354$		0			0
$355$	−14.3931	+	14.3931i	−0.763907	+	0.763907i
$356$		0			0
$357$	−9.80936	−	5.22390i	−0.519167	−	0.276478i
$358$		0			0
$359$			18.3408i			0.967993i	0.875070	+	0.483996i	$0.160815\pi$
$359$			18.3408i			0.967993i	−0.875070	+	0.483996i	$0.839185\pi$
$360$		0			0
$361$			14.5640i			0.766528i
$362$		0			0
$363$	8.24490	+	4.39076i	0.432745	+	0.230455i
$364$		0			0
$365$	14.7523	−	14.7523i	0.772172	−	0.772172i
$366$		0			0
$367$			2.86833i			0.149725i	0.997194	+	0.0748627i	$0.0238519\pi$
$367$			2.86833i			0.149725i	−0.997194	+	0.0748627i	$0.976148\pi$
$368$		0			0
$369$	−1.02142	−	1.51857i	−0.0531731	−	0.0790536i
$370$		0			0
$371$	0.188638	+	0.188638i	0.00979359	+	0.00979359i
$372$		0			0
$373$	−17.2253	+	17.2253i	−0.891894	+	0.891894i	−0.994701	−	0.102808i	$-0.967217\pi$
$373$	−17.2253	+	17.2253i	−0.891894	+	0.891894i	0.102808	+	0.994701i	$0.467217\pi$
$374$		0			0
$375$	−1.95715	−	6.41646i	−0.101067	−	0.331344i
$376$		0			0
$377$	−1.02844			−0.0529672
$378$		0			0
$379$	−5.83956	−	5.83956i	−0.299958	−	0.299958i	0.541039	−	0.840997i	$-0.318031\pi$
$379$	−5.83956	−	5.83956i	−0.299958	−	0.299958i	−0.840997	+	0.541039i	$0.818031\pi$
$380$		0			0
$381$	−11.0132	−	5.86499i	−0.564223	−	0.300473i
$382$		0			0
$383$	−30.7659			−1.57206			−0.786031	−	0.618187i	$-0.787867\pi$
$383$	−30.7659			−1.57206			−0.786031	+	0.618187i	$0.787867\pi$
$384$		0			0
$385$	−8.00000			−0.407718
$386$		0			0
$387$	1.21368	−	6.20086i	0.0616949	−	0.315207i
$388$		0			0
$389$	−11.0299	−	11.0299i	−0.559237	−	0.559237i	0.369853	−	0.929090i	$-0.379408\pi$
$389$	−11.0299	−	11.0299i	−0.559237	−	0.559237i	−0.929090	+	0.369853i	$0.879408\pi$
$390$		0			0
$391$	−18.7434			−0.947894
$392$		0			0
$393$	−21.2047	+	6.46787i	−1.06963	+	0.326261i
$394$		0			0
$395$	20.4900	−	20.4900i	1.03096	−	1.03096i
$396$		0			0
$397$	−1.75325	−	1.75325i	−0.0879931	−	0.0879931i	0.661740	−	0.749733i	$-0.269818\pi$
$397$	−1.75325	−	1.75325i	−0.0879931	−	0.0879931i	−0.749733	+	0.661740i	$0.769818\pi$
$398$		0			0
$399$	1.22008	+	4.00000i	0.0610806	+	0.200250i
$400$		0			0
$401$		−	24.4693i		−	1.22194i	−0.791654	−	0.610970i	$-0.790780\pi$
$401$		−	24.4693i		−	1.22194i	0.791654	−	0.610970i	$-0.209220\pi$
$402$		0			0
$403$	−0.853635	+	0.853635i	−0.0425226	+	0.0425226i
$404$		0			0
$405$	−24.4428	+	10.3005i	−1.21457	+	0.511838i
$406$		0			0
$407$		−	16.1816i		−	0.802093i
$408$		0			0
$409$		−	8.78623i		−	0.434451i	−0.976121	−	0.217226i	$-0.930299\pi$
$409$		−	8.78623i		−	0.434451i	0.976121	−	0.217226i	$-0.0697007\pi$
$410$		0			0
$411$	10.9445	−	20.5513i	0.539851	−	1.01372i
$412$		0			0
$413$	10.3752	−	10.3752i	0.510530	−	0.510530i
$414$		0			0
$415$			33.7220i			1.65535i
$416$		0			0
$417$	−20.2327	+	6.17139i	−0.990798	+	0.302214i
$418$		0			0
$419$	−3.52202	−	3.52202i	−0.172062	−	0.172062i	0.615823	−	0.787885i	$-0.288824\pi$
$419$	−3.52202	−	3.52202i	−0.172062	−	0.172062i	−0.787885	+	0.615823i	$0.788824\pi$
$420$		0			0
$421$	11.2253	−	11.2253i	0.547089	−	0.547089i	−0.378509	−	0.925598i	$-0.623563\pi$
$421$	11.2253	−	11.2253i	0.547089	−	0.547089i	0.925598	+	0.378509i	$0.123563\pi$
$422$		0			0
$423$	10.7434	+	15.9724i	0.522361	+	0.776605i
$424$		0			0
$425$	20.6305			1.00073
$426$		0			0
$427$	5.20390	+	5.20390i	0.251835	+	0.251835i
$428$		0			0
$429$	−0.399038	+	0.749307i	−0.0192657	+	0.0361769i
$430$		0			0
$431$	−12.1336			−0.584454			−0.292227	−	0.956349i	$-0.594396\pi$
$431$	−12.1336			−0.584454			−0.292227	+	0.956349i	$0.594396\pi$
$432$		0			0
$433$	−12.1495			−0.583868			−0.291934	−	0.956439i	$-0.594299\pi$
$433$	−12.1495			−0.583868			−0.291934	+	0.956439i	$0.594299\pi$
$434$		0			0
$435$	−11.9215	+	22.3860i	−0.571591	+	1.07332i
$436$		0			0
$437$	4.98718	+	4.98718i	0.238569	+	0.238569i
$438$		0			0
$439$	−27.1035			−1.29358			−0.646790	−	0.762668i	$-0.723889\pi$
$439$	−27.1035			−1.29358			−0.646790	+	0.762668i	$0.723889\pi$
$440$		0			0
$441$	9.52009	+	14.1537i	0.453337	+	0.673986i
$442$		0			0
$443$	−28.8412	+	28.8412i	−1.37029	+	1.37029i	−0.510276	+	0.860011i	$0.670457\pi$
$443$	−28.8412	+	28.8412i	−1.37029	+	1.37029i	−0.860011	+	0.510276i	$0.829543\pi$
$444$		0			0
$445$	1.02142	+	1.02142i	0.0484201	+	0.0484201i
$446$		0			0
$447$	27.2714	−	8.31836i	1.28990	−	0.393445i
$448$		0			0
$449$		−	9.67586i		−	0.456632i	−0.973587	−	0.228316i	$-0.926678\pi$
$449$		−	9.67586i		−	0.456632i	0.973587	−	0.228316i	$-0.0733220\pi$
$450$		0			0
$451$	−1.02142	+	1.02142i	−0.0480969	+	0.0480969i
$452$		0			0
$453$	0.660097	−	1.23952i	0.0310140	−	0.0582377i
$454$		0			0
$455$			0.699331i			0.0327851i
$456$		0			0
$457$			4.20077i			0.196504i	0.995162	+	0.0982518i	$0.0313251\pi$
$457$			4.20077i			0.196504i	−0.995162	+	0.0982518i	$0.968675\pi$
$458$		0			0
$459$	2.98377	+	28.9305i	0.139271	+	1.35036i
$460$		0			0
$461$	−27.5406	+	27.5406i	−1.28269	+	1.28269i	−0.343565	+	0.939129i	$0.611634\pi$
$461$	−27.5406	+	27.5406i	−1.28269	+	1.28269i	−0.939129	+	0.343565i	$0.888366\pi$
$462$		0			0
$463$		−	37.4109i		−	1.73863i	−0.494255	−	0.869317i	$-0.664559\pi$
$463$		−	37.4109i		−	1.73863i	0.494255	−	0.869317i	$-0.335441\pi$
$464$		0			0
$465$	8.68585	+	28.4762i	0.402796	+	1.32055i
$466$		0			0
$467$	−16.9168	−	16.9168i	−0.782817	−	0.782817i	0.197489	−	0.980305i	$-0.436721\pi$
$467$	−16.9168	−	16.9168i	−0.782817	−	0.782817i	−0.980305	+	0.197489i	$0.936721\pi$
$468$		0			0
$469$	0.728692	−	0.728692i	0.0336479	−	0.0336479i
$470$		0			0
$471$	12.9284	−	3.94343i	0.595709	−	0.181704i
$472$		0			0
$473$	−4.98718			−0.229311
$474$		0			0
$475$	−5.48929	−	5.48929i	−0.251866	−	0.251866i
$476$		0			0
$477$	0.134101	−	0.685139i	0.00614005	−	0.0313703i
$478$		0			0
$479$	−18.5500			−0.847573			−0.423786	−	0.905762i	$-0.639299\pi$
$479$	−18.5500			−0.847573			−0.423786	+	0.905762i	$0.639299\pi$
$480$		0			0
$481$	−1.41454			−0.0644974
$482$		0			0
$483$	−5.86873	−	3.12535i	−0.267037	−	0.142208i
$484$		0			0
$485$	25.7376	+	25.7376i	1.16868	+	1.16868i
$486$		0			0
$487$	40.9259			1.85453			0.927264	−	0.374408i	$-0.122154\pi$
$487$	40.9259			1.85453			0.927264	+	0.374408i	$0.122154\pi$
$488$		0			0
$489$	7.19983	+	23.6044i	0.325587	+	1.06743i
$490$		0			0
$491$	−5.04360	+	5.04360i	−0.227615	+	0.227615i	−0.811696	−	0.584081i	$-0.801455\pi$
$491$	−5.04360	+	5.04360i	−0.227615	+	0.227615i	0.584081	+	0.811696i	$0.301455\pi$
$492$		0			0
$493$	19.6644	+	19.6644i	0.885641	+	0.885641i
$494$		0			0
$495$	11.6846	+	17.3717i	0.525182	+	0.780800i
$496$		0			0
$497$			7.91748i			0.355147i
$498$		0			0
$499$	11.4647	−	11.4647i	0.513232	−	0.513232i	−0.402283	−	0.915515i	$-0.631783\pi$
$499$	11.4647	−	11.4647i	0.513232	−	0.513232i	0.915515	+	0.402283i	$0.131783\pi$
$500$		0			0
$501$	3.62081	+	1.92824i	0.161766	+	0.0861472i
$502$		0			0
$503$		−	32.7159i		−	1.45873i	−0.684125	−	0.729365i	$-0.739816\pi$
$503$		−	32.7159i		−	1.45873i	0.684125	−	0.729365i	$-0.260184\pi$
$504$		0			0
$505$		−	34.5573i		−	1.53778i
$506$		0			0
$507$	−19.8087	−	10.5490i	−0.879734	−	0.468495i
$508$		0			0
$509$	10.1389	−	10.1389i	0.449399	−	0.449399i	−0.445756	−	0.895155i	$-0.647065\pi$
$509$	10.1389	−	10.1389i	0.449399	−	0.449399i	0.895155	+	0.445756i	$0.147065\pi$
$510$		0			0
$511$		−	8.11508i		−	0.358990i
$512$		0			0
$513$	6.90383	−	8.49165i	0.304811	−	0.374916i
$514$		0			0
$515$	25.4772	+	25.4772i	1.12266	+	1.12266i
$516$		0			0
$517$	10.7434	−	10.7434i	0.472494	−	0.472494i
$518$		0			0
$519$	−3.73290	−	12.2382i	−0.163856	−	0.537197i
$520$		0			0
$521$	6.08735			0.266692			0.133346	−	0.991070i	$-0.457428\pi$
$521$	6.08735			0.266692			0.133346	+	0.991070i	$0.457428\pi$
$522$		0			0
$523$	−15.8824	−	15.8824i	−0.694489	−	0.694489i	0.268727	−	0.963216i	$-0.413397\pi$
$523$	−15.8824	−	15.8824i	−0.694489	−	0.694489i	−0.963216	+	0.268727i	$0.913397\pi$
$524$		0			0
$525$	6.45960	+	3.44001i	0.281920	+	0.150134i
$526$		0			0
$527$	32.6442			1.42200
$528$		0			0
$529$	11.7862			0.512445
$530$		0			0
$531$	−37.6831	−	7.37563i	−1.63531	−	0.320075i
$532$		0			0
$533$	0.0892891	+	0.0892891i	0.00386754	+	0.00386754i
$534$		0			0
$535$	2.97858			0.128775
$536$		0			0
$537$	−16.7076	+	5.09617i	−0.720987	+	0.219916i
$538$		0			0
$539$	9.52009	−	9.52009i	0.410059	−	0.410059i
$540$		0			0
$541$	−25.6184	−	25.6184i	−1.10142	−	1.10142i	−0.994239	−	0.107184i	$-0.965817\pi$
$541$	−25.6184	−	25.6184i	−1.10142	−	1.10142i	−0.107184	−	0.994239i	$-0.534183\pi$
$542$		0			0
$543$	4.81084	+	15.7722i	0.206453	+	0.676848i
$544$		0			0
$545$		−	52.0852i		−	2.23108i
$546$		0			0
$547$	27.2113	−	27.2113i	1.16347	−	1.16347i	0.179758	−	0.983711i	$-0.442468\pi$
$547$	27.2113	−	27.2113i	1.16347	−	1.16347i	0.983711	−	0.179758i	$-0.0575315\pi$
$548$		0			0
$549$	3.69941	−	18.9007i	0.157887	−	0.806664i
$550$		0			0
$551$		−	10.4645i		−	0.445802i
$552$		0			0
$553$		−	11.2713i		−	0.479305i
$554$		0			0
$555$	−16.3971	+	30.7902i	−0.696018	+	1.30697i
$556$		0			0
$557$	−26.1831	+	26.1831i	−1.10941	+	1.10941i	−0.116184	+	0.993228i	$0.537066\pi$
$557$	−26.1831	+	26.1831i	−1.10941	+	1.10941i	−0.993228	+	0.116184i	$0.962934\pi$
$558$		0			0
$559$			0.435961i			0.0184392i
$560$		0			0
$561$	21.9572	−	6.69739i	0.927032	−	0.282764i
$562$		0			0
$563$	25.0435	+	25.0435i	1.05546	+	1.05546i	0.998369	+	0.0570880i	$0.0181816\pi$
$563$	25.0435	+	25.0435i	1.05546	+	1.05546i	0.0570880	+	0.998369i	$0.481818\pi$
$564$		0			0
$565$	−11.4145	+	11.4145i	−0.480213	+	0.480213i
$566$		0			0
$567$	−3.88975	+	9.55596i	−0.163354	+	0.401312i
$568$		0			0
$569$	−12.5449			−0.525911			−0.262955	−	0.964808i	$-0.584697\pi$
$569$	−12.5449			−0.525911			−0.262955	+	0.964808i	$0.584697\pi$
$570$		0			0
$571$	4.48615	+	4.48615i	0.187740	+	0.187740i	0.794718	−	0.606979i	$-0.207619\pi$
$571$	4.48615	+	4.48615i	0.187740	+	0.187740i	−0.606979	+	0.794718i	$0.707619\pi$
$572$		0			0
$573$	20.7837	−	39.0273i	0.868251	−	1.63039i
$574$		0			0
$575$	12.3428			0.514730
$576$		0			0
$577$	4.48508			0.186716			0.0933581	−	0.995633i	$-0.470240\pi$
$577$	4.48508			0.186716			0.0933581	+	0.995633i	$0.470240\pi$
$578$		0			0
$579$	7.39156	−	13.8798i	0.307183	−	0.576823i
$580$		0			0
$581$	9.27502	+	9.27502i	0.384793	+	0.384793i
$582$		0			0
$583$	−0.551038			−0.0228217
$584$		0			0
$585$	1.51857	−	1.02142i	0.0627852	−	0.0422306i
$586$		0			0
$587$	−11.9808	+	11.9808i	−0.494501	+	0.494501i	−0.909721	−	0.415220i	$-0.863705\pi$
$587$	−11.9808	+	11.9808i	−0.494501	+	0.494501i	0.415220	+	0.909721i	$0.363705\pi$
$588$		0			0
$589$	−8.68585	−	8.68585i	−0.357894	−	0.357894i
$590$		0			0
$591$	7.46020	−	2.27552i	0.306872	−	0.0936023i
$592$		0			0
$593$		−	3.27696i		−	0.134569i	−0.997734	−	0.0672843i	$-0.978567\pi$
$593$		−	3.27696i		−	0.134569i	0.997734	−	0.0672843i	$-0.0214334\pi$
$594$		0			0
$595$	13.3717	−	13.3717i	0.548186	−	0.548186i
$596$		0			0
$597$	−15.9199	+	29.8941i	−0.651556	+	1.22348i
$598$		0			0
$599$			38.9889i			1.59304i	0.604611	+	0.796521i	$0.293329\pi$
$599$			38.9889i			1.59304i	−0.604611	+	0.796521i	$0.706671\pi$
$600$		0			0
$601$		−	23.5787i		−	0.961797i	−0.876776	−	0.480898i	$-0.840311\pi$
$601$		−	23.5787i		−	0.961797i	0.876776	−	0.480898i	$-0.159689\pi$
$602$		0			0
$603$	−2.64663	−	0.518020i	−0.107779	−	0.0210954i
$604$		0			0
$605$	−11.2391	+	11.2391i	−0.456934	+	0.456934i
$606$		0			0
$607$			22.2829i			0.904434i	0.891908	+	0.452217i	$0.149367\pi$
$607$			22.2829i			0.904434i	−0.891908	+	0.452217i	$0.850633\pi$
$608$		0			0
$609$	2.87819	+	9.43605i	0.116630	+	0.382368i
$610$		0			0
$611$	−0.939148	−	0.939148i	−0.0379939	−	0.0379939i
$612$		0			0
$613$	22.1611	−	22.1611i	0.895077	−	0.895077i	−0.0999189	−	0.994996i	$-0.531858\pi$
$613$	22.1611	−	22.1611i	0.895077	−	0.895077i	0.994996	+	0.0999189i	$0.0318583\pi$
$614$		0			0
$615$	2.97858	−	0.908529i	0.120108	−	0.0366354i
$616$		0			0
$617$	−25.7376			−1.03616			−0.518078	−	0.855334i	$-0.673352\pi$
$617$	−25.7376			−1.03616			−0.518078	+	0.855334i	$0.673352\pi$
$618$		0			0
$619$	−7.71462	−	7.71462i	−0.310077	−	0.310077i	0.534863	−	0.844939i	$-0.320363\pi$
$619$	−7.71462	−	7.71462i	−0.310077	−	0.310077i	−0.844939	+	0.534863i	$0.820363\pi$
$620$		0			0
$621$	1.78513	+	17.3085i	0.0716347	+	0.694567i
$622$		0			0
$623$	0.561872			0.0225109
$624$		0			0
$625$	29.8438			1.19375
$626$		0			0
$627$	−7.62430	−	4.06027i	−0.304485	−	0.162151i
$628$		0			0
$629$	27.0469	+	27.0469i	1.07843	+	1.07843i
$630$		0			0
$631$	−2.26817			−0.0902945			−0.0451473	−	0.998980i	$-0.514376\pi$
$631$	−2.26817			−0.0902945			−0.0451473	+	0.998980i	$0.514376\pi$
$632$		0			0
$633$	−7.39147	−	24.2327i	−0.293785	−	0.963162i
$634$		0			0
$635$	15.0127	−	15.0127i	0.595761	−	0.595761i
$636$		0			0
$637$	−0.832212	−	0.832212i	−0.0329734	−	0.0329734i
$638$		0			0
$639$	17.1925	−	11.5640i	0.680125	−	0.457466i
$640$		0			0
$641$		−	20.0686i		−	0.792662i	−0.918108	−	0.396331i	$-0.870283\pi$
$641$		−	20.0686i		−	0.792662i	0.918108	−	0.396331i	$-0.129717\pi$
$642$		0			0
$643$	−14.0748	+	14.0748i	−0.555054	+	0.555054i	−0.927895	−	0.372841i	$-0.878384\pi$
$643$	−14.0748	+	14.0748i	−0.555054	+	0.555054i	0.372841	+	0.927895i	$0.378384\pi$
$644$		0			0
$645$	9.48955	+	5.05359i	0.373651	+	0.198985i
$646$		0			0
$647$		−	1.95003i		−	0.0766638i	−0.999265	−	0.0383319i	$-0.987796\pi$
$647$		−	1.95003i		−	0.0766638i	0.999265	−	0.0383319i	$-0.0122044\pi$
$648$		0			0
$649$			30.3074i			1.18967i
$650$		0			0
$651$	10.2212	+	5.44322i	0.400600	+	0.213337i
$652$		0			0
$653$	5.80289	−	5.80289i	0.227085	−	0.227085i	−0.584389	−	0.811474i	$-0.698666\pi$
$653$	5.80289	−	5.80289i	0.227085	−	0.227085i	0.811474	+	0.584389i	$0.198666\pi$
$654$		0			0
$655$		−	37.7220i		−	1.47392i
$656$		0			0
$657$	−17.6216	+	11.8526i	−0.687483	+	0.462416i
$658$		0			0
$659$	−5.49262	−	5.49262i	−0.213962	−	0.213962i	0.591986	−	0.805948i	$-0.298344\pi$
$659$	−5.49262	−	5.49262i	−0.213962	−	0.213962i	−0.805948	+	0.591986i	$0.798344\pi$
$660$		0			0
$661$	−5.86833	+	5.86833i	−0.228251	+	0.228251i	−0.811962	−	0.583710i	$-0.801600\pi$
$661$	−5.86833	+	5.86833i	−0.228251	+	0.228251i	0.583710	+	0.811962i	$0.301600\pi$
$662$		0			0
$663$	−0.585462	−	1.91942i	−0.0227375	−	0.0745439i
$664$		0			0
$665$	−7.11579			−0.275938
$666$		0			0
$667$	11.7648	+	11.7648i	0.455535	+	0.455535i
$668$		0			0
$669$	34.5787	+	18.4146i	1.33689	+	0.711950i
$670$		0			0
$671$	−15.2013			−0.586841
$672$		0			0
$673$	−22.8929			−0.882456			−0.441228	−	0.897395i	$-0.645457\pi$
$673$	−22.8929			−0.882456			−0.441228	+	0.897395i	$0.645457\pi$
$674$		0			0
$675$	−1.96486	−	19.0512i	−0.0756273	−	0.733280i
$676$		0			0
$677$	−13.7685	−	13.7685i	−0.529168	−	0.529168i	0.391156	−	0.920324i	$-0.372075\pi$
$677$	−13.7685	−	13.7685i	−0.529168	−	0.529168i	−0.920324	+	0.391156i	$0.872075\pi$
$678$		0			0
$679$	14.1579			0.543331
$680$		0			0
$681$	−3.43274	+	1.04706i	−0.131543	+	0.0401233i
$682$		0			0
$683$	5.72238	−	5.72238i	0.218961	−	0.218961i	−0.589100	−	0.808060i	$-0.700517\pi$
$683$	5.72238	−	5.72238i	0.218961	−	0.218961i	0.808060	+	0.589100i	$0.200517\pi$
$684$		0			0
$685$	28.0147	+	28.0147i	1.07039	+	1.07039i
$686$		0			0
$687$	5.37271	+	17.6142i	0.204982	+	0.672025i
$688$		0			0
$689$			0.0481697i			0.00183512i
$690$		0			0
$691$	−24.2327	+	24.2327i	−0.921854	+	0.921854i	−0.997160	−	0.0753061i	$-0.976007\pi$
$691$	−24.2327	+	24.2327i	−0.921854	+	0.921854i	0.0753061	+	0.997160i	$0.476007\pi$
$692$		0			0
$693$	7.99175	+	1.56421i	0.303581	+	0.0594194i
$694$		0			0
$695$		−	35.9929i		−	1.36529i
$696$		0			0
$697$		−	3.41454i		−	0.129335i
$698$		0			0
$699$	−14.9655	+	28.1020i	−0.566048	+	1.06292i
$700$		0			0
$701$	−10.9100	+	10.9100i	−0.412064	+	0.412064i	−0.882457	−	0.470393i	$-0.844112\pi$
$701$	−10.9100	+	10.9100i	−0.412064	+	0.412064i	0.470393	+	0.882457i	$0.344112\pi$
$702$		0			0
$703$		−	14.3931i		−	0.542847i
$704$		0			0
$705$	−31.3288	+	9.55596i	−1.17991	+	0.359898i
$706$		0			0
$707$	−9.50478	−	9.50478i	−0.357464	−	0.357464i
$708$		0			0
$709$	−14.0031	+	14.0031i	−0.525899	+	0.525899i	−0.919347	−	0.393448i	$-0.871282\pi$
$709$	−14.0031	+	14.0031i	−0.525899	+	0.525899i	0.393448	+	0.919347i	$0.371282\pi$
$710$		0			0
$711$	−24.4752	+	16.4625i	−0.917892	+	0.617394i
$712$		0			0
$713$	19.5303			0.731416
$714$		0			0
$715$	−1.02142	−	1.02142i	−0.0381990	−	0.0381990i
$716$		0			0
$717$	11.0172	−	20.6879i	0.411443	−	0.772602i
$718$		0			0
$719$	−30.0665			−1.12129			−0.560646	−	0.828055i	$-0.689447\pi$
$719$	−30.0665			−1.12129			−0.560646	+	0.828055i	$0.689447\pi$
$720$		0			0
$721$	14.0147			0.521934
$722$		0			0
$723$	3.97154	−	7.45769i	0.147703	−	0.277355i
$724$		0			0
$725$	−12.9493	−	12.9493i	−0.480925	−	0.480925i
$726$		0			0
$727$	−9.48194			−0.351666			−0.175833	−	0.984420i	$-0.556262\pi$
$727$	−9.48194			−0.351666			−0.175833	+	0.984420i	$0.556262\pi$
$728$		0			0
$729$	26.4316	−	5.51071i	0.978950	−	0.204100i
$730$		0			0
$731$	8.33587	−	8.33587i	0.308313	−	0.308313i
$732$		0			0
$733$	−29.4752	−	29.4752i	−1.08869	−	1.08869i	−0.995663	−	0.0930283i	$-0.970345\pi$
$733$	−29.4752	−	29.4752i	−1.08869	−	1.08869i	−0.0930283	−	0.995663i	$-0.529655\pi$
$734$		0			0
$735$	−27.7616	+	8.46787i	−1.02400	+	0.312342i
$736$		0			0
$737$			2.12861i			0.0784085i
$738$		0			0
$739$	−22.1077	+	22.1077i	−0.813246	+	0.813246i	−0.985119	−	0.171873i	$-0.945018\pi$
$739$	−22.1077	+	22.1077i	−0.813246	+	0.813246i	0.171873	+	0.985119i	$0.445018\pi$
$740$		0			0
$741$	−0.354934	+	0.666489i	−0.0130388	+	0.0244841i
$742$		0			0
$743$		−	0.908529i		−	0.0333307i	−0.999861	−	0.0166653i	$-0.994695\pi$
$743$		−	0.908529i		−	0.0333307i	0.999861	−	0.0166653i	$-0.00530499\pi$
$744$		0			0
$745$			48.5145i			1.77743i
$746$		0			0
$747$	6.59352	−	33.6872i	0.241244	−	1.23255i
$748$		0			0
$749$	0.819240	−	0.819240i	0.0299344	−	0.0299344i
$750$		0			0
$751$			39.1182i			1.42744i	0.700429	+	0.713722i	$0.252992\pi$
$751$			39.1182i			1.42744i	−0.700429	+	0.713722i	$0.747008\pi$
$752$		0			0
$753$	3.73917	+	12.2587i	0.136263	+	0.446733i
$754$		0			0
$755$	1.68966	+	1.68966i	0.0614930	+	0.0614930i
$756$		0			0
$757$	−8.97544	+	8.97544i	−0.326218	+	0.326218i	−0.851146	−	0.524928i	$-0.824092\pi$
$757$	−8.97544	+	8.97544i	−0.326218	+	0.326218i	0.524928	+	0.851146i	$0.324092\pi$
$758$		0			0
$759$	13.1365	−	4.00691i	0.476825	−	0.145442i
$760$		0			0
$761$	30.6766			1.11202			0.556012	−	0.831174i	$-0.312331\pi$
$761$	30.6766			1.11202			0.556012	+	0.831174i	$0.312331\pi$
$762$		0			0
$763$	−14.3257	−	14.3257i	−0.518626	−	0.518626i
$764$		0			0
$765$	−48.5664	−	9.50581i	−1.75592	−	0.343683i
$766$		0			0
$767$	2.64937			0.0956630
$768$		0			0
$769$	−41.7795			−1.50661			−0.753304	−	0.657673i	$-0.771541\pi$
$769$	−41.7795			−1.50661			−0.753304	+	0.657673i	$0.771541\pi$
$770$		0			0
$771$	19.6187	+	10.4478i	0.706551	+	0.376268i
$772$		0			0
$773$	−17.6074	−	17.6074i	−0.633293	−	0.633293i	0.315599	−	0.948892i	$-0.397794\pi$
$773$	−17.6074	−	17.6074i	−0.633293	−	0.633293i	−0.948892	+	0.315599i	$0.897794\pi$
$774$		0			0
$775$	−21.4966			−0.772182
$776$		0			0
$777$	3.95874	+	12.9786i	0.142019	+	0.465604i
$778$		0			0
$779$	−0.908529	+	0.908529i	−0.0325514	+	0.0325514i
$780$		0			0
$781$	−11.5640	−	11.5640i	−0.413794	−	0.413794i
$782$		0			0
$783$	16.2862	−	20.0319i	0.582022	−	0.715882i
$784$		0			0
$785$			22.9989i			0.820866i
$786$		0			0
$787$	−1.69006	+	1.69006i	−0.0602440	+	0.0602440i	−0.736587	−	0.676343i	$-0.763564\pi$
$787$	−1.69006	+	1.69006i	−0.0602440	+	0.0602440i	0.676343	+	0.736587i	$0.263564\pi$
$788$		0			0
$789$	−43.2878	−	23.0526i	−1.54108	−	0.820693i
$790$		0			0
$791$			6.27900i			0.223255i
$792$		0			0
$793$			1.32885i			0.0471887i
$794$		0			0
$795$	1.04851	+	0.558376i	0.0371868	+	0.0198035i
$796$		0			0
$797$	5.76177	−	5.76177i	0.204092	−	0.204092i	−0.597658	−	0.801751i	$-0.703902\pi$
$797$	5.76177	−	5.76177i	0.204092	−	0.204092i	0.801751	+	0.597658i	$0.203902\pi$
$798$		0			0
$799$			35.9143i			1.27056i
$800$		0			0
$801$	−0.820654	−	1.22008i	−0.0289964	−	0.0431096i
$802$		0			0
$803$	11.8526	+	11.8526i	0.418271	+	0.418271i
$804$		0			0
$805$	8.00000	−	8.00000i	0.281963	−	0.281963i
$806$		0			0
$807$	−4.70306	−	15.4188i	−0.165555	−	0.542767i
$808$		0			0
$809$	−14.1012			−0.495771			−0.247885	−	0.968789i	$-0.579736\pi$
$809$	−14.1012			−0.495771			−0.247885	+	0.968789i	$0.579736\pi$
$810$		0			0
$811$	16.2327	+	16.2327i	0.570006	+	0.570006i	0.932130	−	0.362124i	$-0.117948\pi$
$811$	16.2327	+	16.2327i	0.570006	+	0.570006i	−0.362124	+	0.932130i	$0.617948\pi$
$812$		0			0
$813$	−13.2412	−	7.05151i	−0.464390	−	0.247307i
$814$		0			0
$815$	−41.9909			−1.47088
$816$		0			0
$817$	−4.43596			−0.155195
$818$		0			0
$819$	0.136737	−	0.698610i	0.00477799	−	0.0244114i
$820$		0			0
$821$	−17.2853	−	17.2853i	−0.603262	−	0.603262i	0.337915	−	0.941177i	$-0.390278\pi$
$821$	−17.2853	−	17.2853i	−0.603262	−	0.603262i	−0.941177	+	0.337915i	$0.890278\pi$
$822$		0			0
$823$	−7.35341			−0.256324			−0.128162	−	0.991753i	$-0.540908\pi$
$823$	−7.35341			−0.256324			−0.128162	+	0.991753i	$0.540908\pi$
$824$		0			0
$825$	−14.4591	+	4.41033i	−0.503401	+	0.153548i
$826$		0			0
$827$	−0.224507	+	0.224507i	−0.00780688	+	0.00780688i	−0.710999	−	0.703193i	$-0.751757\pi$
$827$	−0.224507	+	0.224507i	−0.00780688	+	0.00780688i	0.703193	+	0.710999i	$0.251757\pi$
$828$		0			0
$829$	29.5181	+	29.5181i	1.02520	+	1.02520i	0.999674	+	0.0255305i	$0.00812749\pi$
$829$	29.5181	+	29.5181i	1.02520	+	1.02520i	0.0255305	+	0.999674i	$0.491873\pi$
$830$		0			0
$831$	−9.37962	−	30.7507i	−0.325375	−	1.06673i
$832$		0			0
$833$			31.8249i			1.10267i
$834$		0			0
$835$	−4.93573	+	4.93573i	−0.170808	+	0.170808i
$836$		0			0
$837$	−3.10904	−	30.1452i	−0.107464	−	1.04197i
$838$		0			0
$839$			14.0224i			0.484106i	0.970263	+	0.242053i	$0.0778208\pi$
$839$			14.0224i			0.484106i	−0.970263	+	0.242053i	$0.922179\pi$
$840$		0			0
$841$			4.31415i			0.148764i
$842$		0			0
$843$	21.2946	−	39.9868i	0.733427	−	1.37722i
$844$		0			0
$845$	27.0023	−	27.0023i	0.928907	−	0.928907i
$846$		0			0
$847$			6.18248i			0.212433i
$848$		0			0
$849$	41.9546	−	12.7970i	1.43988	−	0.439193i
$850$		0			0
$851$	16.1816	+	16.1816i	0.554698	+	0.554698i
$852$		0			0
$853$	−8.55417	+	8.55417i	−0.292889	+	0.292889i	−0.838221	−	0.545331i	$-0.816404\pi$
$853$	−8.55417	+	8.55417i	−0.292889	+	0.292889i	0.545331	+	0.838221i	$0.316404\pi$
$854$		0			0
$855$	10.3931	+	15.4517i	0.355437	+	0.528436i
$856$		0			0
$857$	43.5095			1.48626			0.743128	−	0.669149i	$-0.233341\pi$
$857$	43.5095			1.48626			0.743128	+	0.669149i	$0.233341\pi$
$858$		0			0
$859$	8.70306	+	8.70306i	0.296945	+	0.296945i	0.839816	−	0.542871i	$-0.182663\pi$
$859$	8.70306	+	8.70306i	0.296945	+	0.296945i	−0.542871	+	0.839816i	$0.682663\pi$
$860$		0			0
$861$	0.569354	−	1.06912i	0.0194035	−	0.0364357i
$862$		0			0
$863$	26.9270			0.916607			0.458303	−	0.888796i	$-0.348457\pi$
$863$	26.9270			0.916607			0.458303	+	0.888796i	$0.348457\pi$
$864$		0			0
$865$	21.7711			0.740239
$866$		0			0
$867$	−11.6657	+	21.9057i	−0.396188	+	0.743956i
$868$		0			0
$869$	16.4625	+	16.4625i	0.558454	+	0.558454i
$870$		0			0
$871$	0.186076			0.00630493
$872$		0			0
$873$	−20.6787	−	30.7434i	−0.699866	−	1.04051i
$874$		0			0
$875$	3.13950	−	3.13950i	0.106134	−	0.106134i
$876$		0			0
$877$	39.7251	+	39.7251i	1.34142	+	1.34142i	0.894646	+	0.446775i	$0.147427\pi$
$877$	39.7251	+	39.7251i	1.34142	+	1.34142i	0.446775	+	0.894646i	$0.352573\pi$
$878$		0			0
$879$	−1.53388	+	0.467866i	−0.0517365	+	0.0157807i
$880$		0			0
$881$		−	1.63848i		−	0.0552018i	−0.999619	−	0.0276009i	$-0.991213\pi$
$881$		−	1.63848i		−	0.0552018i	0.999619	−	0.0276009i	$-0.00878675\pi$
$882$		0			0
$883$	31.7967	−	31.7967i	1.07004	−	1.07004i	0.0726900	−	0.997355i	$-0.476842\pi$
$883$	31.7967	−	31.7967i	1.07004	−	1.07004i	0.997355	−	0.0726900i	$-0.0231584\pi$
$884$		0			0
$885$	30.7110	−	57.6687i	1.03234	−	1.93851i
$886$		0			0
$887$			29.8573i			1.00251i	0.865299	+	0.501256i	$0.167128\pi$
$887$			29.8573i			1.00251i	−0.865299	+	0.501256i	$0.832872\pi$
$888$		0			0
$889$		−	8.25831i		−	0.276975i
$890$		0			0
$891$	−8.27590	−	19.6384i	−0.277253	−	0.657912i
$892$		0			0
$893$	9.55596	−	9.55596i	0.319778	−	0.319778i
$894$		0			0
$895$		−	29.7220i		−	0.993496i
$896$		0			0
$897$	−0.350269	−	1.14835i	−0.0116952	−	0.0383421i
$898$		0			0
$899$	−20.4900	−	20.4900i	−0.683380	−	0.683380i
$900$		0			0
$901$	0.921039	−	0.921039i	0.0306842	−	0.0306842i
$902$		0			0
$903$	4.00000	−	1.22008i	0.133112	−	0.0406019i
$904$		0			0
$905$	−28.0578			−0.932674
$906$		0			0
$907$	12.1176	+	12.1176i	0.402358	+	0.402358i	0.879063	−	0.476705i	$-0.158169\pi$
$907$	12.1176	+	12.1176i	0.402358	+	0.402358i	−0.476705	+	0.879063i	$0.658169\pi$
$908$		0			0
$909$	−6.75686	+	34.5217i	−0.224111	+	1.14501i
$910$		0			0
$911$	−4.53816			−0.150356			−0.0751780	−	0.997170i	$-0.523952\pi$
$911$	−4.53816			−0.150356			−0.0751780	+	0.997170i	$0.523952\pi$
$912$		0			0
$913$	−27.0937			−0.896669
$914$		0			0
$915$	28.9250	+	15.4038i	0.956230	+	0.509233i
$916$		0			0
$917$	−10.3752	−	10.3752i	−0.342619	−	0.342619i
$918$		0			0
$919$	33.6461			1.10988			0.554942	−	0.831889i	$-0.312741\pi$
$919$	33.6461			1.10988			0.554942	+	0.831889i	$0.312741\pi$
$920$		0			0
$921$	−0.694081	−	2.27552i	−0.0228707	−	0.0749809i
$922$		0			0
$923$	−1.01089	+	1.01089i	−0.0332737	+	0.0332737i
$924$		0			0
$925$	−17.8108	−	17.8108i	−0.585615	−	0.585615i
$926$		0			0
$927$	−20.4695	−	30.4324i	−0.672305	−	0.999530i
$928$		0			0
$929$			27.1844i			0.891891i	0.895060	+	0.445946i	$0.147133\pi$
$929$			27.1844i			0.891891i	−0.895060	+	0.445946i	$0.852867\pi$
$930$		0			0
$931$	8.46787	−	8.46787i	0.277523	−	0.277523i
$932$		0			0
$933$	50.6551	+	26.9760i	1.65837	+	0.883154i
$934$		0			0
$935$			39.0606i			1.27742i
$936$		0			0
$937$		−	22.1495i		−	0.723593i	−0.932257	−	0.361796i	$-0.882164\pi$
$937$		−	22.1495i		−	0.723593i	0.932257	−	0.361796i	$-0.117836\pi$
$938$		0			0
$939$	20.2234	+	10.7698i	0.659967	+	0.351460i
$940$		0			0
$941$	−7.35208	+	7.35208i	−0.239671	+	0.239671i	−0.816714	−	0.577043i	$-0.804207\pi$
$941$	−7.35208	+	7.35208i	−0.239671	+	0.239671i	0.577043	+	0.816714i	$0.304207\pi$
$942$		0			0
$943$		−	2.04285i		−	0.0665242i
$944$		0			0
$945$	−13.6216	−	11.0745i	−0.443110	−	0.360254i
$946$		0			0
$947$	−9.29033	−	9.29033i	−0.301895	−	0.301895i	0.539860	−	0.841755i	$-0.318477\pi$
$947$	−9.29033	−	9.29033i	−0.301895	−	0.301895i	−0.841755	+	0.539860i	$0.818477\pi$
$948$		0			0
$949$	1.03612	−	1.03612i	0.0336337	−	0.0336337i
$950$		0			0
$951$	5.63879	+	18.4866i	0.182850	+	0.599468i
$952$		0			0
$953$	12.6413			0.409491			0.204745	−	0.978815i	$-0.434363\pi$
$953$	12.6413			0.409491			0.204745	+	0.978815i	$0.434363\pi$
$954$		0			0
$955$	53.2003	+	53.2003i	1.72152	+	1.72152i
$956$		0			0
$957$	−17.9858	−	9.57821i	−0.581399	−	0.309620i
$958$		0			0
$959$	15.4105			0.497632
$960$		0			0
$961$	−3.01469			−0.0972482
$962$		0			0
$963$	−2.97550	−	0.582390i	−0.0958843	−	0.0187672i
$964$		0			0
$965$	18.9203	+	18.9203i	0.609065	+	0.609065i
$966$		0			0
$967$	−23.3043			−0.749415			−0.374708	−	0.927143i	$-0.622257\pi$
$967$	−23.3043			−0.749415			−0.374708	+	0.927143i	$0.622257\pi$
$968$		0			0
$969$	19.5303	−	5.95715i	0.627404	−	0.191371i
$970$		0			0
$971$	−6.17139	+	6.17139i	−0.198049	+	0.198049i	−0.799163	−	0.601114i	$-0.794724\pi$
$971$	−6.17139	+	6.17139i	−0.198049	+	0.198049i	0.601114	+	0.799163i	$0.294724\pi$
$972$		0			0
$973$	−9.89962	−	9.89962i	−0.317367	−	0.317367i
$974$		0			0
$975$	0.385535	+	1.26396i	0.0123470	+	0.0404792i
$976$		0			0
$977$			9.43605i			0.301886i	0.988542	+	0.150943i	$0.0482310\pi$
$977$			9.43605i			0.301886i	−0.988542	+	0.150943i	$0.951769\pi$
$978$		0			0
$979$	−0.820654	+	0.820654i	−0.0262282	+	0.0262282i
$980$		0			0
$981$	−10.1840	+	52.0315i	−0.325150	+	1.66124i
$982$		0			0
$983$		−	25.8750i		−	0.825285i	−0.910893	−	0.412643i	$-0.864606\pi$
$983$		−	25.8750i		−	0.825285i	0.910893	−	0.412643i	$-0.135394\pi$
$984$		0			0
$985$			13.2713i			0.422859i
$986$		0			0
$987$	−5.98850	+	11.2451i	−0.190616	+	0.357936i
$988$		0			0
$989$	4.98718	−	4.98718i	0.158583	−	0.158583i
$990$		0			0
$991$		−	23.5886i		−	0.749316i	−0.927163	−	0.374658i	$-0.877760\pi$
$991$		−	23.5886i		−	0.749316i	0.927163	−	0.374658i	$-0.122240\pi$
$992$		0			0
$993$	7.09617	−	2.16448i	0.225190	−	0.0686878i
$994$		0			0
$995$	−40.7503	−	40.7503i	−1.29187	−	1.29187i
$996$		0			0
$997$	3.16779	−	3.16779i	0.100325	−	0.100325i	−0.655163	−	0.755488i	$-0.727400\pi$
$997$	3.16779	−	3.16779i	0.100325	−	0.100325i	0.755488	+	0.655163i	$0.227400\pi$
$998$		0			0
$999$	22.4005	−	27.5524i	0.708719	−	0.871719i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	192.2.k.a.47.4		12
3.2	odd	2	inner	192.2.k.a.47.6		12
4.3	odd	2		48.2.k.a.35.1	yes	12
8.3	odd	2		384.2.k.b.95.4		12
8.5	even	2		384.2.k.a.95.3		12
12.11	even	2		48.2.k.a.35.6	yes	12
16.3	odd	4		384.2.k.a.287.1		12
16.5	even	4		48.2.k.a.11.6	yes	12
16.11	odd	4	inner	192.2.k.a.143.6		12
16.13	even	4		384.2.k.b.287.6		12
24.5	odd	2		384.2.k.a.95.1		12
24.11	even	2		384.2.k.b.95.6		12
48.5	odd	4		48.2.k.a.11.1	✓	12
48.11	even	4	inner	192.2.k.a.143.4		12
48.29	odd	4		384.2.k.b.287.4		12
48.35	even	4		384.2.k.a.287.3		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
48.2.k.a.11.1	✓	12	48.5	odd	4
48.2.k.a.11.6	yes	12	16.5	even	4
48.2.k.a.35.1	yes	12	4.3	odd	2
48.2.k.a.35.6	yes	12	12.11	even	2
192.2.k.a.47.4		12	1.1	even	1	trivial
192.2.k.a.47.6		12	3.2	odd	2	inner
192.2.k.a.143.4		12	48.11	even	4	inner
192.2.k.a.143.6		12	16.11	odd	4	inner
384.2.k.a.95.1		12	24.5	odd	2
384.2.k.a.95.3		12	8.5	even	2
384.2.k.a.287.1		12	16.3	odd	4
384.2.k.a.287.3		12	48.35	even	4
384.2.k.b.95.4		12	8.3	odd	2
384.2.k.b.95.6		12	24.11	even	2
384.2.k.b.287.4		12	48.29	odd	4
384.2.k.b.287.6		12	16.13	even	4

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:	\( N \)	\(=\)	\( 192 = 2^{6} \cdot 3 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	192.k (of order \(4\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.814141 - 1.52878i) q^{3} +(2.08397 + 2.08397i) q^{5} +1.14637 q^{7} +(-1.67435 - 2.48929i) q^{9} +O(q^{10})\)	\(q+(0.814141 - 1.52878i) q^{3} +(2.08397 + 2.08397i) q^{5} +1.14637 q^{7} +(-1.67435 - 2.48929i) q^{9} +(-1.67435 + 1.67435i) q^{11} +(0.146365 + 0.146365i) q^{13} +(4.88258 - 1.48929i) q^{15} -5.59722i q^{17} +(-1.48929 + 1.48929i) q^{19} +(0.933303 - 1.75254i) q^{21} -3.34870i q^{23} +3.68585i q^{25} +(-5.16874 + 0.533081i) q^{27} +(-3.51325 + 3.51325i) q^{29} +5.83221i q^{31} +(1.19656 + 3.92287i) q^{33} +(2.38899 + 2.38899i) q^{35} +(-4.83221 + 4.83221i) q^{37} +(0.342923 - 0.104599i) q^{39} +0.610042 q^{41} +(1.48929 + 1.48929i) q^{43} +(1.69831 - 8.67689i) q^{45} -6.41646 q^{47} -5.68585 q^{49} +(-8.55693 - 4.55693i) q^{51} +(0.164553 + 0.164553i) q^{53} -6.97858 q^{55} +(1.06431 + 3.48929i) q^{57} +(9.05051 - 9.05051i) q^{59} +(4.53948 + 4.53948i) q^{61} +(-1.91942 - 2.85363i) q^{63} +0.610042i q^{65} +(0.635654 - 0.635654i) q^{67} +(-5.11943 - 2.72631i) q^{69} +6.90659i q^{71} -7.07896i q^{73} +(5.63485 + 3.00080i) q^{75} +(-1.91942 + 1.91942i) q^{77} -9.83221i q^{79} +(-3.39312 + 8.33587i) q^{81} +(8.09081 + 8.09081i) q^{83} +(11.6644 - 11.6644i) q^{85} +(2.51071 + 8.23127i) q^{87} +0.490134 q^{89} +(0.167788 + 0.167788i) q^{91} +(8.91618 + 4.74824i) q^{93} -6.20726 q^{95} +12.3503 q^{97} +(6.97138 + 1.36449i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 2 q^{3} + 8 q^{7}+O(q^{10}) \) 12 * q + 2 * q^3 + 8 * q^7	\( 12 q + 2 q^{3} + 8 q^{7} - 4 q^{13} + 12 q^{19} - 8 q^{21} - 10 q^{27} - 4 q^{33} - 4 q^{37} - 20 q^{39} - 12 q^{43} - 12 q^{45} - 20 q^{49} - 24 q^{51} - 24 q^{55} + 12 q^{61} - 28 q^{67} + 4 q^{69} + 34 q^{75} - 4 q^{81} + 32 q^{85} + 60 q^{87} + 56 q^{91} + 28 q^{93} - 8 q^{97} + 52 q^{99}+O(q^{100}) \) 12 * q + 2 * q^3 + 8 * q^7 - 4 * q^13 + 12 * q^19 - 8 * q^21 - 10 * q^27 - 4 * q^33 - 4 * q^37 - 20 * q^39 - 12 * q^43 - 12 * q^45 - 20 * q^49 - 24 * q^51 - 24 * q^55 + 12 * q^61 - 28 * q^67 + 4 * q^69 + 34 * q^75 - 4 * q^81 + 32 * q^85 + 60 * q^87 + 56 * q^91 + 28 * q^93 - 8 * q^97 + 52 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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