LMFDB - Embedded newform 189.2.p.d.80.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [189,2,Mod(26,189)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(189, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 5]))

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

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

chi := DirichletCharacter("189.26");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 189 = 3^{3} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	189.p (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:	$1.50917259820$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$6$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 9x^{10} + 59x^{8} - 180x^{6} + 403x^{4} - 198x^{2} + 81 $ x^12 - 9x^10 + 59x^8 - 180x^6 + 403x^4 - 198*x^2 + 81
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 3^{4} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			80.1
Root			$0.617942 - 0.356769i$ of defining polynomial
Character	$\chi$	$=$	189.80
Dual form			189.2.p.d.26.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.15715 + 1.24543i) q^{2} +(2.10220 - 3.64112i) q^{4} +(-0.617942 - 1.07031i) q^{5} +(-1.53189 + 2.15715i) q^{7} +5.49086i q^{8} +O(q^{10})$	\(q+(-2.15715 + 1.24543i) q^{2} +(2.10220 - 3.64112i) q^{4} +(-0.617942 - 1.07031i) q^{5} +(-1.53189 + 2.15715i) q^{7} +5.49086i q^{8} +(2.66599 + 1.53921i) q^{10} +(4.75523 + 2.74543i) q^{11} +2.96793i q^{13} +(0.617942 - 6.56117i) q^{14} +(-2.63409 - 4.56239i) q^{16} +(-2.15715 + 3.73630i) q^{17} +(-4.80660 + 2.77509i) q^{19} -5.19615 q^{20} -13.6770 q^{22} +(-1.41290 + 0.815739i) q^{23} +(1.73630 - 3.00735i) q^{25} +(-3.69636 - 6.40228i) q^{26} +(4.63409 + 10.1126i) q^{28} +0.509136i q^{29} +(7.04290 + 4.06622i) q^{31} +(1.85383 + 1.07031i) q^{32} -10.7463i q^{34} +(3.25544 + 0.306602i) q^{35} +(1.53189 + 2.65332i) q^{37} +(6.91238 - 11.9726i) q^{38} +(5.87691 - 3.39304i) q^{40} +0.354034 q^{41} -0.0637877 q^{43} +(19.9929 - 11.5429i) q^{44} +(2.03189 - 3.51934i) q^{46} +(4.93224 + 8.54290i) q^{47} +(-2.30660 - 6.60905i) q^{49} +8.64975i q^{50} +(10.8066 + 6.23919i) q^{52} +(-3.57005 - 2.06117i) q^{53} -6.78607i q^{55} +(-11.8446 - 8.41142i) q^{56} +(-0.634095 - 1.09828i) q^{58} +(1.53921 - 2.66599i) q^{59} +(-5.97259 + 3.44828i) q^{61} -20.2568 q^{62} +5.20440 q^{64} +(3.17660 - 1.83401i) q^{65} +(6.16599 - 10.6798i) q^{67} +(9.06953 + 15.7089i) q^{68} +(-7.40432 + 3.39304i) q^{70} -4.63148i q^{71} +(-6.09568 - 3.51934i) q^{73} +(-6.60905 - 3.81574i) q^{74} +23.3352i q^{76} +(-13.2068 + 6.05203i) q^{77} +(0.165989 + 0.287501i) q^{79} +(-3.25544 + 5.63858i) q^{80} +(-0.763705 + 0.440925i) q^{82} +7.39272 q^{83} +5.33198 q^{85} +(0.137600 - 0.0794433i) q^{86} +(-15.0748 + 26.1103i) q^{88} +(-1.71623 - 2.97259i) q^{89} +(-6.40228 - 4.54656i) q^{91} +6.85939i q^{92} +(-21.2792 - 12.2855i) q^{94} +(5.94040 + 3.42969i) q^{95} -4.45644i q^{97} +(13.2068 + 11.3840i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + 8 q^{4} - 8 q^{7}+O(q^{10}) $ 12 * q + 8 * q^4 - 8 * q^7	$ 12 q + 8 q^{4} - 8 q^{7} - 6 q^{10} - 4 q^{16} - 6 q^{19} - 40 q^{22} - 24 q^{25} + 28 q^{28} - 12 q^{31} + 8 q^{37} + 12 q^{40} + 20 q^{43} + 14 q^{46} + 24 q^{49} + 78 q^{52} + 20 q^{58} + 18 q^{61} + 28 q^{64} + 36 q^{67} - 120 q^{70} - 42 q^{73} - 36 q^{79} - 54 q^{82} - 12 q^{85} - 74 q^{88} + 6 q^{91} - 114 q^{94}+O(q^{100}) $ 12 * q + 8 * q^4 - 8 * q^7 - 6 * q^10 - 4 * q^16 - 6 * q^19 - 40 * q^22 - 24 * q^25 + 28 * q^28 - 12 * q^31 + 8 * q^37 + 12 * q^40 + 20 * q^43 + 14 * q^46 + 24 * q^49 + 78 * q^52 + 20 * q^58 + 18 * q^61 + 28 * q^64 + 36 * q^67 - 120 * q^70 - 42 * q^73 - 36 * q^79 - 54 * q^82 - 12 * q^85 - 74 * q^88 + 6 * q^91 - 114 * q^94

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/189\mathbb{Z}\right)^\times$.

$n$	$29$	$136$
$\chi(n)$	$-1$	$e\left(\frac{1}{6}\right)$

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 $

$2$	−2.15715	+	1.24543i	−1.52534	+	0.880653i	−0.525787	+	0.850616i	$0.676229\pi$
$2$	−2.15715	+	1.24543i	−1.52534	+	0.880653i	−0.999549	+	0.0300373i	$0.990437\pi$
$3$		0			0
$3$		0			0
$4$	2.10220	−	3.64112i	1.05110	−	1.82056i
$5$	−0.617942	−	1.07031i	−0.276352	−	0.478656i	0.694123	−	0.719856i	$-0.255792\pi$
$5$	−0.617942	−	1.07031i	−0.276352	−	0.478656i	−0.970475	+	0.241200i	$0.922459\pi$
$6$		0			0
$7$	−1.53189	+	2.15715i	−0.579001	+	0.815327i
$7$	−1.53189	+	2.15715i	−0.579001	+	0.815327i
$8$			5.49086i			1.94131i
$9$		0			0
$10$	2.66599	+	1.53921i	0.843060	+	0.486741i
$11$	4.75523	+	2.74543i	1.43376	+	0.827779i	0.997405	−	0.0719981i	$-0.0229375\pi$
$11$	4.75523	+	2.74543i	1.43376	+	0.827779i	0.436350	+	0.899777i	$0.356271\pi$
$12$		0			0
$13$			2.96793i			0.823157i	0.911374	+	0.411578i	$0.135022\pi$
$13$			2.96793i			0.823157i	−0.911374	+	0.411578i	$0.864978\pi$
$14$	0.617942	−	6.56117i	0.165152	−	1.75355i
$15$		0			0
$16$	−2.63409	−	4.56239i	−0.658524	−	1.14060i
$17$	−2.15715	+	3.73630i	−0.523186	+	0.906185i	0.476450	+	0.879202i	$0.341923\pi$
$17$	−2.15715	+	3.73630i	−0.523186	+	0.906185i	−0.999636	+	0.0269831i	$0.991410\pi$
$18$		0			0
$19$	−4.80660	+	2.77509i	−1.10271	+	0.636650i	−0.936932	−	0.349513i	$-0.886347\pi$
$19$	−4.80660	+	2.77509i	−1.10271	+	0.636650i	−0.165779	+	0.986163i	$0.553014\pi$
$20$	−5.19615			−1.16190
$21$		0			0
$22$	−13.6770			−2.91594
$23$	−1.41290	+	0.815739i	−0.294610	+	0.170093i	−0.640019	−	0.768359i	$-0.721074\pi$
$23$	−1.41290	+	0.815739i	−0.294610	+	0.170093i	0.345409	+	0.938452i	$0.387740\pi$
$24$		0			0
$25$	1.73630	−	3.00735i	0.347259	−	0.601470i
$26$	−3.69636	−	6.40228i	−0.724916	−	1.25559i
$27$		0			0
$28$	4.63409	+	10.1126i	0.875762	+	1.91110i
$29$			0.509136i			0.0945443i	0.998882	+	0.0472721i	$0.0150528\pi$
$29$			0.509136i			0.0945443i	−0.998882	+	0.0472721i	$0.984947\pi$
$30$		0			0
$31$	7.04290	+	4.06622i	1.26494	+	0.730314i	0.974026	−	0.226434i	$-0.0727069\pi$
$31$	7.04290	+	4.06622i	1.26494	+	0.730314i	0.290915	+	0.956749i	$0.406040\pi$
$32$	1.85383	+	1.07031i	0.327713	+	0.189205i
$33$		0			0
$34$		−	10.7463i		−	1.84298i
$35$	3.25544	+	0.306602i	0.550269	+	0.0518253i
$36$		0			0
$37$	1.53189	+	2.65332i	0.251842	+	0.436203i	0.964033	−	0.265783i	$-0.0856304\pi$
$37$	1.53189	+	2.65332i	0.251842	+	0.436203i	−0.712191	+	0.701986i	$0.752297\pi$
$38$	6.91238	−	11.9726i	1.12134	−	1.94221i
$39$		0			0
$40$	5.87691	−	3.39304i	0.929221	−	0.536486i
$41$	0.354034			0.0552908			0.0276454	−	0.999618i	$-0.491199\pi$
$41$	0.354034			0.0552908			0.0276454	+	0.999618i	$0.491199\pi$
$42$		0			0
$43$	−0.0637877			−0.00972754			−0.00486377	−	0.999988i	$-0.501548\pi$
$43$	−0.0637877			−0.00972754			−0.00486377	+	0.999988i	$0.501548\pi$
$44$	19.9929	−	11.5429i	3.01404	−	1.74016i
$45$		0			0
$46$	2.03189	−	3.51934i	0.299586	−	0.518899i
$47$	4.93224	+	8.54290i	0.719442	+	1.24611i	0.961221	+	0.275778i	$0.0889356\pi$
$47$	4.93224	+	8.54290i	0.719442	+	1.24611i	−0.241779	+	0.970331i	$0.577731\pi$
$48$		0			0
$49$	−2.30660	−	6.60905i	−0.329515	−	0.944150i
$50$			8.64975i			1.22326i
$51$		0			0
$52$	10.8066	+	6.23919i	1.49861	+	0.865221i
$53$	−3.57005	−	2.06117i	−0.490384	−	0.283124i	0.234350	−	0.972152i	$-0.424704\pi$
$53$	−3.57005	−	2.06117i	−0.490384	−	0.283124i	−0.724734	+	0.689029i	$0.758037\pi$
$54$		0			0
$55$		−	6.78607i		−	0.915034i
$56$	−11.8446	−	8.41142i	−1.58280	−	1.12402i
$57$		0			0
$58$	−0.634095	−	1.09828i	−0.0832607	−	0.144212i
$59$	1.53921	−	2.66599i	0.200388	−	0.347082i	−0.748266	−	0.663399i	$-0.769113\pi$
$59$	1.53921	−	2.66599i	0.200388	−	0.347082i	0.948653	+	0.316317i	$0.102446\pi$
$60$		0			0
$61$	−5.97259	+	3.44828i	−0.764712	+	0.441507i	−0.830985	−	0.556295i	$-0.812222\pi$
$61$	−5.97259	+	3.44828i	−0.764712	+	0.441507i	0.0662730	+	0.997802i	$0.478889\pi$
$62$	−20.2568			−2.57262
$63$		0			0
$64$	5.20440			0.650550
$65$	3.17660	−	1.83401i	0.394009	−	0.227481i
$66$		0			0
$67$	6.16599	−	10.6798i	0.753295	−	1.30475i	−0.192922	−	0.981214i	$-0.561796\pi$
$67$	6.16599	−	10.6798i	0.753295	−	1.30475i	0.946217	−	0.323532i	$-0.104870\pi$
$68$	9.06953	+	15.7089i	1.09984	+	1.90498i
$69$		0			0
$70$	−7.40432	+	3.39304i	−0.884985	+	0.405545i
$71$		−	4.63148i		−	0.549655i	−0.961494	−	0.274828i	$-0.911379\pi$
$71$		−	4.63148i		−	0.549655i	0.961494	−	0.274828i	$-0.0886208\pi$
$72$		0			0
$73$	−6.09568	−	3.51934i	−0.713446	−	0.411908i	0.0988899	−	0.995098i	$-0.468471\pi$
$73$	−6.09568	−	3.51934i	−0.713446	−	0.411908i	−0.812336	+	0.583190i	$0.801804\pi$
$74$	−6.60905	−	3.81574i	−0.768287	−	0.443571i
$75$		0			0
$76$			23.3352i			2.67673i
$77$	−13.2068	+	6.05203i	−1.50506	+	0.689693i
$78$		0			0
$79$	0.165989	+	0.287501i	0.0186752	+	0.0323463i	0.875212	−	0.483740i	$-0.160722\pi$
$79$	0.165989	+	0.287501i	0.0186752	+	0.0323463i	−0.856537	+	0.516086i	$0.827388\pi$
$80$	−3.25544	+	5.63858i	−0.363969	+	0.630412i
$81$		0			0
$82$	−0.763705	+	0.440925i	−0.0843371	+	0.0486920i
$83$	7.39272			0.811457			0.405728	−	0.913994i	$-0.367018\pi$
$83$	7.39272			0.811457			0.405728	+	0.913994i	$0.367018\pi$
$84$		0			0
$85$	5.33198			0.578334
$86$	0.137600	−	0.0794433i	0.0148378	−	0.00856659i
$87$		0			0
$88$	−15.0748	+	26.1103i	−1.60698	+	2.78337i
$89$	−1.71623	−	2.97259i	−0.181920	−	0.315094i	0.760615	−	0.649204i	$-0.224898\pi$
$89$	−1.71623	−	2.97259i	−0.181920	−	0.315094i	−0.942534	+	0.334110i	$0.891564\pi$
$90$		0			0
$91$	−6.40228	−	4.54656i	−0.671142	−	0.476609i
$92$			6.85939i			0.715140i
$93$		0			0
$94$	−21.2792	−	12.2855i	−2.19478	−	1.26716i
$95$	5.94040	+	3.42969i	0.609472	+	0.351879i
$96$		0			0
$97$		−	4.45644i		−	0.452482i	−0.974071	−	0.226241i	$-0.927356\pi$
$97$		−	4.45644i		−	0.452482i	0.974071	−	0.226241i	$-0.0726438\pi$
$98$	13.2068	+	11.3840i	1.33409	+	1.14996i
$99$		0			0
$100$	−7.30008	−	12.6441i	−0.730008	−	1.26441i
$101$	−4.57821	+	7.92969i	−0.455549	+	0.789034i	−0.998720	−	0.0505884i	$-0.983890\pi$
$101$	−4.57821	+	7.92969i	−0.455549	+	0.789034i	0.543171	+	0.839622i	$0.317224\pi$
$102$		0			0
$103$	−3.64061	+	2.10191i	−0.358720	+	0.207107i	−0.668519	−	0.743695i	$-0.733072\pi$
$103$	−3.64061	+	2.10191i	−0.358720	+	0.207107i	0.309799	+	0.950802i	$0.399738\pi$
$104$	−16.2965			−1.59801
$105$		0			0
$106$	10.2682			0.997335
$107$	8.93193	−	5.15685i	0.863482	−	0.498532i	−0.00169460	−	0.999999i	$-0.500539\pi$
$107$	8.93193	−	5.15685i	0.863482	−	0.498532i	0.865177	+	0.501467i	$0.167206\pi$
$108$		0			0
$109$	−0.0637877	+	0.110484i	−0.00610976	+	0.0105824i	−0.869064	−	0.494699i	$-0.835278\pi$
$109$	−0.0637877	+	0.110484i	−0.00610976	+	0.0105824i	0.862954	+	0.505282i	$0.168611\pi$
$110$	8.45159	+	14.6386i	0.805827	+	1.39573i
$111$		0			0
$112$	13.8769	+	1.30695i	1.31124	+	0.123495i
$113$		−	2.29950i		−	0.216319i	−0.994134	−	0.108159i	$-0.965504\pi$
$113$		−	2.29950i		−	0.216319i	0.994134	−	0.108159i	$-0.0344957\pi$
$114$		0			0
$115$	1.74618	+	1.00816i	0.162832	+	0.0940113i
$116$	1.85383	+	1.07031i	0.172123	+	0.0993755i
$117$		0			0
$118$			7.66792i			0.705889i
$119$	−4.75523	−	10.3769i	−0.435911	−	0.951250i
$120$		0			0
$121$	9.57479	+	16.5840i	0.870436	+	1.50764i
$122$	8.58919	−	14.8769i	0.777629	−	1.34689i
$123$		0			0
$124$	29.6112	−	17.0960i	2.65916	−	1.53527i
$125$	−10.4711			−0.936567
$126$		0			0
$127$	−0.386795			−0.0343225			−0.0171613	−	0.999853i	$-0.505463\pi$
$127$	−0.386795			−0.0343225			−0.0171613	+	0.999853i	$0.505463\pi$
$128$	−14.9343	+	8.62234i	−1.32002	+	0.762114i
$129$		0			0
$130$	−4.56827	+	7.91248i	−0.400664	+	0.693970i
$131$	−10.4317	−	18.0683i	−0.911424	−	1.57863i	−0.812054	−	0.583582i	$-0.801651\pi$
$131$	−10.4317	−	18.0683i	−0.911424	−	1.57863i	−0.0993693	−	0.995051i	$-0.531683\pi$
$132$		0			0
$133$	1.37691	−	14.6197i	0.119393	−	1.26769i
$134$			30.7173i			2.65357i
$135$		0			0
$136$	−20.5155	−	11.8446i	−1.75919	−	1.01567i
$137$	−0.606650	−	0.350250i	−0.0518296	−	0.0299239i	0.473861	−	0.880600i	$-0.342860\pi$
$137$	−0.606650	−	0.350250i	−0.0518296	−	0.0299239i	−0.525691	+	0.850676i	$0.676193\pi$
$138$		0			0
$139$		−	11.5965i		−	0.983606i	−0.870707	−	0.491803i	$-0.836338\pi$
$139$		−	11.5965i		−	0.983606i	0.870707	−	0.491803i	$-0.163662\pi$
$140$	7.95995	−	11.2089i	0.672739	−	0.947324i
$141$		0			0
$142$	5.76819	+	9.99080i	0.484056	+	0.838409i
$143$	−8.14826	+	14.1132i	−0.681392	+	1.18021i
$144$		0			0
$145$	0.544932	−	0.314617i	0.0452542	−	0.0261275i
$146$	17.5324			1.45099
$147$		0			0
$148$	12.8814			1.05884
$149$	−0.303325	+	0.175125i	−0.0248494	+	0.0143468i	−0.512373	−	0.858763i	$-0.671234\pi$
$149$	−0.303325	+	0.175125i	−0.0248494	+	0.0143468i	0.487524	+	0.873110i	$0.337900\pi$
$150$		0			0
$151$	−2.32749	+	4.03133i	−0.189409	+	0.328065i	−0.945053	−	0.326916i	$-0.893990\pi$
$151$	−2.32749	+	4.03133i	−0.189409	+	0.328065i	0.755645	+	0.654982i	$0.227324\pi$
$152$	−15.2377	−	26.3924i	−1.23594	−	2.14071i
$153$		0			0
$154$	20.9517	−	29.5033i	1.68834	−	2.37745i
$155$		−	10.0507i		−	0.807296i
$156$		0			0
$157$	−1.07031	−	0.617942i	−0.0854198	−	0.0493171i	0.456682	−	0.889630i	$-0.349038\pi$
$157$	−1.07031	−	0.617942i	−0.0854198	−	0.0493171i	−0.542101	+	0.840313i	$0.682371\pi$
$158$	−0.716125	−	0.413455i	−0.0569718	−	0.0328927i
$159$		0			0
$160$		−	2.64555i		−	0.209149i
$161$	0.404743	−	4.29747i	0.0318982	−	0.338688i
$162$		0			0
$163$	9.80660	+	16.9855i	0.768112	+	1.33041i	0.938585	+	0.345047i	$0.112137\pi$
$163$	9.80660	+	16.9855i	0.768112	+	1.33041i	−0.170473	+	0.985362i	$0.554530\pi$
$164$	0.744250	−	1.28908i	0.0581162	−	0.100660i
$165$		0			0
$166$	−15.9472	+	9.20713i	−1.23774	+	0.714612i
$167$	23.6892			1.83313			0.916564	−	0.399887i	$-0.130951\pi$
$167$	23.6892			1.83313			0.916564	+	0.399887i	$0.130951\pi$
$168$		0			0
$169$	4.19136			0.322413
$170$	−11.5019	+	6.64061i	−0.882154	+	0.509312i
$171$		0			0
$172$	−0.134095	+	0.232259i	−0.0102246	+	0.0177096i
$173$	−5.99111	−	10.3769i	−0.455496	−	0.788942i	0.543221	−	0.839590i	$-0.317205\pi$
$173$	−5.99111	−	10.3769i	−0.455496	−	0.788942i	−0.998717	+	0.0506481i	$0.983871\pi$
$174$		0			0
$175$	3.82749	+	8.35240i	0.289331	+	0.631382i
$176$		−	28.9269i		−	2.18045i
$177$		0			0
$178$	7.40432	+	4.27489i	0.554977	+	0.320416i
$179$	19.3862	+	11.1926i	1.44900	+	0.836578i	0.998422	−	0.0561615i	$-0.0178862\pi$
$179$	19.3862	+	11.1926i	1.44900	+	0.836578i	0.450574	+	0.892739i	$0.351220\pi$
$180$		0			0
$181$			8.90380i			0.661815i	0.943663	+	0.330907i	$0.107355\pi$
$181$			8.90380i			0.661815i	−0.943663	+	0.330907i	$0.892645\pi$
$182$	19.4731	+	1.83401i	1.44344	+	0.135946i
$183$		0			0
$184$	−4.47911	−	7.75805i	−0.330204	−	0.571931i
$185$	1.89324	−	3.27919i	0.139194	−	0.241091i
$186$		0			0
$187$	−20.5155	+	11.8446i	−1.50024	+	0.866165i
$188$	41.4743			3.02482
$189$		0			0
$190$	−17.0858			−1.23953
$191$	−9.95138	+	5.74543i	−0.720057	+	0.415725i	−0.814774	−	0.579779i	$-0.803139\pi$
$191$	−9.95138	+	5.74543i	−0.720057	+	0.415725i	0.0947169	+	0.995504i	$0.469805\pi$
$192$		0			0
$193$	−5.51100	+	9.54534i	−0.396691	+	0.687089i	−0.993315	−	0.115432i	$-0.963175\pi$
$193$	−5.51100	+	9.54534i	−0.396691	+	0.687089i	0.596625	+	0.802520i	$0.296508\pi$
$194$	5.55019	+	9.61320i	0.398480	+	0.690188i
$195$		0			0
$196$	−28.9133	−	5.49494i	−2.06523	−	0.392496i
$197$		−	19.8228i		−	1.41232i	−0.708053	−	0.706159i	$-0.750426\pi$
$197$		−	19.8228i		−	1.41232i	0.708053	−	0.706159i	$-0.249574\pi$
$198$		0			0
$199$	−7.50000	−	4.33013i	−0.531661	−	0.306955i	0.210032	−	0.977695i	$-0.432643\pi$
$199$	−7.50000	−	4.33013i	−0.531661	−	0.306955i	−0.741693	+	0.670740i	$0.765977\pi$
$200$	16.5130	+	9.53376i	1.16764	+	0.674139i
$201$		0			0
$202$		−	22.8074i		−	1.60472i
$203$	−1.09828	−	0.779943i	−0.0770844	−	0.0547413i
$204$		0			0
$205$	−0.218772	−	0.378925i	−0.0152797	−	0.0264653i
$206$	5.23557	−	9.06827i	0.364779	−	0.631816i
$207$		0			0
$208$	13.5409	−	7.81782i	0.938890	−	0.542068i
$209$	−30.4753			−2.10802
$210$		0			0
$211$	22.1626			1.52574			0.762869	−	0.646553i	$-0.223790\pi$
$211$	22.1626			1.52574			0.762869	+	0.646553i	$0.223790\pi$
$212$	−15.0099	+	8.66599i	−1.03089	+	0.595183i
$213$		0			0
$214$	−12.8450	+	22.2482i	−0.878067	+	1.52086i
$215$	0.0394171	+	0.0682725i	0.00268823	+	0.00465614i
$216$		0			0
$217$	−19.5604	+	8.96358i	−1.32785	+	0.608487i
$218$		−	0.317773i		−	0.0215223i
$219$		0			0
$220$	−24.7089	−	14.2657i	−1.66587	−	0.961792i
$221$	−11.0891	−	6.40228i	−0.745932	−	0.430664i
$222$		0			0
$223$			18.7457i			1.25531i	0.778493	+	0.627653i	$0.215984\pi$
$223$			18.7457i			1.25531i	−0.778493	+	0.627653i	$0.784016\pi$
$224$	−5.14868	+	2.35939i	−0.344011	+	0.157643i
$225$		0			0
$226$	2.86387	+	4.96037i	0.190502	+	0.329959i
$227$	7.08940	−	12.2792i	0.470540	−	0.814999i	−0.528893	−	0.848689i	$-0.677393\pi$
$227$	7.08940	−	12.2792i	0.470540	−	0.814999i	0.999432	+	0.0336901i	$0.0107259\pi$
$228$		0			0
$229$	−3.52537	+	2.03538i	−0.232963	+	0.134501i	−0.611938	−	0.790905i	$-0.709610\pi$
$229$	−3.52537	+	2.03538i	−0.232963	+	0.134501i	0.378975	+	0.925407i	$0.376277\pi$
$230$	−5.02237			−0.331165
$231$		0			0
$232$	−2.79560			−0.183540
$233$	−6.03053	+	3.48173i	−0.395073	+	0.228096i	−0.684356	−	0.729148i	$-0.739917\pi$
$233$	−6.03053	+	3.48173i	−0.395073	+	0.228096i	0.289283	+	0.957244i	$0.406583\pi$
$234$		0			0
$235$	6.09568	−	10.5580i	0.397638	−	0.688730i
$236$	−6.47145	−	11.2089i	−0.421256	−	0.729636i
$237$		0			0
$238$	23.1815	+	16.4623i	1.50263	+	1.06709i
$239$			26.5401i			1.71674i	0.513033	+	0.858369i	$0.328522\pi$
$239$			26.5401i			1.71674i	−0.513033	+	0.858369i	$0.671478\pi$
$240$		0			0
$241$	11.7812	+	6.80189i	0.758896	+	0.438149i	0.828899	−	0.559398i	$-0.188968\pi$
$241$	11.7812	+	6.80189i	0.758896	+	0.438149i	−0.0700035	+	0.997547i	$0.522301\pi$
$242$	−41.3085	−	23.8495i	−2.65541	−	1.53310i
$243$		0			0
$244$			28.9959i			1.85627i
$245$	−5.64837	+	6.55278i	−0.360861	+	0.418642i
$246$		0			0
$247$	−8.23630	−	14.2657i	−0.524063	−	0.907704i
$248$	−22.3271	+	38.6716i	−1.41777	+	2.45565i
$249$		0			0
$250$	22.5878	−	13.0411i	1.42858	−	0.824791i
$251$	−2.55060			−0.160993			−0.0804963	−	0.996755i	$-0.525651\pi$
$251$	−2.55060			−0.160993			−0.0804963	+	0.996755i	$0.525651\pi$
$252$		0			0
$253$	−8.95822			−0.563198
$254$	0.834376	−	0.481727i	0.0523534	−	0.0302263i
$255$		0			0
$256$	16.2727	−	28.1851i	1.01704	−	1.76157i
$257$	9.03011	+	15.6406i	0.563283	+	0.975635i	0.997207	+	0.0746853i	$0.0237952\pi$
$257$	9.03011	+	15.6406i	0.563283	+	0.975635i	−0.433924	+	0.900949i	$0.642871\pi$
$258$		0			0
$259$	−8.07031	−	0.760075i	−0.501464	−	0.0472288i
$260$		−	15.4218i		−	0.956422i
$261$		0			0
$262$	45.0056	+	25.9840i	2.78046	+	1.60530i
$263$	6.98798	+	4.03451i	0.430897	+	0.248779i	0.699729	−	0.714409i	$-0.253304\pi$
$263$	6.98798	+	4.03451i	0.430897	+	0.248779i	−0.268832	+	0.963187i	$0.586638\pi$
$264$		0			0
$265$			5.09474i			0.312967i
$266$	15.2377	+	33.2518i	0.934281	+	2.03880i
$267$		0			0
$268$	−25.9243	−	44.9022i	−1.58358	−	2.74284i
$269$	−1.04758	+	1.81445i	−0.0638718	+	0.110629i	−0.896193	−	0.443664i	$-0.853678\pi$
$269$	−1.04758	+	1.81445i	−0.0638718	+	0.110629i	0.832321	+	0.554294i	$0.187012\pi$
$270$		0			0
$271$	21.3066	−	12.3014i	1.29428	−	0.747255i	0.314873	−	0.949134i	$-0.398038\pi$
$271$	21.3066	−	12.3014i	1.29428	−	0.747255i	0.979411	+	0.201879i	$0.0647046\pi$
$272$	22.7286			1.37812
$273$		0			0
$274$	1.74485			0.105410
$275$	16.5130	−	9.53376i	0.995769	−	0.574907i
$276$		0			0
$277$	10.8495	−	18.7919i	0.651883	−	1.12909i	−0.330782	−	0.943707i	$-0.607313\pi$
$277$	10.8495	−	18.7919i	0.651883	−	1.12909i	0.982665	−	0.185388i	$-0.0593541\pi$
$278$	14.4427	+	25.0155i	0.866216	+	1.50033i
$279$		0			0
$280$	−1.68351	+	17.8752i	−0.100609	+	1.06824i
$281$		−	22.6315i		−	1.35008i	−0.737781	−	0.675040i	$-0.764126\pi$
$281$		−	22.6315i		−	1.35008i	0.737781	−	0.675040i	$-0.235874\pi$
$282$		0			0
$283$	−8.26370	−	4.77105i	−0.491226	−	0.283610i	0.233857	−	0.972271i	$-0.424865\pi$
$283$	−8.26370	−	4.77105i	−0.491226	−	0.283610i	−0.725083	+	0.688661i	$0.758199\pi$
$284$	−16.8638	−	9.73630i	−1.00068	−	0.577743i
$285$		0			0
$286$		−	40.5924i		−	2.40028i
$287$	−0.542342	+	0.763705i	−0.0320135	+	0.0450801i
$288$		0			0
$289$	−0.806602	−	1.39708i	−0.0474472	−	0.0821810i
$290$	−0.783667	+	1.35735i	−0.0460185	+	0.0797064i
$291$		0			0
$292$	−25.6287	+	14.7967i	−1.49981	+	0.865913i
$293$	26.3348			1.53850			0.769248	−	0.638951i	$-0.220631\pi$
$293$	26.3348			1.53850			0.769248	+	0.638951i	$0.220631\pi$
$294$		0			0
$295$	−3.80457			−0.221511
$296$	−14.5690	+	8.41142i	−0.846806	+	0.488904i
$297$		0			0
$298$	0.436212	−	0.755542i	0.0252691	−	0.0437674i
$299$	−2.42106	−	4.19340i	−0.140013	−	0.242510i
$300$		0			0
$301$	0.0977161	−	0.137600i	0.00563226	−	0.00793112i
$302$		−	11.5949i		−	0.667213i
$303$		0			0
$304$	25.3221	+	14.6197i	1.45232	+	0.838498i
$305$	7.38143	+	4.26167i	0.422659	+	0.244023i
$306$		0			0
$307$		−	6.81772i		−	0.389108i	−0.980892	−	0.194554i	$-0.937674\pi$
$307$		−	6.81772i		−	0.389108i	0.980892	−	0.194554i	$-0.0623259\pi$
$308$	−5.72720	+	60.8102i	−0.326338	+	3.46498i
$309$		0			0
$310$	12.5175	+	21.6810i	0.710948	+	1.23140i
$311$	−13.4707	+	23.3320i	−0.763855	+	1.32304i	0.176995	+	0.984212i	$0.443362\pi$
$311$	−13.4707	+	23.3320i	−0.763855	+	1.32304i	−0.940850	+	0.338823i	$0.889971\pi$
$312$		0			0
$313$	20.0584	−	11.5807i	1.13377	−	0.654581i	0.188887	−	0.981999i	$-0.439512\pi$
$313$	20.0584	−	11.5807i	1.13377	−	0.654581i	0.944880	+	0.327418i	$0.106179\pi$
$314$	3.07842			0.173725
$315$		0			0
$316$	1.39576			0.0785179
$317$	21.7091	−	12.5338i	1.21931	−	0.703966i	0.254536	−	0.967063i	$-0.418077\pi$
$317$	21.7091	−	12.5338i	1.21931	−	0.703966i	0.964769	+	0.263097i	$0.0847440\pi$
$318$		0			0
$319$	−1.39780	+	2.42106i	−0.0782617	+	0.135553i
$320$	−3.21602	−	5.57031i	−0.179781	−	0.311390i
$321$		0			0
$322$	4.47911	+	9.77436i	0.249611	+	0.544704i
$323$		−	23.9452i		−	1.33235i
$324$		0			0
$325$	8.92562	+	5.15321i	0.495105	+	0.285849i
$326$	−42.3086	−	24.4269i	−2.34326	−	1.35288i
$327$		0			0
$328$			1.94395i			0.107337i
$329$	−25.9840	−	2.44722i	−1.43254	−	0.134919i
$330$		0			0
$331$	4.19788	+	7.27095i	0.230736	+	0.399647i	0.958025	−	0.286684i	$-0.0925531\pi$
$331$	4.19788	+	7.27095i	0.230736	+	0.399647i	−0.727289	+	0.686332i	$0.759220\pi$
$332$	15.5410	−	26.9178i	0.852922	−	1.47730i
$333$		0			0
$334$	−51.1013	+	29.5033i	−2.79614	+	1.61435i
$335$	−15.2409			−0.832699
$336$		0			0
$337$	−28.2902			−1.54107			−0.770533	−	0.637401i	$-0.780010\pi$
$337$	−28.2902			−1.54107			−0.770533	+	0.637401i	$0.780010\pi$
$338$	−9.04140	+	5.22006i	−0.491788	+	0.283934i
$339$		0			0
$340$	11.2089	−	19.4144i	0.607887	−	1.05289i
$341$	22.3271	+	38.6716i	1.20908	+	2.09418i
$342$		0			0
$343$	17.7902	+	5.14868i	0.960580	+	0.278003i
$344$		−	0.350250i		−	0.0188842i
$345$		0			0
$346$	25.8475	+	14.9230i	1.38957	+	0.802268i
$347$	8.62860	+	4.98173i	0.463208	+	0.267433i	0.713392	−	0.700765i	$-0.247158\pi$
$347$	8.62860	+	4.98173i	0.463208	+	0.267433i	−0.250184	+	0.968198i	$0.580491\pi$
$348$		0			0
$349$		−	22.4624i		−	1.20239i	−0.799104	−	0.601193i	$-0.794692\pi$
$349$		−	22.4624i		−	1.20239i	0.799104	−	0.601193i	$-0.205308\pi$
$350$	−18.6588	−	13.2505i	−0.997356	−	0.708269i
$351$		0			0
$352$	5.87691	+	10.1791i	0.313240	+	0.542548i
$353$	−16.0326	+	27.7693i	−0.853330	+	1.47801i	0.0248555	+	0.999691i	$0.492087\pi$
$353$	−16.0326	+	27.7693i	−0.853330	+	1.47801i	−0.878186	+	0.478320i	$0.841246\pi$
$354$		0			0
$355$	−4.95710	+	2.86198i	−0.263096	+	0.151898i
$356$	−14.4314			−0.764863
$357$		0			0
$358$	−55.7587			−2.94694
$359$	−10.2828	+	5.93680i	−0.542707	+	0.313332i	−0.746175	−	0.665749i	$-0.768112\pi$
$359$	−10.2828	+	5.93680i	−0.542707	+	0.313332i	0.203468	+	0.979082i	$0.434779\pi$
$360$		0			0
$361$	5.90228	−	10.2231i	0.310647	−	0.538056i
$362$	−11.0891	−	19.2069i	−0.582829	−	1.00949i
$363$		0			0
$364$	−30.0135	+	13.7537i	−1.57313	+	0.720889i
$365$			8.69900i			0.455326i
$366$		0			0
$367$	−11.7538	−	6.78607i	−0.613544	−	0.354230i	0.160807	−	0.986986i	$-0.448590\pi$
$367$	−11.7538	−	6.78607i	−0.613544	−	0.354230i	−0.774351	+	0.632756i	$0.781924\pi$
$368$	7.44343	+	4.29747i	0.388016	+	0.224021i
$369$		0			0
$370$			9.43162i			0.490327i
$371$	9.91520	−	4.54365i	0.514771	−	0.235894i
$372$		0			0
$373$	−15.0858	−	26.1294i	−0.781113	−	1.35293i	−0.931294	−	0.364269i	$-0.881319\pi$
$373$	−15.0858	−	26.1294i	−0.781113	−	1.35293i	0.150181	−	0.988659i	$-0.452014\pi$
$374$	29.5033	−	51.1013i	1.52558	−	2.64238i
$375$		0			0
$376$	−46.9079	+	27.0823i	−2.41909	+	1.39666i
$377$	−1.51108			−0.0778248
$378$		0			0
$379$	−12.6770			−0.651173			−0.325587	−	0.945512i	$-0.605562\pi$
$379$	−12.6770			−0.651173			−0.325587	+	0.945512i	$0.605562\pi$
$380$	24.9758	−	14.4198i	1.28123	−	0.739720i
$381$		0			0
$382$	14.3111	−	24.7875i	0.732219	−	1.26824i
$383$	−15.9932	−	27.7010i	−0.817214	−	1.41546i	−0.907727	−	0.419561i	$-0.862184\pi$
$383$	−15.9932	−	27.7010i	−0.817214	−	1.41546i	0.0905126	−	0.995895i	$-0.471149\pi$
$384$		0			0
$385$	14.6386	+	10.3955i	0.746051	+	0.529806i
$386$		−	27.4543i		−	1.39739i
$387$		0			0
$388$	−16.2264	−	9.36832i	−0.823771	−	0.475604i
$389$	6.56158	+	3.78833i	0.332685	+	0.192076i	0.657033	−	0.753862i	$-0.271811\pi$
$389$	6.56158	+	3.78833i	0.332685	+	0.192076i	−0.324347	+	0.945938i	$0.605145\pi$
$390$		0			0
$391$		−	7.03869i		−	0.355962i
$392$	36.2894	−	12.6652i	1.83289	−	0.639691i
$393$		0			0
$394$	24.6880	+	42.7609i	1.24376	+	2.15426i
$395$	0.205143	−	0.355317i	0.0103218	−	0.0178780i
$396$		0			0
$397$	−0.824125	+	0.475809i	−0.0413617	+	0.0238802i	−0.520538	−	0.853838i	$-0.674269\pi$
$397$	−0.824125	+	0.475809i	−0.0413617	+	0.0238802i	0.479177	+	0.877719i	$0.340935\pi$
$398$	21.5715			1.08128
$399$		0			0
$400$	−18.2943			−0.914713
$401$	18.2147	−	10.5162i	0.909597	−	0.525156i	0.0292953	−	0.999571i	$-0.490674\pi$
$401$	18.2147	−	10.5162i	0.909597	−	0.525156i	0.880301	+	0.474415i	$0.157340\pi$
$402$		0			0
$403$	−12.0683	+	20.9029i	−0.601163	+	1.04125i
$404$	19.2486	+	33.3396i	0.957655	+	1.65871i
$405$		0			0
$406$	3.34053	+	0.314617i	0.165788	+	0.0156142i
$407$			16.8228i			0.833877i
$408$		0			0
$409$	17.4472	+	10.0732i	0.862709	+	0.498085i	0.864919	−	0.501912i	$-0.167370\pi$
$409$	17.4472	+	10.0732i	0.862709	+	0.498085i	−0.00220932	+	0.999998i	$0.500703\pi$
$410$	0.943850	+	0.544932i	0.0466134	+	0.0269123i
$411$		0			0
$412$			17.6745i			0.870762i
$413$	3.39304	+	7.40432i	0.166960	+	0.364343i
$414$		0			0
$415$	−4.56827	−	7.91248i	−0.224248	−	0.388408i
$416$	−3.17660	+	5.50203i	−0.155746	+	0.269759i
$417$		0			0
$418$	65.7399	−	37.9549i	3.21544	−	1.85644i
$419$	9.58929			0.468467			0.234234	−	0.972180i	$-0.424742\pi$
$419$	9.58929			0.468467			0.234234	+	0.972180i	$0.424742\pi$
$420$		0			0
$421$	8.61320			0.419782			0.209891	−	0.977725i	$-0.432689\pi$
$421$	8.61320			0.419782			0.209891	+	0.977725i	$0.432689\pi$
$422$	−47.8081	+	27.6020i	−2.32726	+	1.34365i
$423$		0			0
$424$	11.3176	−	19.6027i	0.549632	−	0.951990i
$425$	7.49090	+	12.9746i	0.363362	+	0.629362i
$426$		0			0
$427$	1.71092	−	18.1662i	0.0827973	−	0.879123i
$428$		−	43.3630i		−	2.09603i
$429$		0			0
$430$	−0.170057	−	0.0981827i	−0.00820090	−	0.00473479i
$431$	9.99885	+	5.77284i	0.481628	+	0.278068i	0.721095	−	0.692837i	$-0.243639\pi$
$431$	9.99885	+	5.77284i	0.481628	+	0.278068i	−0.239467	+	0.970905i	$0.576973\pi$
$432$		0			0
$433$		−	22.8707i		−	1.09910i	−0.835462	−	0.549548i	$-0.814800\pi$
$433$		−	22.8707i		−	1.09910i	0.835462	−	0.549548i	$-0.185200\pi$
$434$	31.0313	−	43.6970i	1.48955	−	2.09752i
$435$		0			0
$436$	0.268189	+	0.464517i	0.0128439	+	0.0222464i
$437$	4.52750	−	7.84186i	0.216580	−	0.375127i
$438$		0			0
$439$	0.218772	−	0.126308i	0.0104414	−	0.00602837i	−0.494770	−	0.869024i	$-0.664748\pi$
$439$	0.218772	−	0.126308i	0.0104414	−	0.00602837i	0.505212	+	0.862995i	$0.331414\pi$
$440$	37.2614			1.77637
$441$		0			0
$442$	31.8944			1.51706
$443$	−18.8552	+	10.8860i	−0.895837	+	0.517212i	−0.875847	−	0.482589i	$-0.839697\pi$
$443$	−18.8552	+	10.8860i	−0.895837	+	0.517212i	−0.0199896	+	0.999800i	$0.506363\pi$
$444$		0			0
$445$	−2.12106	+	3.67378i	−0.100548	+	0.174154i
$446$	−23.3465	−	40.4373i	−1.10549	−	1.91476i
$447$		0			0
$448$	−7.97259	+	11.2267i	−0.376670	+	0.530411i
$449$			10.7904i			0.509229i	0.967043	+	0.254614i	$0.0819485\pi$
$449$			10.7904i			0.509229i	−0.967043	+	0.254614i	$0.918051\pi$
$450$		0			0
$451$	1.68351	+	0.971976i	0.0792735	+	0.0457686i
$452$	−8.37275	−	4.83401i	−0.393821	−	0.227373i
$453$		0			0
$454$			35.3174i			1.65753i
$455$	−0.909976	+	9.66192i	−0.0426603	+	0.452958i
$456$		0			0
$457$	−17.5110	−	30.3299i	−0.819130	−	1.41878i	−0.906324	−	0.422584i	$-0.861123\pi$
$457$	−17.5110	−	30.3299i	−0.819130	−	1.41878i	0.0871937	−	0.996191i	$-0.472210\pi$
$458$	5.06984	−	8.78123i	0.236898	−	0.410320i
$459$		0			0
$460$	7.34165	−	4.23870i	0.342306	−	0.197631i
$461$	32.9471			1.53450			0.767249	−	0.641349i	$-0.221625\pi$
$461$	32.9471			1.53450			0.767249	+	0.641349i	$0.221625\pi$
$462$		0			0
$463$	−5.22641			−0.242892			−0.121446	−	0.992598i	$-0.538753\pi$
$463$	−5.22641			−0.242892			−0.121446	+	0.992598i	$0.538753\pi$
$464$	2.32288	−	1.34111i	0.107837	−	0.0622596i
$465$		0			0
$466$	8.67251	−	15.0212i	0.401746	−	0.695845i
$467$	−10.8332	−	18.7637i	−0.501302	−	0.868281i	−0.999999	−	0.00150418i	$-0.999521\pi$
$467$	−10.8332	−	18.7637i	−0.501302	−	0.868281i	0.498697	−	0.866777i	$-0.333812\pi$
$468$		0			0
$469$	13.5923	+	29.6613i	0.627635	+	1.36963i
$470$			30.3670i			1.40073i
$471$		0			0
$472$	14.6386	+	8.45159i	0.673795	+	0.389016i
$473$	−0.303325	−	0.175125i	−0.0139469	−	0.00805225i
$474$		0			0
$475$			19.2735i			0.884330i
$476$	−47.7800	−	4.50000i	−2.18999	−	0.206257i
$477$		0			0
$478$	−33.0539	−	57.2510i	−1.51185	−	2.61860i
$479$	−11.2154	+	19.4256i	−0.512444	+	0.887579i	0.487452	+	0.873150i	$0.337927\pi$
$479$	−11.2154	+	19.4256i	−0.512444	+	0.887579i	−0.999896	+	0.0144295i	$0.995407\pi$
$480$		0			0
$481$	−7.87487	+	4.54656i	−0.359063	+	0.207305i
$482$	−33.8852			−1.54343
$483$		0			0
$484$	80.5125			3.65966
$485$	−4.76975	+	2.75382i	−0.216583	+	0.125044i
$486$		0			0
$487$	−11.0813	+	19.1934i	−0.502142	+	0.869736i	0.497855	+	0.867260i	$0.334121\pi$
$487$	−11.0813	+	19.1934i	−0.502142	+	0.869736i	−0.999997	+	0.00247528i	$0.999212\pi$
$488$	−18.9340	−	32.7947i	−0.857103	−	1.48455i
$489$		0			0
$490$	4.02334	−	21.1700i	0.181756	−	0.956363i
$491$			15.4543i			0.697444i	0.937226	+	0.348722i	$0.113384\pi$
$491$			15.4543i			0.697444i	−0.937226	+	0.348722i	$0.886616\pi$
$492$		0			0
$493$	−1.90228	−	1.09828i	−0.0856746	−	0.0494642i
$494$	35.5339	+	20.5155i	1.59874	+	0.923035i
$495$		0			0
$496$		−	42.8432i		−	1.92372i
$497$	9.99080	+	7.09493i	0.448148	+	0.318251i
$498$		0			0
$499$	0.672508	+	1.16482i	0.0301056	+	0.0521444i	0.880686	−	0.473701i	$-0.157082\pi$
$499$	0.672508	+	1.16482i	0.0301056	+	0.0521444i	−0.850580	+	0.525846i	$0.823749\pi$
$500$	−22.0124	+	38.1267i	−0.984426	+	1.70508i
$501$		0			0
$502$	5.50203	−	3.17660i	0.245568	−	0.141779i
$503$	−18.1391			−0.808781			−0.404390	−	0.914586i	$-0.632516\pi$
$503$	−18.1391			−0.808781			−0.404390	+	0.914586i	$0.632516\pi$
$504$		0			0
$505$	11.3163			0.503568
$506$	19.3242	−	11.1569i	0.859067	−	0.495983i
$507$		0			0
$508$	−0.813121	+	1.40837i	−0.0360764	+	0.0624862i
$509$	−14.0919	−	24.4079i	−0.624612	−	1.08186i	−0.988616	−	0.150463i	$-0.951924\pi$
$509$	−14.0919	−	24.4079i	−0.624612	−	1.08186i	0.364003	−	0.931398i	$-0.381410\pi$
$510$		0			0
$511$	16.9297	−	7.75805i	0.748926	−	0.343196i
$512$			46.5767i			2.05842i
$513$		0			0
$514$	−38.9586	−	22.4928i	−1.71839	−	0.992114i
$515$	4.49938	+	2.59772i	0.198266	+	0.114469i
$516$		0			0
$517$			54.1646i			2.38215i
$518$	18.3555	−	8.41142i	0.806494	−	0.369577i
$519$		0			0
$520$	10.0703	+	17.4423i	0.441612	+	0.764895i
$521$	17.0915	−	29.6033i	0.748792	−	1.29694i	−0.199611	−	0.979875i	$-0.563968\pi$
$521$	17.0915	−	29.6033i	0.748792	−	1.29694i	0.948402	−	0.317070i	$-0.102699\pi$
$522$		0			0
$523$	31.9157	−	18.4266i	1.39558	−	0.805737i	0.401652	−	0.915792i	$-0.368436\pi$
$523$	31.9157	−	18.4266i	1.39558	−	0.805737i	0.993925	+	0.110055i	$0.0351027\pi$
$524$	−87.7183			−3.83199
$525$		0			0
$526$	−20.0988			−0.876351
$527$	−30.3852	+	17.5429i	−1.32360	+	0.764181i
$528$		0			0
$529$	−10.1691	+	17.6135i	−0.442137	+	0.765803i
$530$	−6.34515	−	10.9901i	−0.275615	−	0.477380i
$531$		0			0
$532$	−50.3376	−	35.7471i	−2.18241	−	1.54983i
$533$			1.05075i			0.0455130i
$534$		0			0
$535$	−11.0388	−	6.37327i	−0.477250	−	0.275541i
$536$	58.6414	+	33.8566i	2.53292	+	1.46238i
$537$		0			0
$538$		−	5.21874i		−	0.224996i
$539$	7.17629	−	37.7602i	0.309105	−	1.62645i
$540$		0			0
$541$	19.2089	+	33.2708i	0.825855	+	1.43042i	0.901264	+	0.433269i	$0.142640\pi$
$541$	19.2089	+	33.2708i	0.825855	+	1.43042i	−0.0754099	+	0.997153i	$0.524027\pi$
$542$	−30.6410	+	53.0718i	−1.31615	+	2.27963i
$543$		0			0
$544$	−7.99797	+	4.61763i	−0.342910	+	0.197979i
$545$	0.157669			0.00675378
$546$		0			0
$547$	11.9959			0.512909			0.256454	−	0.966556i	$-0.417446\pi$
$547$	11.9959			0.512909			0.256454	+	0.966556i	$0.417446\pi$
$548$	−2.55060	+	1.47259i	−0.108956	+	0.0629060i
$549$		0			0
$550$	−23.7473	+	41.1315i	−1.01259	+	1.75385i
$551$	−1.41290	−	2.44722i	−0.0601916	−	0.104255i
$552$		0			0
$553$	−0.874459	−	0.0823580i	−0.0371858	−	0.00350222i
$554$			54.0492i			2.29633i
$555$		0			0
$556$	−42.2244	−	24.3783i	−1.79071	−	1.03387i
$557$	−7.53838	−	4.35228i	−0.319411	−	0.184412i	0.331719	−	0.943378i	$-0.392371\pi$
$557$	−7.53838	−	4.35228i	−0.319411	−	0.184412i	−0.651130	+	0.758966i	$0.725705\pi$
$558$		0			0
$559$		−	0.189318i		−	0.00800729i
$560$	−7.17629	−	15.6602i	−0.303253	−	0.661763i
$561$		0			0
$562$	28.1860	+	48.8195i	1.18895	+	2.05933i
$563$	11.7183	−	20.2967i	0.493868	−	0.855405i	−0.506107	−	0.862471i	$-0.668916\pi$
$563$	11.7183	−	20.2967i	0.493868	−	0.855405i	0.999975	+	0.00706612i	$0.00224924\pi$
$564$		0			0
$565$	−2.46117	+	1.42096i	−0.103542	+	0.0597801i
$566$	23.7681			0.999047
$567$		0			0
$568$	25.4308			1.06705
$569$	29.7165	−	17.1569i	1.24578	−	0.719253i	0.275517	−	0.961296i	$-0.411151\pi$
$569$	29.7165	−	17.1569i	1.24578	−	0.719253i	0.970265	+	0.242044i	$0.0778177\pi$
$570$		0			0
$571$	−10.7363	+	18.5958i	−0.449300	+	0.778210i	−0.998341	−	0.0575853i	$-0.981660\pi$
$571$	−10.7363	+	18.5958i	−0.449300	+	0.778210i	0.549041	+	0.835796i	$0.314993\pi$
$572$	34.2586	+	59.3376i	1.43242	+	2.48103i
$573$		0			0
$574$	0.218772	−	2.32288i	0.00913138	−	0.0969550i
$575$			5.66545i			0.236266i
$576$		0			0
$577$	−24.7850	−	14.3096i	−1.03181	−	0.595718i	−0.114310	−	0.993445i	$-0.536466\pi$
$577$	−24.7850	−	14.3096i	−1.03181	−	0.595718i	−0.917504	+	0.397727i	$0.869799\pi$
$578$	3.47993	+	2.00914i	0.144746	+	0.0835691i
$579$		0			0
$580$		−	2.64555i		−	0.109850i
$581$	−11.3249	+	15.9472i	−0.469835	+	0.661602i
$582$		0			0
$583$	−11.3176	−	19.6027i	−0.468727	−	0.811860i
$584$	19.3242	−	33.4706i	0.799643	−	1.38502i
$585$		0			0
$586$	−56.8081	+	32.7982i	−2.34672	+	1.35488i
$587$	18.5157			0.764224			0.382112	−	0.924116i	$-0.375197\pi$
$587$	18.5157			0.764224			0.382112	+	0.924116i	$0.375197\pi$
$588$		0			0
$589$	−45.1365			−1.85982
$590$	8.20703	−	4.73833i	0.337878	−	0.195074i
$591$		0			0
$592$	8.07031	−	13.9782i	0.331688	−	0.574500i
$593$	9.37285	+	16.2343i	0.384897	+	0.666661i	0.991755	−	0.128149i	$-0.0409036\pi$
$593$	9.37285	+	16.2343i	0.384897	+	0.666661i	−0.606858	+	0.794810i	$0.707570\pi$
$594$		0			0
$595$	−8.16802	+	11.5019i	−0.334856	+	0.471531i
$596$			1.47259i			0.0603197i
$597$		0			0
$598$	10.4452	+	6.03053i	0.427135	+	0.246607i
$599$	−22.4059	−	12.9360i	−0.915480	−	0.528552i	−0.0332896	−	0.999446i	$-0.510598\pi$
$599$	−22.4059	−	12.9360i	−0.915480	−	0.528552i	−0.882190	+	0.470893i	$0.843932\pi$
$600$		0			0
$601$			14.5735i			0.594467i	0.954805	+	0.297234i	$0.0960640\pi$
$601$			14.5735i			0.594467i	−0.954805	+	0.297234i	$0.903936\pi$
$602$	−0.0394171	+	0.418522i	−0.00160652	+	0.0170577i
$603$		0			0
$604$	9.78571	+	16.9494i	0.398175	+	0.689659i
$605$	11.8333	−	20.4959i	0.481093	−	0.833278i
$606$		0			0
$607$	19.2947	−	11.1398i	0.783147	−	0.452150i	−0.0543974	−	0.998519i	$-0.517324\pi$
$607$	19.2947	−	11.1398i	0.783147	−	0.452150i	0.837544	+	0.546369i	$0.183990\pi$
$608$	−11.8808			−0.481830
$609$		0			0
$610$	−21.2305			−0.859597
$611$	−25.3548	+	14.6386i	−1.02574	+	0.592214i
$612$		0			0
$613$	−12.6112	+	21.8432i	−0.509360	+	0.882238i	0.490581	+	0.871396i	$0.336785\pi$
$613$	−12.6112	+	21.8432i	−0.509360	+	0.882238i	−0.999941	+	0.0108424i	$0.996549\pi$
$614$	8.49100	+	14.7069i	0.342669	+	0.593520i
$615$		0			0
$616$	−33.2309	−	72.5168i	−1.33891	−	2.92179i
$617$			2.03655i			0.0819882i	0.999159	+	0.0409941i	$0.0130525\pi$
$617$			2.03655i			0.0819882i	−0.999159	+	0.0409941i	$0.986948\pi$
$618$		0			0
$619$	32.9099	+	19.0006i	1.32276	+	0.763697i	0.984168	−	0.177236i	$-0.0567157\pi$
$619$	32.9099	+	19.0006i	1.32276	+	0.763697i	0.338593	+	0.940933i	$0.390049\pi$
$620$	−36.5960	−	21.1287i	−1.46973	−	0.848549i
$621$		0			0
$622$		−	67.1075i		−	2.69076i
$623$	9.04140	+	0.851535i	0.362236	+	0.0341160i
$624$		0			0
$625$	−2.21092	−	3.82943i	−0.0884368	−	0.153177i
$626$	−28.8460	+	49.9627i	−1.15292	+	1.99691i
$627$		0			0
$628$	−4.50000	+	2.59808i	−0.179570	+	0.103675i
$629$	−13.2181			−0.527040
$630$		0			0
$631$	2.80457			0.111648			0.0558240	−	0.998441i	$-0.482221\pi$
$631$	2.80457			0.111648			0.0558240	+	0.998441i	$0.482221\pi$
$632$	−1.57863	+	0.911420i	−0.0627944	+	0.0362544i
$633$		0			0
$634$	−31.2199	+	54.0744i	−1.23990	+	2.14757i
$635$	0.239017	+	0.413990i	0.00948510	+	0.0164287i
$636$		0			0
$637$	19.6152	−	6.84585i	0.777184	−	0.271242i
$638$		−	6.96345i		−	0.275686i
$639$		0			0
$640$	18.4571	+	10.6562i	0.729581	+	0.421224i
$641$	1.62610	+	0.938829i	0.0642271	+	0.0370815i	0.531770	−	0.846889i	$-0.321527\pi$
$641$	1.62610	+	0.938829i	0.0642271	+	0.0370815i	−0.467543	+	0.883971i	$0.654861\pi$
$642$		0			0
$643$		−	14.5735i		−	0.574724i	−0.957822	−	0.287362i	$-0.907222\pi$
$643$		−	14.5735i		−	0.574724i	0.957822	−	0.287362i	$-0.0927783\pi$
$644$	−14.7967	−	10.5079i	−0.583073	−	0.414067i
$645$		0			0
$646$	29.8221	+	51.6534i	1.17333	+	2.03227i
$647$	−18.2292	+	31.5739i	−0.716663	+	1.24130i	0.245651	+	0.969358i	$0.420998\pi$
$647$	−18.2292	+	31.5739i	−0.716663	+	1.24130i	−0.962315	+	0.271939i	$0.912335\pi$
$648$		0			0
$649$	14.6386	−	8.45159i	0.574615	−	0.331754i
$650$	−25.6719			−1.00693
$651$		0			0
$652$	82.4618			3.22945
$653$	13.0524	−	7.53580i	0.510779	−	0.294898i	−0.222375	−	0.974961i	$-0.571381\pi$
$653$	13.0524	−	7.53580i	0.510779	−	0.294898i	0.733154	+	0.680063i	$0.238048\pi$
$654$		0			0
$655$	−12.8924	+	22.3303i	−0.503748	+	0.872517i
$656$	−0.932559	−	1.61524i	−0.0364103	−	0.0630645i
$657$		0			0
$658$	59.0992	−	27.0823i	2.30393	−	1.05578i
$659$		−	31.4670i		−	1.22578i	−0.790168	−	0.612891i	$-0.790007\pi$
$659$		−	31.4670i		−	1.22578i	0.790168	−	0.612891i	$-0.209993\pi$
$660$		0			0
$661$	−11.9099	−	6.87620i	−0.463242	−	0.267453i	0.250164	−	0.968203i	$-0.419515\pi$
$661$	−11.9099	−	6.87620i	−0.463242	−	0.267453i	−0.713407	+	0.700750i	$0.752849\pi$
$662$	−18.1109	−	10.4564i	−0.703901	−	0.406398i
$663$		0			0
$664$			40.5924i			1.57529i
$665$	−16.4984	+	7.56042i	−0.639782	+	0.293181i
$666$		0			0
$667$	−0.415322	−	0.719359i	−0.0160813	−	0.0278537i
$668$	49.7996	−	86.2554i	1.92680	−	3.33732i
$669$		0			0
$670$	32.8769	−	18.9815i	1.27015	−	0.733319i
$671$	−37.8680			−1.46188
$672$		0			0
$673$	11.7448			0.452731			0.226365	−	0.974042i	$-0.427316\pi$
$673$	11.7448			0.452731			0.226365	+	0.974042i	$0.427316\pi$
$674$	61.0262	−	35.2335i	2.35064	−	1.35714i
$675$		0			0
$676$	8.81109	−	15.2613i	0.338888	−	0.586971i
$677$	10.8726	+	18.8320i	0.417870	+	0.723772i	0.995725	−	0.0923676i	$-0.0294435\pi$
$677$	10.8726	+	18.8320i	0.417870	+	0.723772i	−0.577855	+	0.816139i	$0.696110\pi$
$678$		0			0
$679$	9.61320	+	6.82679i	0.368921	+	0.261988i
$680$			29.2772i			1.12273i
$681$		0			0
$682$	−96.3257	−	55.6136i	−3.68850	−	2.12956i
$683$	−11.1647	−	6.44593i	−0.427205	−	0.246647i	0.270950	−	0.962593i	$-0.412662\pi$
$683$	−11.1647	−	6.44593i	−0.427205	−	0.246647i	−0.698155	+	0.715947i	$0.745995\pi$
$684$		0			0
$685$			0.865736i			0.0330781i
$686$	−44.7885	+	11.0500i	−1.71003	+	0.421891i
$687$		0			0
$688$	0.168023	+	0.291024i	0.00640582	+	0.0110952i
$689$	6.11742	−	10.5957i	0.233055	−	0.403663i
$690$		0			0
$691$	−8.95303	+	5.16904i	−0.340589	+	0.196639i	−0.660533	−	0.750797i	$-0.729669\pi$
$691$	−8.95303	+	5.16904i	−0.340589	+	0.196639i	0.319943	+	0.947437i	$0.396336\pi$
$692$	−50.3781			−1.91509
$693$		0			0
$694$	−24.8176			−0.942063
$695$	−12.4119	+	7.16599i	−0.470809	+	0.271821i
$696$		0			0
$697$	−0.763705	+	1.32278i	−0.0289274	+	0.0501037i
$698$	27.9754	+	48.4549i	1.05889	+	1.83404i
$699$		0			0
$700$	38.4582	+	3.62206i	1.45358	+	0.136901i
$701$		−	41.2056i		−	1.55631i	−0.628071	−	0.778156i	$-0.716155\pi$
$701$		−	41.2056i		−	1.55631i	0.628071	−	0.778156i	$-0.283845\pi$
$702$		0			0
$703$	−14.7264	−	8.50230i	−0.555417	−	0.320670i
$704$	24.7481	+	14.2883i	0.932730	+	0.538512i
$705$		0			0
$706$		−	79.8701i		−	3.00595i
$707$	−10.0922	−	22.0233i	−0.379557	−	0.828273i
$708$		0			0
$709$	−14.3001	−	24.7685i	−0.537051	−	0.930199i	−0.999061	−	0.0433248i	$-0.986205\pi$
$709$	−14.3001	−	24.7685i	−0.537051	−	0.930199i	0.462010	−	0.886875i	$-0.347128\pi$
$710$	7.12881	−	12.3475i	0.267540	−	0.463392i
$711$		0			0
$712$	16.3221	−	9.42356i	0.611696	−	0.353163i
$713$	−13.2679			−0.496886
$714$		0			0
$715$	20.1406			0.753216
$716$	81.5075	−	47.0584i	3.04608	−	1.75865i
$717$		0			0
$718$	14.7877	−	25.6131i	0.551874	−	0.955873i
$719$	0.881850	+	1.52741i	0.0328875	+	0.0569627i	0.882001	−	0.471248i	$-0.156196\pi$
$719$	0.881850	+	1.52741i	0.0328875	+	0.0569627i	−0.849113	+	0.528211i	$0.822863\pi$
$720$		0			0
$721$	1.04290	−	11.0733i	0.0388395	−	0.412390i
$722$			29.4036i			1.09429i
$723$		0			0
$724$	32.4198	+	18.7176i	1.20487	+	0.695634i
$725$	1.53115	+	0.884011i	0.0568656	+	0.0328314i
$726$		0			0
$727$			20.0358i			0.743088i	0.928415	+	0.371544i	$0.121171\pi$
$727$			20.0358i			0.743088i	−0.928415	+	0.371544i	$0.878829\pi$
$728$	24.9645	−	35.1541i	0.925248	−	1.30290i
$729$		0			0
$730$	−10.8340	−	18.7651i	−0.400985	−	0.694526i
$731$	0.137600	−	0.238330i	0.00508931	−	0.00881495i
$732$		0			0
$733$	13.3574	−	7.71187i	0.493365	−	0.284844i	−0.232604	−	0.972571i	$-0.574725\pi$
$733$	13.3574	−	7.71187i	0.493365	−	0.284844i	0.725969	+	0.687727i	$0.241391\pi$
$734$	33.8064			1.24782
$735$		0			0
$736$	−3.49236			−0.128730
$737$	58.6414	−	33.8566i	2.16008	−	1.24712i
$738$		0			0
$739$	16.2284	−	28.1085i	0.596973	−	1.03399i	−0.396292	−	0.918124i	$-0.629703\pi$
$739$	16.2284	−	28.1085i	0.596973	−	1.03399i	0.993265	−	0.115863i	$-0.0369634\pi$
$740$	−7.95995	−	13.7870i	−0.292614	−	0.506822i
$741$		0			0
$742$	−15.7298	+	22.1500i	−0.577458	+	0.813153i
$743$		−	7.52184i		−	0.275950i	−0.990436	−	0.137975i	$-0.955941\pi$
$743$		−	7.52184i		−	0.275950i	0.990436	−	0.137975i	$-0.0440593\pi$
$744$		0			0
$745$	0.374875	+	0.216434i	0.0137343	+	0.00792953i
$746$	65.0847	+	37.5767i	2.38292	+	1.37578i
$747$		0			0
$748$			99.5991i			3.64170i
$749$	−2.55866	+	27.1673i	−0.0934914	+	0.992671i
$750$		0			0
$751$	−12.9232	−	22.3836i	−0.471573	−	0.816789i	0.527898	−	0.849308i	$-0.322980\pi$
$751$	−12.9232	−	22.3836i	−0.471573	−	0.816789i	−0.999471	+	0.0325190i	$0.989647\pi$
$752$	25.9840	−	45.0056i	0.947539	−	1.64119i
$753$		0			0
$754$	3.25964	−	1.88195i	0.118709	−	0.0685366i
$755$	5.75302			0.209374
$756$		0			0
$757$	33.5103			1.21795			0.608976	−	0.793188i	$-0.291580\pi$
$757$	33.5103			1.21795			0.608976	+	0.793188i	$0.291580\pi$
$758$	27.3462	−	15.7883i	0.993258	−	0.573458i
$759$		0			0
$760$	−18.8320	+	32.6179i	−0.683108	+	1.18318i
$761$	4.36501	+	7.56042i	0.158232	+	0.274065i	0.934231	−	0.356668i	$-0.116087\pi$
$761$	4.36501	+	7.56042i	0.158232	+	0.274065i	−0.775999	+	0.630734i	$0.782754\pi$
$762$		0			0
$763$	−0.140614	−	0.306849i	−0.00509056	−	0.0111087i
$764$			48.3122i			1.74787i
$765$		0			0
$766$	68.9995	+	39.8369i	2.49305	+	1.43936i
$767$	7.91248	+	4.56827i	0.285703	+	0.164951i
$768$		0			0
$769$		−	5.04495i		−	0.181926i	−0.995854	−	0.0909628i	$-0.971006\pi$
$769$		−	5.04495i		−	0.181926i	0.995854	−	0.0909628i	$-0.0289944\pi$
$770$	−44.5246	−	4.19340i	−1.60455	−	0.151120i
$771$		0			0
$772$	23.1705	+	40.1324i	0.833924	+	1.44440i
$773$	−2.90140	+	5.02537i	−0.104356	+	0.180750i	−0.913475	−	0.406895i	$-0.866612\pi$
$773$	−2.90140	+	5.02537i	−0.104356	+	0.180750i	0.809119	+	0.587645i	$0.199945\pi$
$774$		0			0
$775$	24.4571	−	14.1203i	0.878525	−	0.507217i
$776$	24.4697			0.878410
$777$		0			0
$778$	−18.8724			−0.676609
$779$	−1.70170	+	0.982477i	−0.0609697	+	0.0352009i
$780$		0			0
$781$	12.7154	−	22.0237i	0.454993	−	0.788071i
$782$	8.76620	+	15.1835i	0.313479	+	0.542961i
$783$		0			0
$784$	−24.0772	+	27.9325i	−0.859901	+	0.997589i
$785$			1.52741i			0.0545156i
$786$		0			0
$787$	−21.3944	−	12.3521i	−0.762629	−	0.440304i	0.0676098	−	0.997712i	$-0.478463\pi$
$787$	−21.3944	−	12.3521i	−0.762629	−	0.440304i	−0.830239	+	0.557408i	$0.811796\pi$
$788$	−72.1773	−	41.6716i	−2.57121	−	1.48449i
$789$		0			0
$790$			1.02196i			0.0363599i
$791$	4.96037	+	3.52259i	0.176370	+	0.125249i
$792$		0			0
$793$	−10.2343	−	17.7263i	−0.363429	−	0.629478i
$794$	1.18518	−	2.05278i	0.0420603	−	0.0728506i
$795$		0			0
$796$	−31.5330	+	18.2056i	−1.11766	+	0.645280i
$797$	4.39314			0.155613			0.0778064	−	0.996968i	$-0.475208\pi$
$797$	4.39314			0.155613			0.0778064	+	0.996968i	$0.475208\pi$
$798$		0			0
$799$	−42.5584			−1.50561
$800$	6.43758	−	3.71674i	0.227603	−	0.131407i
$801$		0			0
$802$	−26.1945	+	45.3702i	−0.924960	+	1.60208i
$803$	−19.3242	−	33.4706i	−0.681937	−	1.18115i
$804$		0			0
$805$	−4.84971	+	2.22239i	−0.170930	+	0.0783288i
$806$		−	60.1208i		−	2.11767i
$807$		0			0
$808$	−43.5409	−	25.1383i	−1.53176	−	0.884363i
$809$	−43.9347	−	25.3657i	−1.54466	−	0.891812i	−0.998535	−	0.0541105i	$-0.982768\pi$
$809$	−43.9347	−	25.3657i	−1.54466	−	0.891812i	−0.546129	−	0.837701i	$-0.683899\pi$
$810$		0			0
$811$			31.8126i			1.11709i	0.829474	+	0.558546i	$0.188641\pi$
$811$			31.8126i			1.11709i	−0.829474	+	0.558546i	$0.811359\pi$
$812$	−5.14868	+	2.35939i	−0.180683	+	0.0827982i
$813$		0			0
$814$	−20.9517	−	36.2894i	−0.734357	−	1.27194i
$815$	12.1198	−	20.9921i	0.424539	−	0.735323i
$816$		0			0
$817$	0.306602	−	0.177017i	0.0107267	−	0.00619304i
$818$	−50.1817			−1.75456
$819$		0			0
$820$	−1.83961			−0.0642421
$821$	−22.4679	+	12.9718i	−0.784135	+	0.452720i	−0.837894	−	0.545834i	$-0.816213\pi$
$821$	−22.4679	+	12.9718i	−0.784135	+	0.452720i	0.0537589	+	0.998554i	$0.482880\pi$
$822$		0			0
$823$	0.0703069	−	0.121775i	0.00245074	−	0.00424481i	−0.864797	−	0.502121i	$-0.832553\pi$
$823$	0.0703069	−	0.121775i	0.00245074	−	0.00424481i	0.867248	+	0.497876i	$0.165887\pi$
$824$	−11.5413	−	19.9901i	−0.402060	−	0.696389i
$825$		0			0
$826$	−16.5409	−	11.7464i	−0.575530	−	0.408711i
$827$			16.1772i			0.562535i	0.959629	+	0.281267i	$0.0907548\pi$
$827$			16.1772i			0.562535i	−0.959629	+	0.281267i	$0.909245\pi$
$828$		0			0
$829$	−28.8592	−	16.6619i	−1.00232	−	0.578690i	−0.0933864	−	0.995630i	$-0.529769\pi$
$829$	−28.8592	−	16.6619i	−1.00232	−	0.578690i	−0.908934	+	0.416940i	$0.863103\pi$
$830$	19.7089	+	11.3789i	0.684106	+	0.394969i
$831$		0			0
$832$			15.4463i			0.535505i
$833$	29.6691	+	5.63858i	1.02797	+	0.195365i
$834$		0			0
$835$	−14.6386	−	25.3548i	−0.506589	−	0.877438i
$836$	−64.0652	+	110.964i	−2.21574	+	3.83778i
$837$		0			0
$838$	−20.6855	+	11.9428i	−0.714570	+	0.412557i
$839$	−21.4701			−0.741230			−0.370615	−	0.928787i	$-0.620853\pi$
$839$	−21.4701			−0.741230			−0.370615	+	0.928787i	$0.620853\pi$
$840$		0			0
$841$	28.7408			0.991061
$842$	−18.5800	+	10.7272i	−0.640309	+	0.369682i
$843$		0			0
$844$	46.5903	−	80.6967i	1.60370	−	2.77770i
$845$	−2.59002	−	4.48605i	−0.0890994	−	0.154325i
$846$		0			0
$847$	−50.4418	−	4.75069i	−1.73320	−	0.163236i
$848$			21.7173i			0.745774i
$849$		0			0
$850$	−32.3180	−	18.6588i	−1.10850	−	0.639992i
$851$	−4.32883	−	2.49925i	−0.148390	−	0.0856732i
$852$		0			0
$853$		−	25.1842i		−	0.862291i	−0.902282	−	0.431146i	$-0.858110\pi$
$853$		−	25.1842i		−	0.862291i	0.902282	−	0.431146i	$-0.141890\pi$
$854$	18.9340	+	41.3180i	0.647909	+	1.41387i
$855$		0			0
$856$	28.3156	+	49.0440i	0.967806	+	1.67629i
$857$	14.5183	−	25.1464i	0.495936	−	0.858986i	−0.504053	−	0.863673i	$-0.668159\pi$
$857$	14.5183	−	25.1464i	0.495936	−	0.858986i	0.999989	+	0.00468678i	$0.00149185\pi$
$858$		0			0
$859$	−20.6386	+	11.9157i	−0.704179	+	0.406558i	−0.808902	−	0.587943i	$-0.799938\pi$
$859$	−20.6386	+	11.9157i	−0.704179	+	0.406558i	0.104723	+	0.994501i	$0.466604\pi$
$860$	0.331451			0.0113024
$861$		0			0
$862$	−28.7587			−0.979526
$863$	−27.6069	+	15.9388i	−0.939749	+	0.542564i	−0.889881	−	0.456192i	$-0.849213\pi$
$863$	−27.6069	+	15.9388i	−0.939749	+	0.542564i	−0.0498671	+	0.998756i	$0.515880\pi$
$864$		0			0
$865$	−7.40432	+	12.8247i	−0.251754	+	0.436051i
$866$	28.4839	+	49.3355i	0.967922	+	1.67649i
$867$		0			0
$868$	−8.48248	+	90.0651i	−0.287914	+	3.05701i
$869$			1.82284i			0.0618356i
$870$		0			0
$871$	31.6970	+	18.3003i	1.07401	+	0.620080i
$872$	−0.606650	−	0.350250i	−0.0205438	−	0.0118610i
$873$		0			0
$874$			22.5548i			0.762927i
$875$	16.0407	−	22.5878i	0.542274	−	0.763608i
$876$		0			0
$877$	1.14061	+	1.97560i	0.0385158	+	0.0667113i	0.884641	−	0.466273i	$-0.154404\pi$
$877$	1.14061	+	1.97560i	0.0385158	+	0.0667113i	−0.846125	+	0.532985i	$0.821070\pi$
$878$	−0.314617	+	0.544932i	−0.0106178	+	0.0183906i
$879$		0			0
$880$	−30.9607	+	17.8752i	−1.04368	+	0.602571i
$881$	11.8808			0.400275			0.200137	−	0.979768i	$-0.435861\pi$
$881$	11.8808			0.400275			0.200137	+	0.979768i	$0.435861\pi$
$882$		0			0
$883$	−49.7120			−1.67294			−0.836472	−	0.548010i	$-0.815385\pi$
$883$	−49.7120			−1.67294			−0.836472	+	0.548010i	$0.815385\pi$
$884$	−46.6229	+	26.9178i	−1.56810	+	0.905343i
$885$		0			0
$886$	27.1157	−	46.9657i	0.910968	−	1.57784i
$887$	−6.17942	−	10.7031i	−0.207485	−	0.359374i	0.743437	−	0.668806i	$-0.233194\pi$
$887$	−6.17942	−	10.7031i	−0.207485	−	0.359374i	−0.950922	+	0.309432i	$0.899861\pi$
$888$		0			0
$889$	0.592529	−	0.834376i	0.0198728	−	0.0279841i
$890$		−	10.5665i		−	0.354191i
$891$		0			0
$892$	68.2554	+	39.4072i	2.28536	+	1.31945i
$893$	−47.4147	−	27.3749i	−1.58667	−	0.916065i
$894$		0			0
$895$		−	27.6656i		−	0.924760i
$896$	4.27812	−	45.4241i	0.142922	−	1.51751i
$897$		0			0
$898$	−13.4387	−	23.2764i	−0.448454	−	0.776745i
$899$	−2.07026	+	3.58580i	−0.0690470	+	0.119593i
$900$		0			0
$901$	15.4023	−	8.89251i	0.513124	−	0.296253i
$902$	−4.84212			−0.161225
$903$		0			0
$904$	12.6262			0.419943
$905$	9.52980	−	5.50203i	0.316781	−	0.182894i
$906$		0			0
$907$	17.8814	−	30.9715i	0.593742	−	1.02839i	−0.399981	−	0.916523i	$-0.630983\pi$
$907$	17.8814	−	30.9715i	0.593742	−	1.02839i	0.993723	−	0.111868i	$-0.0356833\pi$
$908$	−29.8067	−	51.6267i	−0.989169	−	1.71329i
$909$		0			0
$910$	−10.0703	−	21.9755i	−0.333827	−	0.728482i
$911$			47.9228i			1.58775i	0.608078	+	0.793877i	$0.291941\pi$
$911$			47.9228i			1.58775i	−0.608078	+	0.793877i	$0.708059\pi$
$912$		0			0
$913$	35.1541	+	20.2962i	1.16343	+	0.671707i
$914$	75.5478	+	43.6175i	2.49890	+	1.44274i
$915$		0			0
$916$			17.1151i			0.565498i
$917$	54.9563	+	5.17587i	1.81482	+	0.170922i
$918$		0			0
$919$	17.2408	+	29.8619i	0.568721	+	0.985053i	0.996693	+	0.0812614i	$0.0258949\pi$
$919$	17.2408	+	29.8619i	0.568721	+	0.985053i	−0.427972	+	0.903792i	$0.640772\pi$
$920$	−5.53566	+	9.58804i	−0.182505	+	0.316108i
$921$		0			0
$922$	−71.0718	+	41.0333i	−2.34063	+	1.35136i
$923$	13.7459			0.452453
$924$		0			0
$925$	10.6393			0.349817
$926$	11.2742	−	6.50914i	0.370492	−	0.213903i
$927$		0			0
$928$	−0.544932	+	0.943850i	−0.0178883	+	0.0309834i
$929$	29.1774	+	50.5368i	0.957280	+	1.65806i	0.729061	+	0.684449i	$0.239957\pi$
$929$	29.1774	+	50.5368i	0.957280	+	1.65806i	0.228219	+	0.973610i	$0.426710\pi$
$930$		0			0
$931$	29.4277	+	25.3661i	0.964453	+	0.831339i
$932$			29.2772i			0.959005i
$933$		0			0
$934$	46.7378	+	26.9841i	1.52931	+	0.882947i
$935$	25.3548	+	14.6386i	0.829189	+	0.478733i
$936$		0			0
$937$		−	29.8596i		−	0.975471i	−0.872992	−	0.487735i	$-0.837823\pi$
$937$		−	29.8596i		−	0.975471i	0.872992	−	0.487735i	$-0.162177\pi$
$938$	−66.2618	−	47.0556i	−2.16352	−	1.53642i
$939$		0			0
$940$	−25.6287	−	44.3902i	−0.835916	−	1.44785i
$941$	−8.10885	+	14.0449i	−0.264341	+	0.457852i	−0.967391	−	0.253289i	$-0.918488\pi$
$941$	−8.10885	+	14.0449i	−0.264341	+	0.457852i	0.703050	+	0.711141i	$0.251821\pi$
$942$		0			0
$943$	−0.500215	+	0.288799i	−0.0162892	+	0.00940459i
$944$	−16.2177			−0.527841
$945$		0			0
$946$	0.872425			0.0283650
$947$	−24.4167	+	14.0970i	−0.793435	+	0.458090i	−0.841170	−	0.540770i	$-0.818133\pi$
$947$	−24.4167	+	14.0970i	−0.793435	+	0.458090i	0.0477355	+	0.998860i	$0.484800\pi$
$948$		0			0
$949$	10.4452	−	18.0916i	0.339065	−	0.587278i
$950$	−24.0039	−	41.5759i	−0.778788	−	1.34890i
$951$		0			0
$952$	56.9782	−	26.1103i	1.84667	−	0.846240i
$953$			56.3488i			1.82532i	0.408725	+	0.912658i	$0.365973\pi$
$953$			56.3488i			1.82532i	−0.408725	+	0.912658i	$0.634027\pi$
$954$		0			0
$955$	12.2988	+	7.10069i	0.397978	+	0.229773i
$956$	96.6357	+	55.7926i	3.12542	+	1.80446i
$957$		0			0
$958$		−	55.8720i		−	1.80514i
$959$	1.68487	−	0.772091i	0.0544072	−	0.0249321i
$960$		0			0
$961$	17.5683	+	30.4291i	0.566718	+	0.981585i
$962$	11.3249	−	19.6152i	0.365128	−	0.632421i
$963$		0			0
$964$	49.5330	−	28.5979i	1.59535	−	0.921076i
$965$	13.6219			0.438505
$966$		0			0
$967$	34.0310			1.09436			0.547181	−	0.837014i	$-0.315701\pi$
$967$	34.0310			1.09436			0.547181	+	0.837014i	$0.315701\pi$
$968$	−91.0606	+	52.5739i	−2.92680	+	1.68979i
$969$		0			0
$970$	6.85939	−	11.8808i	0.220242	−	0.381470i
$971$	−16.3472	−	28.3142i	−0.524608	−	0.908647i	−0.999589	−	0.0286515i	$-0.990879\pi$
$971$	−16.3472	−	28.3142i	−0.524608	−	0.908647i	0.474982	−	0.879996i	$-0.342455\pi$
$972$		0			0
$973$	25.0155	+	17.7647i	0.801960	+	0.569509i
$974$		−	55.2041i		−	1.76885i
$975$		0			0
$976$	31.4647	+	18.1662i	1.00716	+	0.581485i
$977$	21.3583	+	12.3312i	0.683313	+	0.394511i	0.801102	−	0.598528i	$-0.204247\pi$
$977$	21.3583	+	12.3312i	0.683313	+	0.394511i	−0.117789	+	0.993039i	$0.537581\pi$
$978$		0			0
$979$		−	18.8471i		−	0.602357i
$980$	11.9855	+	34.3416i	0.382861	+	1.09700i
$981$		0			0
$982$	−19.2473	−	33.3373i	−0.614206	−	1.06384i
$983$	8.89575	−	15.4079i	0.283730	−	0.491435i	−0.688570	−	0.725170i	$-0.741761\pi$
$983$	8.89575	−	15.4079i	0.283730	−	0.491435i	0.972300	+	0.233734i	$0.0750946\pi$
$984$		0			0
$985$	−21.2165	+	12.2494i	−0.676015	+	0.390297i
$986$	5.47135			0.174243
$987$		0			0
$988$	−69.2574			−2.20337
$989$	0.0901258	−	0.0520341i	0.00286583	−	0.00165459i
$990$		0			0
$991$	15.9517	−	27.6292i	0.506722	−	0.877669i	−0.493247	−	0.869889i	$-0.664190\pi$
$991$	15.9517	−	27.6292i	0.506722	−	0.877669i	0.999970	−	0.00777992i	$-0.00247645\pi$
$992$	8.70420	+	15.0761i	0.276359	+	0.478667i
$993$		0			0
$994$	−30.3879	−	2.86198i	−0.963846	−	0.0907766i
$995$			10.7031i			0.339310i
$996$		0			0
$997$	−33.7363	−	19.4777i	−1.06844	−	0.616864i	−0.140685	−	0.990054i	$-0.544930\pi$
$997$	−33.7363	−	19.4777i	−1.06844	−	0.616864i	−0.927755	+	0.373191i	$0.878264\pi$
$998$	−2.90140	−	1.67512i	−0.0918423	−	0.0530252i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	189.2.p.d.80.1	yes	12
3.2	odd	2	inner	189.2.p.d.80.6	yes	12
7.3	odd	6		1323.2.c.d.1322.1		12
7.4	even	3		1323.2.c.d.1322.2		12
7.5	odd	6	inner	189.2.p.d.26.6	yes	12
9.2	odd	6		567.2.s.f.458.1		12
9.4	even	3		567.2.i.f.269.1		12
9.5	odd	6		567.2.i.f.269.6		12
9.7	even	3		567.2.s.f.458.6		12
21.5	even	6	inner	189.2.p.d.26.1	✓	12
21.11	odd	6		1323.2.c.d.1322.11		12
21.17	even	6		1323.2.c.d.1322.12		12
63.5	even	6		567.2.s.f.26.6		12
63.40	odd	6		567.2.s.f.26.1		12
63.47	even	6		567.2.i.f.215.6		12
63.61	odd	6		567.2.i.f.215.1		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
189.2.p.d.26.1	✓	12	21.5	even	6	inner
189.2.p.d.26.6	yes	12	7.5	odd	6	inner
189.2.p.d.80.1	yes	12	1.1	even	1	trivial
189.2.p.d.80.6	yes	12	3.2	odd	2	inner
567.2.i.f.215.1		12	63.61	odd	6
567.2.i.f.215.6		12	63.47	even	6
567.2.i.f.269.1		12	9.4	even	3
567.2.i.f.269.6		12	9.5	odd	6
567.2.s.f.26.1		12	63.40	odd	6
567.2.s.f.26.6		12	63.5	even	6
567.2.s.f.458.1		12	9.2	odd	6
567.2.s.f.458.6		12	9.7	even	3
1323.2.c.d.1322.1		12	7.3	odd	6
1323.2.c.d.1322.2		12	7.4	even	3
1323.2.c.d.1322.11		12	21.11	odd	6
1323.2.c.d.1322.12		12	21.17	even	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 189 = 3^{3} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	189.p (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-2.15715 + 1.24543i) q^{2} +(2.10220 - 3.64112i) q^{4} +(-0.617942 - 1.07031i) q^{5} +(-1.53189 + 2.15715i) q^{7} +5.49086i q^{8} +O(q^{10})\)	\(q+(-2.15715 + 1.24543i) q^{2} +(2.10220 - 3.64112i) q^{4} +(-0.617942 - 1.07031i) q^{5} +(-1.53189 + 2.15715i) q^{7} +5.49086i q^{8} +(2.66599 + 1.53921i) q^{10} +(4.75523 + 2.74543i) q^{11} +2.96793i q^{13} +(0.617942 - 6.56117i) q^{14} +(-2.63409 - 4.56239i) q^{16} +(-2.15715 + 3.73630i) q^{17} +(-4.80660 + 2.77509i) q^{19} -5.19615 q^{20} -13.6770 q^{22} +(-1.41290 + 0.815739i) q^{23} +(1.73630 - 3.00735i) q^{25} +(-3.69636 - 6.40228i) q^{26} +(4.63409 + 10.1126i) q^{28} +0.509136i q^{29} +(7.04290 + 4.06622i) q^{31} +(1.85383 + 1.07031i) q^{32} -10.7463i q^{34} +(3.25544 + 0.306602i) q^{35} +(1.53189 + 2.65332i) q^{37} +(6.91238 - 11.9726i) q^{38} +(5.87691 - 3.39304i) q^{40} +0.354034 q^{41} -0.0637877 q^{43} +(19.9929 - 11.5429i) q^{44} +(2.03189 - 3.51934i) q^{46} +(4.93224 + 8.54290i) q^{47} +(-2.30660 - 6.60905i) q^{49} +8.64975i q^{50} +(10.8066 + 6.23919i) q^{52} +(-3.57005 - 2.06117i) q^{53} -6.78607i q^{55} +(-11.8446 - 8.41142i) q^{56} +(-0.634095 - 1.09828i) q^{58} +(1.53921 - 2.66599i) q^{59} +(-5.97259 + 3.44828i) q^{61} -20.2568 q^{62} +5.20440 q^{64} +(3.17660 - 1.83401i) q^{65} +(6.16599 - 10.6798i) q^{67} +(9.06953 + 15.7089i) q^{68} +(-7.40432 + 3.39304i) q^{70} -4.63148i q^{71} +(-6.09568 - 3.51934i) q^{73} +(-6.60905 - 3.81574i) q^{74} +23.3352i q^{76} +(-13.2068 + 6.05203i) q^{77} +(0.165989 + 0.287501i) q^{79} +(-3.25544 + 5.63858i) q^{80} +(-0.763705 + 0.440925i) q^{82} +7.39272 q^{83} +5.33198 q^{85} +(0.137600 - 0.0794433i) q^{86} +(-15.0748 + 26.1103i) q^{88} +(-1.71623 - 2.97259i) q^{89} +(-6.40228 - 4.54656i) q^{91} +6.85939i q^{92} +(-21.2792 - 12.2855i) q^{94} +(5.94040 + 3.42969i) q^{95} -4.45644i q^{97} +(13.2068 + 11.3840i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 8 q^{4} - 8 q^{7}+O(q^{10}) \) 12 * q + 8 * q^4 - 8 * q^7	\( 12 q + 8 q^{4} - 8 q^{7} - 6 q^{10} - 4 q^{16} - 6 q^{19} - 40 q^{22} - 24 q^{25} + 28 q^{28} - 12 q^{31} + 8 q^{37} + 12 q^{40} + 20 q^{43} + 14 q^{46} + 24 q^{49} + 78 q^{52} + 20 q^{58} + 18 q^{61} + 28 q^{64} + 36 q^{67} - 120 q^{70} - 42 q^{73} - 36 q^{79} - 54 q^{82} - 12 q^{85} - 74 q^{88} + 6 q^{91} - 114 q^{94}+O(q^{100}) \) 12 * q + 8 * q^4 - 8 * q^7 - 6 * q^10 - 4 * q^16 - 6 * q^19 - 40 * q^22 - 24 * q^25 + 28 * q^28 - 12 * q^31 + 8 * q^37 + 12 * q^40 + 20 * q^43 + 14 * q^46 + 24 * q^49 + 78 * q^52 + 20 * q^58 + 18 * q^61 + 28 * q^64 + 36 * q^67 - 120 * q^70 - 42 * q^73 - 36 * q^79 - 54 * q^82 - 12 * q^85 - 74 * q^88 + 6 * q^91 - 114 * q^94

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