LMFDB - Embedded newform 966.2.h.a.827.11

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [966,2,Mod(827,966)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(966, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([1, 0, 1]))

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

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

chi := DirichletCharacter("966.827");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 966 = 2 \cdot 3 \cdot 7 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	966.h (of order $2$, degree $1$, 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:	$7.71354883526$
Analytic rank:	$0$
Dimension:	$24$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			827.11
Character	$\chi$	$=$	966.827
Dual form			966.2.h.a.827.23

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000i q^{2} +(1.59575 + 0.673481i) q^{3} -1.00000 q^{4} +2.44752 q^{5} +(0.673481 - 1.59575i) q^{6} +1.00000i q^{7} +1.00000i q^{8} +(2.09285 + 2.14942i) q^{9} +O(q^{10})$	\(q-1.00000i q^{2} +(1.59575 + 0.673481i) q^{3} -1.00000 q^{4} +2.44752 q^{5} +(0.673481 - 1.59575i) q^{6} +1.00000i q^{7} +1.00000i q^{8} +(2.09285 + 2.14942i) q^{9} -2.44752i q^{10} -1.24636 q^{11} +(-1.59575 - 0.673481i) q^{12} +4.09869 q^{13} +1.00000 q^{14} +(3.90563 + 1.64836i) q^{15} +1.00000 q^{16} -0.678121 q^{17} +(2.14942 - 2.09285i) q^{18} +1.06726i q^{19} -2.44752 q^{20} +(-0.673481 + 1.59575i) q^{21} +1.24636i q^{22} +(-4.68817 + 1.01050i) q^{23} +(-0.673481 + 1.59575i) q^{24} +0.990347 q^{25} -4.09869i q^{26} +(1.89207 + 4.83943i) q^{27} -1.00000i q^{28} -0.121891i q^{29} +(1.64836 - 3.90563i) q^{30} +9.43198 q^{31} -1.00000i q^{32} +(-1.98889 - 0.839401i) q^{33} +0.678121i q^{34} +2.44752i q^{35} +(-2.09285 - 2.14942i) q^{36} -4.01789i q^{37} +1.06726 q^{38} +(6.54050 + 2.76039i) q^{39} +2.44752i q^{40} -6.95722i q^{41} +(1.59575 + 0.673481i) q^{42} +10.8525i q^{43} +1.24636 q^{44} +(5.12228 + 5.26074i) q^{45} +(1.01050 + 4.68817i) q^{46} -6.85977i q^{47} +(1.59575 + 0.673481i) q^{48} -1.00000 q^{49} -0.990347i q^{50} +(-1.08211 - 0.456701i) q^{51} -4.09869 q^{52} -10.1388 q^{53} +(4.83943 - 1.89207i) q^{54} -3.05050 q^{55} -1.00000 q^{56} +(-0.718778 + 1.70308i) q^{57} -0.121891 q^{58} +4.05242i q^{59} +(-3.90563 - 1.64836i) q^{60} -7.68567i q^{61} -9.43198i q^{62} +(-2.14942 + 2.09285i) q^{63} -1.00000 q^{64} +10.0316 q^{65} +(-0.839401 + 1.98889i) q^{66} -7.06957i q^{67} +0.678121 q^{68} +(-8.16170 - 1.54489i) q^{69} +2.44752 q^{70} +5.06078i q^{71} +(-2.14942 + 2.09285i) q^{72} +2.93708 q^{73} -4.01789 q^{74} +(1.58035 + 0.666980i) q^{75} -1.06726i q^{76} -1.24636i q^{77} +(2.76039 - 6.54050i) q^{78} +2.85953i q^{79} +2.44752 q^{80} +(-0.239981 + 8.99680i) q^{81} -6.95722 q^{82} +3.55124 q^{83} +(0.673481 - 1.59575i) q^{84} -1.65971 q^{85} +10.8525 q^{86} +(0.0820912 - 0.194508i) q^{87} -1.24636i q^{88} -1.72988 q^{89} +(5.26074 - 5.12228i) q^{90} +4.09869i q^{91} +(4.68817 - 1.01050i) q^{92} +(15.0511 + 6.35225i) q^{93} -6.85977 q^{94} +2.61213i q^{95} +(0.673481 - 1.59575i) q^{96} -3.78055i q^{97} +1.00000i q^{98} +(-2.60845 - 2.67895i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q + 4 q^{3} - 24 q^{4} - 4 q^{5} - 4 q^{9}+O(q^{10}) $ 24 * q + 4 * q^3 - 24 * q^4 - 4 * q^5 - 4 * q^9	$ 24 q + 4 q^{3} - 24 q^{4} - 4 q^{5} - 4 q^{9} - 4 q^{12} + 8 q^{13} + 24 q^{14} - 4 q^{15} + 24 q^{16} + 32 q^{17} + 4 q^{18} + 4 q^{20} - 8 q^{23} - 12 q^{25} + 16 q^{27} - 4 q^{30} - 16 q^{31} + 20 q^{33} + 4 q^{36} - 8 q^{39} + 4 q^{42} + 24 q^{45} - 4 q^{46} + 4 q^{48} - 24 q^{49} + 24 q^{51} - 8 q^{52} + 24 q^{53} - 12 q^{54} + 16 q^{55} - 24 q^{56} + 4 q^{57} + 4 q^{58} + 4 q^{60} - 4 q^{63} - 24 q^{64} - 12 q^{66} - 32 q^{68} - 24 q^{69} - 4 q^{70} - 4 q^{72} - 32 q^{73} - 16 q^{74} + 48 q^{75} + 12 q^{78} - 4 q^{80} - 8 q^{81} - 8 q^{82} + 16 q^{83} - 16 q^{85} + 16 q^{86} + 20 q^{87} + 24 q^{89} - 28 q^{90} + 8 q^{92} + 16 q^{93} + 8 q^{94} - 48 q^{99}+O(q^{100}) $ 24 * q + 4 * q^3 - 24 * q^4 - 4 * q^5 - 4 * q^9 - 4 * q^12 + 8 * q^13 + 24 * q^14 - 4 * q^15 + 24 * q^16 + 32 * q^17 + 4 * q^18 + 4 * q^20 - 8 * q^23 - 12 * q^25 + 16 * q^27 - 4 * q^30 - 16 * q^31 + 20 * q^33 + 4 * q^36 - 8 * q^39 + 4 * q^42 + 24 * q^45 - 4 * q^46 + 4 * q^48 - 24 * q^49 + 24 * q^51 - 8 * q^52 + 24 * q^53 - 12 * q^54 + 16 * q^55 - 24 * q^56 + 4 * q^57 + 4 * q^58 + 4 * q^60 - 4 * q^63 - 24 * q^64 - 12 * q^66 - 32 * q^68 - 24 * q^69 - 4 * q^70 - 4 * q^72 - 32 * q^73 - 16 * q^74 + 48 * q^75 + 12 * q^78 - 4 * q^80 - 8 * q^81 - 8 * q^82 + 16 * q^83 - 16 * q^85 + 16 * q^86 + 20 * q^87 + 24 * q^89 - 28 * q^90 + 8 * q^92 + 16 * q^93 + 8 * q^94 - 48 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/966\mathbb{Z}\right)^\times$.

$n$	$323$	$829$	$925$
$\chi(n)$	$-1$	$1$	$-1$

Coefficient data

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

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

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

$2$		−	1.00000i		−	0.707107i
$2$		−	1.00000i		−	0.707107i
$3$	1.59575	+	0.673481i	0.921308	+	0.388834i
$3$	1.59575	+	0.673481i	0.921308	+	0.388834i
$4$	−1.00000			−0.500000
$5$	2.44752			1.09456			0.547282	−	0.836948i	$-0.315663\pi$
$5$	2.44752			1.09456			0.547282	+	0.836948i	$0.315663\pi$
$6$	0.673481	−	1.59575i	0.274947	−	0.651463i
$7$			1.00000i			0.377964i
$7$			1.00000i			0.377964i
$8$			1.00000i			0.353553i
$9$	2.09285	+	2.14942i	0.697616	+	0.716472i
$10$		−	2.44752i		−	0.773973i
$11$	−1.24636			−0.375792			−0.187896	−	0.982189i	$-0.560167\pi$
$11$	−1.24636			−0.375792			−0.187896	+	0.982189i	$0.560167\pi$
$12$	−1.59575	−	0.673481i	−0.460654	−	0.194417i
$13$	4.09869			1.13677			0.568386	−	0.822762i	$-0.307568\pi$
$13$	4.09869			1.13677			0.568386	+	0.822762i	$0.307568\pi$
$14$	1.00000			0.267261
$15$	3.90563	+	1.64836i	1.00843	+	0.425604i
$16$	1.00000			0.250000
$17$	−0.678121			−0.164468			−0.0822342	−	0.996613i	$-0.526206\pi$
$17$	−0.678121			−0.164468			−0.0822342	+	0.996613i	$0.526206\pi$
$18$	2.14942	−	2.09285i	0.506622	−	0.493289i
$19$			1.06726i			0.244846i	0.992478	+	0.122423i	$0.0390664\pi$
$19$			1.06726i			0.244846i	−0.992478	+	0.122423i	$0.960934\pi$
$20$	−2.44752			−0.547282
$21$	−0.673481	+	1.59575i	−0.146966	+	0.348222i
$22$			1.24636i			0.265725i
$23$	−4.68817	+	1.01050i	−0.977550	+	0.210703i
$23$	−4.68817	+	1.01050i	−0.977550	+	0.210703i
$24$	−0.673481	+	1.59575i	−0.137474	+	0.325731i
$25$	0.990347			0.198069
$26$		−	4.09869i		−	0.803820i
$27$	1.89207	+	4.83943i	0.364130	+	0.931348i
$28$		−	1.00000i		−	0.188982i
$29$		−	0.121891i		−	0.0226346i	−0.999936	−	0.0113173i	$-0.996398\pi$
$29$		−	0.121891i		−	0.0226346i	0.999936	−	0.0113173i	$-0.00360248\pi$
$30$	1.64836	−	3.90563i	0.300947	−	0.713068i
$31$	9.43198			1.69403			0.847016	−	0.531567i	$-0.178397\pi$
$31$	9.43198			1.69403			0.847016	+	0.531567i	$0.178397\pi$
$32$		−	1.00000i		−	0.176777i
$33$	−1.98889	−	0.839401i	−0.346220	−	0.146121i
$34$			0.678121i			0.116297i
$35$			2.44752i			0.413706i
$36$	−2.09285	−	2.14942i	−0.348808	−	0.358236i
$37$		−	4.01789i		−	0.660536i	−0.943887	−	0.330268i	$-0.892861\pi$
$37$		−	4.01789i		−	0.660536i	0.943887	−	0.330268i	$-0.107139\pi$
$38$	1.06726			0.173132
$39$	6.54050	+	2.76039i	1.04732	+	0.442016i
$40$			2.44752i			0.386987i
$41$		−	6.95722i		−	1.08653i	−0.839560	−	0.543267i	$-0.817187\pi$
$41$		−	6.95722i		−	1.08653i	0.839560	−	0.543267i	$-0.182813\pi$
$42$	1.59575	+	0.673481i	0.246230	+	0.103920i
$43$			10.8525i			1.65499i	0.561476	+	0.827493i	$0.310234\pi$
$43$			10.8525i			1.65499i	−0.561476	+	0.827493i	$0.689766\pi$
$44$	1.24636			0.187896
$45$	5.12228	+	5.26074i	0.763585	+	0.784224i
$46$	1.01050	+	4.68817i	0.148989	+	0.691232i
$47$		−	6.85977i		−	1.00060i	−0.865852	−	0.500300i	$-0.833223\pi$
$47$		−	6.85977i		−	1.00060i	0.865852	−	0.500300i	$-0.166777\pi$
$48$	1.59575	+	0.673481i	0.230327	+	0.0972086i
$49$	−1.00000			−0.142857
$50$		−	0.990347i		−	0.140056i
$51$	−1.08211	−	0.456701i	−0.151526	−	0.0639510i
$52$	−4.09869			−0.568386
$53$	−10.1388			−1.39268			−0.696338	−	0.717714i	$-0.745189\pi$
$53$	−10.1388			−1.39268			−0.696338	+	0.717714i	$0.745189\pi$
$54$	4.83943	−	1.89207i	0.658563	−	0.257479i
$55$	−3.05050			−0.411329
$56$	−1.00000			−0.133631
$57$	−0.718778	+	1.70308i	−0.0952045	+	0.225578i
$58$	−0.121891			−0.0160051
$59$			4.05242i			0.527580i	0.964580	+	0.263790i	$0.0849726\pi$
$59$			4.05242i			0.527580i	−0.964580	+	0.263790i	$0.915027\pi$
$60$	−3.90563	−	1.64836i	−0.504215	−	0.212802i
$61$		−	7.68567i		−	0.984050i	−0.870581	−	0.492025i	$-0.836257\pi$
$61$		−	7.68567i		−	0.984050i	0.870581	−	0.492025i	$-0.163743\pi$
$62$		−	9.43198i		−	1.19786i
$63$	−2.14942	+	2.09285i	−0.270801	+	0.263674i
$64$	−1.00000			−0.125000
$65$	10.0316			1.24427
$66$	−0.839401	+	1.98889i	−0.103323	+	0.244815i
$67$		−	7.06957i		−	0.863686i	−0.901949	−	0.431843i	$-0.857863\pi$
$67$		−	7.06957i		−	0.863686i	0.901949	−	0.431843i	$-0.142137\pi$
$68$	0.678121			0.0822342
$69$	−8.16170	−	1.54489i	−0.982553	−	0.185983i
$70$	2.44752			0.292534
$71$			5.06078i			0.600604i	0.953844	+	0.300302i	$0.0970874\pi$
$71$			5.06078i			0.600604i	−0.953844	+	0.300302i	$0.902913\pi$
$72$	−2.14942	+	2.09285i	−0.253311	+	0.246644i
$73$	2.93708			0.343759			0.171880	−	0.985118i	$-0.445016\pi$
$73$	2.93708			0.343759			0.171880	+	0.985118i	$0.445016\pi$
$74$	−4.01789			−0.467070
$75$	1.58035	+	0.666980i	0.182483	+	0.0770162i
$76$		−	1.06726i		−	0.122423i
$77$		−	1.24636i		−	0.142036i
$78$	2.76039	−	6.54050i	0.312553	−	0.740565i
$79$			2.85953i			0.321722i	0.986977	+	0.160861i	$0.0514271\pi$
$79$			2.85953i			0.321722i	−0.986977	+	0.160861i	$0.948573\pi$
$80$	2.44752			0.273641
$81$	−0.239981	+	8.99680i	−0.0266646	+	0.999644i
$82$	−6.95722			−0.768296
$83$	3.55124			0.389800			0.194900	−	0.980823i	$-0.437562\pi$
$83$	3.55124			0.389800			0.194900	+	0.980823i	$0.437562\pi$
$84$	0.673481	−	1.59575i	0.0734828	−	0.174111i
$85$	−1.65971			−0.180021
$86$	10.8525			1.17025
$87$	0.0820912	−	0.194508i	0.00880110	−	0.0208534i
$88$		−	1.24636i		−	0.132863i
$89$	−1.72988			−0.183367			−0.0916833	−	0.995788i	$-0.529225\pi$
$89$	−1.72988			−0.183367			−0.0916833	+	0.995788i	$0.529225\pi$
$90$	5.26074	−	5.12228i	0.554530	−	0.539936i
$91$			4.09869i			0.429660i
$92$	4.68817	−	1.01050i	0.488775	−	0.105351i
$93$	15.0511	+	6.35225i	1.56073	+	0.658698i
$94$	−6.85977			−0.707531
$95$			2.61213i			0.267999i
$96$	0.673481	−	1.59575i	0.0687368	−	0.162866i
$97$		−	3.78055i		−	0.383857i	−0.981409	−	0.191928i	$-0.938526\pi$
$97$		−	3.78055i		−	0.383857i	0.981409	−	0.191928i	$-0.0614741\pi$
$98$			1.00000i			0.101015i
$99$	−2.60845	−	2.67895i	−0.262159	−	0.269245i
$100$	−0.990347			−0.0990347
$101$		−	5.63445i		−	0.560649i	−0.959905	−	0.280325i	$-0.909558\pi$
$101$		−	5.63445i		−	0.560649i	0.959905	−	0.280325i	$-0.0904421\pi$
$102$	−0.456701	+	1.08211i	−0.0452202	+	0.107145i
$103$		−	4.21240i		−	0.415060i	−0.978229	−	0.207530i	$-0.933458\pi$
$103$		−	4.21240i		−	0.415060i	0.978229	−	0.207530i	$-0.0665425\pi$
$104$			4.09869i			0.401910i
$105$	−1.64836	+	3.90563i	−0.160863	+	0.381151i
$106$			10.1388i			0.984771i
$107$	5.08016			0.491117			0.245559	−	0.969382i	$-0.421029\pi$
$107$	5.08016			0.491117			0.245559	+	0.969382i	$0.421029\pi$
$108$	−1.89207	−	4.83943i	−0.182065	−	0.465674i
$109$		−	20.6152i		−	1.97458i	−0.158926	−	0.987290i	$-0.550803\pi$
$109$		−	20.6152i		−	1.97458i	0.158926	−	0.987290i	$-0.449197\pi$
$110$			3.05050i			0.290853i
$111$	2.70597	−	6.41155i	0.256839	−	0.608557i
$112$			1.00000i			0.0944911i
$113$	18.5411			1.74420			0.872102	−	0.489324i	$-0.162756\pi$
$113$	18.5411			1.74420			0.872102	+	0.489324i	$0.162756\pi$
$114$	1.70308	+	0.718778i	0.159508	+	0.0673197i
$115$	−11.4744	+	2.47321i	−1.06999	+	0.230628i
$116$			0.121891i			0.0113173i
$117$	8.57794	+	8.80980i	0.793031	+	0.814466i
$118$	4.05242			0.373055
$119$		−	0.678121i		−	0.0621632i
$120$	−1.64836	+	3.90563i	−0.150474	+	0.356534i
$121$	−9.44658			−0.858780
$122$	−7.68567			−0.695828
$123$	4.68555	−	11.1020i	0.422482	−	1.00103i
$124$	−9.43198			−0.847016
$125$	−9.81370			−0.877764
$126$	2.09285	+	2.14942i	0.186446	+	0.191485i
$127$	−19.4672			−1.72744			−0.863718	−	0.503976i	$-0.831870\pi$
$127$	−19.4672			−1.72744			−0.863718	+	0.503976i	$0.831870\pi$
$128$			1.00000i			0.0883883i
$129$	−7.30893	+	17.3179i	−0.643516	+	1.52475i
$130$		−	10.0316i		−	0.879832i
$131$		−	10.5381i		−	0.920720i	−0.887732	−	0.460360i	$-0.847720\pi$
$131$		−	10.5381i		−	0.920720i	0.887732	−	0.460360i	$-0.152280\pi$
$132$	1.98889	+	0.839401i	0.173110	+	0.0730605i
$133$	−1.06726			−0.0925430
$134$	−7.06957			−0.610718
$135$	4.63089	+	11.8446i	0.398563	+	1.01942i
$136$		−	0.678121i		−	0.0581484i
$137$	−16.7463			−1.43074			−0.715368	−	0.698748i	$-0.753741\pi$
$137$	−16.7463			−1.43074			−0.715368	+	0.698748i	$0.753741\pi$
$138$	−1.54489	+	8.16170i	−0.131510	+	0.694770i
$139$	−20.1914			−1.71261			−0.856305	−	0.516470i	$-0.827246\pi$
$139$	−20.1914			−1.71261			−0.856305	+	0.516470i	$0.827246\pi$
$140$		−	2.44752i		−	0.206853i
$141$	4.61992	−	10.9465i	0.389068	−	0.921861i
$142$	5.06078			0.424691
$143$	−5.10846			−0.427191
$144$	2.09285	+	2.14942i	0.174404	+	0.179118i
$145$		−	0.298330i		−	0.0247750i
$146$		−	2.93708i		−	0.243075i
$147$	−1.59575	−	0.673481i	−0.131615	−	0.0555478i
$148$			4.01789i			0.330268i
$149$	15.8409			1.29774			0.648869	−	0.760900i	$-0.275242\pi$
$149$	15.8409			1.29774			0.648869	+	0.760900i	$0.275242\pi$
$150$	0.666980	−	1.58035i	0.0544587	−	0.129035i
$151$	0.722786			0.0588195			0.0294097	−	0.999567i	$-0.490637\pi$
$151$	0.722786			0.0588195			0.0294097	+	0.999567i	$0.490637\pi$
$152$	−1.06726			−0.0865661
$153$	−1.41920	−	1.45756i	−0.114736	−	0.117837i
$154$	−1.24636			−0.100435
$155$	23.0849			1.85423
$156$	−6.54050	−	2.76039i	−0.523659	−	0.221008i
$157$			2.86796i			0.228888i	0.993430	+	0.114444i	$0.0365087\pi$
$157$			2.86796i			0.228888i	−0.993430	+	0.114444i	$0.963491\pi$
$158$	2.85953			0.227492
$159$	−16.1791	−	6.82831i	−1.28308	−	0.541520i
$160$		−	2.44752i		−	0.193493i
$161$	−1.01050	−	4.68817i	−0.0796382	−	0.369479i
$162$	8.99680	+	0.239981i	0.706855	+	0.0188547i
$163$	0.605646			0.0474379			0.0237189	−	0.999719i	$-0.492449\pi$
$163$	0.605646			0.0474379			0.0237189	+	0.999719i	$0.492449\pi$
$164$			6.95722i			0.543267i
$165$	−4.86783	−	2.05445i	−0.378960	−	0.159939i
$166$		−	3.55124i		−	0.275630i
$167$			7.53147i			0.582803i	0.956601	+	0.291401i	$0.0941215\pi$
$167$			7.53147i			0.582803i	−0.956601	+	0.291401i	$0.905878\pi$
$168$	−1.59575	−	0.673481i	−0.123115	−	0.0519602i
$169$	3.79928			0.292253
$170$			1.65971i			0.127294i
$171$	−2.29398	+	2.23361i	−0.175425	+	0.170808i
$172$		−	10.8525i		−	0.827493i
$173$		−	17.9644i		−	1.36581i	−0.730507	−	0.682906i	$-0.760716\pi$
$173$		−	17.9644i		−	1.36581i	0.730507	−	0.682906i	$-0.239284\pi$
$174$	−0.194508	−	0.0820912i	−0.0147456	−	0.00622332i
$175$			0.990347i			0.0748632i
$176$	−1.24636			−0.0939481
$177$	−2.72923	+	6.46665i	−0.205141	+	0.486063i
$178$			1.72988i			0.129660i
$179$		−	3.17838i		−	0.237563i	−0.992920	−	0.118782i	$-0.962101\pi$
$179$		−	3.17838i		−	0.237563i	0.992920	−	0.118782i	$-0.0378988\pi$
$180$	−5.12228	−	5.26074i	−0.381792	−	0.392112i
$181$			23.1527i			1.72092i	0.509515	+	0.860462i	$0.329825\pi$
$181$			23.1527i			1.72092i	−0.509515	+	0.860462i	$0.670175\pi$
$182$	4.09869			0.303815
$183$	5.17615	−	12.2644i	0.382632	−	0.906613i
$184$	−1.01050	−	4.68817i	−0.0744947	−	0.345616i
$185$		−	9.83385i		−	0.722999i
$186$	6.35225	−	15.0511i	0.465770	−	1.10360i
$187$	0.845184			0.0618060
$188$			6.85977i			0.500300i
$189$	−4.83943	+	1.89207i	−0.352017	+	0.137628i
$190$	2.61213			0.189504
$191$	−10.8172			−0.782707			−0.391353	−	0.920240i	$-0.627993\pi$
$191$	−10.8172			−0.782707			−0.391353	+	0.920240i	$0.627993\pi$
$192$	−1.59575	−	0.673481i	−0.115163	−	0.0486043i
$193$	−20.0319			−1.44193			−0.720964	−	0.692972i	$-0.756301\pi$
$193$	−20.0319			−1.44193			−0.720964	+	0.692972i	$0.756301\pi$
$194$	−3.78055			−0.271428
$195$	16.0080	+	6.75611i	1.14636	+	0.483815i
$196$	1.00000			0.0714286
$197$			17.3395i			1.23539i	0.786418	+	0.617695i	$0.211933\pi$
$197$			17.3395i			1.23539i	−0.786418	+	0.617695i	$0.788067\pi$
$198$	−2.67895	+	2.60845i	−0.190385	+	0.185374i
$199$			12.0842i			0.856623i	0.903631	+	0.428312i	$0.140891\pi$
$199$			12.0842i			0.856623i	−0.903631	+	0.428312i	$0.859109\pi$
$200$			0.990347i			0.0700281i
$201$	4.76122	−	11.2813i	0.335831	−	0.795721i
$202$	−5.63445			−0.396439
$203$	0.121891			0.00855506
$204$	1.08211	+	0.456701i	0.0757630	+	0.0319755i
$205$		−	17.0279i		−	1.18928i
$206$	−4.21240			−0.293492
$207$	−11.9836	−	7.96201i	−0.832917	−	0.553398i
$208$	4.09869			0.284193
$209$		−	1.33019i		−	0.0920112i
$210$	3.90563	+	1.64836i	0.269514	+	0.113747i
$211$	−8.13866			−0.560289			−0.280144	−	0.959958i	$-0.590382\pi$
$211$	−8.13866			−0.560289			−0.280144	+	0.959958i	$0.590382\pi$
$212$	10.1388			0.696338
$213$	−3.40834	+	8.07574i	−0.233535	+	0.553341i
$214$		−	5.08016i		−	0.347272i
$215$			26.5616i			1.81149i
$216$	−4.83943	+	1.89207i	−0.329281	+	0.128739i
$217$			9.43198i			0.640284i
$218$	−20.6152			−1.39624
$219$	4.68685	+	1.97807i	0.316708	+	0.133665i
$220$	3.05050			0.205664
$221$	−2.77941			−0.186963
$222$	−6.41155	−	2.70597i	−0.430315	−	0.181613i
$223$	17.0807			1.14381			0.571903	−	0.820321i	$-0.306205\pi$
$223$	17.0807			1.14381			0.571903	+	0.820321i	$0.306205\pi$
$224$	1.00000			0.0668153
$225$	2.07265	+	2.12867i	0.138176	+	0.141911i
$226$		−	18.5411i		−	1.23334i
$227$	−10.2150			−0.677994			−0.338997	−	0.940787i	$-0.610088\pi$
$227$	−10.2150			−0.677994			−0.338997	+	0.940787i	$0.610088\pi$
$228$	0.718778	−	1.70308i	0.0476022	−	0.112789i
$229$			11.2623i			0.744235i	0.928186	+	0.372118i	$0.121368\pi$
$229$			11.2623i			0.744235i	−0.928186	+	0.372118i	$0.878632\pi$
$230$	2.47321	+	11.4744i	0.163078	+	0.756598i
$231$	0.839401	−	1.98889i	0.0552285	−	0.130859i
$232$	0.121891			0.00800253
$233$		−	18.0033i		−	1.17943i	−0.807610	−	0.589717i	$-0.799239\pi$
$233$		−	18.0033i		−	1.17943i	0.807610	−	0.589717i	$-0.200761\pi$
$234$	8.80980	−	8.57794i	0.575914	−	0.560757i
$235$		−	16.7894i		−	1.09522i
$236$		−	4.05242i		−	0.263790i
$237$	−1.92584	+	4.56310i	−0.125097	+	0.296405i
$238$	−0.678121			−0.0439560
$239$			27.7414i			1.79444i	0.441580	+	0.897222i	$0.354418\pi$
$239$			27.7414i			1.79444i	−0.441580	+	0.897222i	$0.645582\pi$
$240$	3.90563	+	1.64836i	0.252107	+	0.106401i
$241$			1.73816i			0.111964i	0.998432	+	0.0559822i	$0.0178290\pi$
$241$			1.73816i			0.111964i	−0.998432	+	0.0559822i	$0.982171\pi$
$242$			9.44658i			0.607249i
$243$	−6.44212	+	14.1950i	−0.413262	+	0.910612i
$244$			7.68567i			0.492025i
$245$	−2.44752			−0.156366
$246$	−11.1020	−	4.68555i	−0.707837	−	0.298740i
$247$			4.37436i			0.278334i
$248$			9.43198i			0.598931i
$249$	5.66690	+	2.39170i	0.359125	+	0.151568i
$250$			9.81370i			0.620673i
$251$	−7.84707			−0.495303			−0.247651	−	0.968849i	$-0.579659\pi$
$251$	−7.84707			−0.495303			−0.247651	+	0.968849i	$0.579659\pi$
$252$	2.14942	−	2.09285i	0.135401	−	0.131837i
$253$	5.84315	−	1.25944i	0.367356	−	0.0791805i
$254$			19.4672i			1.22148i
$255$	−2.64849	−	1.11779i	−0.165855	−	0.0699984i
$256$	1.00000			0.0625000
$257$			2.12103i			0.132306i	0.997809	+	0.0661532i	$0.0210726\pi$
$257$			2.12103i			0.132306i	−0.997809	+	0.0661532i	$0.978927\pi$
$258$	17.3179	+	7.30893i	1.07816	+	0.455034i
$259$	4.01789			0.249659
$260$	−10.0316			−0.622135
$261$	0.261994	−	0.255099i	0.0162170	−	0.0157902i
$262$	−10.5381			−0.651047
$263$	−14.8089			−0.913155			−0.456577	−	0.889684i	$-0.650925\pi$
$263$	−14.8089			−0.913155			−0.456577	+	0.889684i	$0.650925\pi$
$264$	0.839401	−	1.98889i	0.0516616	−	0.122407i
$265$	−24.8150			−1.52437
$266$			1.06726i			0.0654378i
$267$	−2.76045	−	1.16504i	−0.168937	−	0.0712992i
$268$			7.06957i			0.431843i
$269$			15.3557i			0.936255i	0.883661	+	0.468128i	$0.155071\pi$
$269$			15.3557i			0.936255i	−0.883661	+	0.468128i	$0.844929\pi$
$270$	11.8446	−	4.63089i	0.720839	−	0.281827i
$271$	−2.20898			−0.134186			−0.0670929	−	0.997747i	$-0.521372\pi$
$271$	−2.20898			−0.134186			−0.0670929	+	0.997747i	$0.521372\pi$
$272$	−0.678121			−0.0411171
$273$	−2.76039	+	6.54050i	−0.167066	+	0.395849i
$274$			16.7463i			1.01168i
$275$	−1.23433			−0.0744330
$276$	8.16170	+	1.54489i	0.491276	+	0.0929915i
$277$	−2.06261			−0.123930			−0.0619651	−	0.998078i	$-0.519737\pi$
$277$	−2.06261			−0.123930			−0.0619651	+	0.998078i	$0.519737\pi$
$278$			20.1914i			1.21100i
$279$	19.7397	+	20.2732i	1.18178	+	1.21373i
$280$	−2.44752			−0.146267
$281$	23.1943			1.38365			0.691827	−	0.722063i	$-0.256806\pi$
$281$	23.1943			1.38365			0.691827	+	0.722063i	$0.256806\pi$
$282$	−10.9465	−	4.61992i	−0.651854	−	0.275112i
$283$		−	21.2771i		−	1.26479i	−0.774646	−	0.632395i	$-0.782072\pi$
$283$		−	21.2771i		−	1.26479i	0.774646	−	0.632395i	$-0.217928\pi$
$284$		−	5.06078i		−	0.300302i
$285$	−1.75922	+	4.16832i	−0.104207	+	0.246910i
$286$			5.10846i			0.302069i
$287$	6.95722			0.410672
$288$	2.14942	−	2.09285i	0.126656	−	0.123322i
$289$	−16.5402			−0.972950
$290$	−0.298330			−0.0175186
$291$	2.54613	−	6.03282i	0.149257	−	0.353650i
$292$	−2.93708			−0.171880
$293$	10.3798			0.606394			0.303197	−	0.952928i	$-0.401946\pi$
$293$	10.3798			0.606394			0.303197	+	0.952928i	$0.401946\pi$
$294$	−0.673481	+	1.59575i	−0.0392782	+	0.0930661i
$295$			9.91837i			0.577470i
$296$	4.01789			0.233535
$297$	−2.35821	−	6.03168i	−0.136837	−	0.349994i
$298$		−	15.8409i		−	0.917639i
$299$	−19.2154	+	4.14171i	−1.11125	+	0.239521i
$300$	−1.58035	−	0.666980i	−0.0912415	−	0.0385081i
$301$	−10.8525			−0.625526
$302$		−	0.722786i		−	0.0415917i
$303$	3.79470	−	8.99119i	0.218000	−	0.516530i
$304$			1.06726i			0.0612115i
$305$		−	18.8108i		−	1.07710i
$306$	−1.45756	+	1.41920i	−0.0833234	+	0.0811305i
$307$	−3.39629			−0.193836			−0.0969182	−	0.995292i	$-0.530899\pi$
$307$	−3.39629			−0.193836			−0.0969182	+	0.995292i	$0.530899\pi$
$308$			1.24636i			0.0710181i
$309$	2.83697	−	6.72195i	0.161390	−	0.382398i
$310$		−	23.0849i		−	1.31114i
$311$			3.21288i			0.182186i	0.995842	+	0.0910928i	$0.0290360\pi$
$311$			3.21288i			0.182186i	−0.995842	+	0.0910928i	$0.970964\pi$
$312$	−2.76039	+	6.54050i	−0.156276	+	0.370283i
$313$			11.7147i			0.662152i	0.943604	+	0.331076i	$0.107412\pi$
$313$			11.7147i			0.662152i	−0.943604	+	0.331076i	$0.892588\pi$
$314$	2.86796			0.161848
$315$	−5.26074	+	5.12228i	−0.296409	+	0.288608i
$316$		−	2.85953i		−	0.160861i
$317$		−	8.78183i		−	0.493237i	−0.969113	−	0.246618i	$-0.920681\pi$
$317$		−	8.78183i		−	0.493237i	0.969113	−	0.246618i	$-0.0793194\pi$
$318$	−6.82831	+	16.1791i	−0.382913	+	0.907277i
$319$			0.151920i			0.00850590i
$320$	−2.44752			−0.136820
$321$	8.10667	+	3.42139i	0.452470	+	0.190963i
$322$	−4.68817	+	1.01050i	−0.261261	+	0.0563127i
$323$		−	0.723730i		−	0.0402694i
$324$	0.239981	−	8.99680i	0.0133323	−	0.499822i
$325$	4.05913			0.225160
$326$		−	0.605646i		−	0.0335436i
$327$	13.8840	−	32.8968i	0.767785	−	1.81920i
$328$	6.95722			0.384148
$329$	6.85977			0.378191
$330$	−2.05445	+	4.86783i	−0.113094	+	0.267965i
$331$	2.73961			0.150583			0.0752913	−	0.997162i	$-0.476011\pi$
$331$	2.73961			0.150583			0.0752913	+	0.997162i	$0.476011\pi$
$332$	−3.55124			−0.194900
$333$	8.63611	−	8.40882i	0.473256	−	0.460801i
$334$	7.53147			0.412104
$335$		−	17.3029i		−	0.945359i
$336$	−0.673481	+	1.59575i	−0.0367414	+	0.0870554i
$337$			8.02671i			0.437243i	0.975810	+	0.218621i	$0.0701560\pi$
$337$			8.02671i			0.437243i	−0.975810	+	0.218621i	$0.929844\pi$
$338$		−	3.79928i		−	0.206654i
$339$	29.5871	+	12.4871i	1.60695	+	0.678206i
$340$	1.65971			0.0900106
$341$	−11.7557			−0.636605
$342$	2.23361	+	2.29398i	0.120780	+	0.124044i
$343$		−	1.00000i		−	0.0539949i
$344$	−10.8525			−0.585126
$345$	−19.9759	−	3.78115i	−1.07547	−	0.203570i
$346$	−17.9644			−0.965774
$347$			6.63663i			0.356273i	0.984006	+	0.178137i	$0.0570069\pi$
$347$			6.63663i			0.356273i	−0.984006	+	0.178137i	$0.942993\pi$
$348$	−0.0820912	+	0.194508i	−0.00440055	+	0.0104267i
$349$	16.9467			0.907134			0.453567	−	0.891222i	$-0.350151\pi$
$349$	16.9467			0.907134			0.453567	+	0.891222i	$0.350151\pi$
$350$	0.990347			0.0529363
$351$	7.75503	+	19.8353i	0.413933	+	1.05873i
$352$			1.24636i			0.0664313i
$353$		−	17.5013i		−	0.931498i	−0.884917	−	0.465749i	$-0.845785\pi$
$353$		−	17.5013i		−	0.931498i	0.884917	−	0.465749i	$-0.154215\pi$
$354$	6.46665	+	2.72923i	0.343699	+	0.145057i
$355$			12.3863i			0.657399i
$356$	1.72988			0.0916833
$357$	0.456701	−	1.08211i	0.0241712	−	0.0572715i
$358$	−3.17838			−0.167983
$359$	−21.9369			−1.15778			−0.578891	−	0.815405i	$-0.696514\pi$
$359$	−21.9369			−1.15778			−0.578891	+	0.815405i	$0.696514\pi$
$360$	−5.26074	+	5.12228i	−0.277265	+	0.269968i
$361$	17.8610			0.940051
$362$	23.1527			1.21688
$363$	−15.0744	−	6.36209i	−0.791201	−	0.333923i
$364$		−	4.09869i		−	0.214830i
$365$	7.18856			0.376267
$366$	−12.2644	−	5.17615i	−0.641072	−	0.270562i
$367$			13.8833i			0.724702i	0.932042	+	0.362351i	$0.118026\pi$
$367$			13.8833i			0.724702i	−0.932042	+	0.362351i	$0.881974\pi$
$368$	−4.68817	+	1.01050i	−0.244388	+	0.0526757i
$369$	14.9540	−	14.5604i	0.778472	−	0.757984i
$370$	−9.83385			−0.511237
$371$		−	10.1388i		−	0.526382i
$372$	−15.0511	−	6.35225i	−0.780363	−	0.329349i
$373$		−	32.8144i		−	1.69907i	−0.527536	−	0.849533i	$-0.676884\pi$
$373$		−	32.8144i		−	1.69907i	0.527536	−	0.849533i	$-0.323116\pi$
$374$		−	0.845184i		−	0.0437034i
$375$	−15.6602	−	6.60934i	−0.808691	−	0.341305i
$376$	6.85977			0.353766
$377$		−	0.499593i		−	0.0257304i
$378$	1.89207	+	4.83943i	0.0973178	+	0.248913i
$379$		−	28.4394i		−	1.46083i	−0.683002	−	0.730416i	$-0.739326\pi$
$379$		−	28.4394i		−	1.46083i	0.683002	−	0.730416i	$-0.260674\pi$
$380$		−	2.61213i		−	0.134000i
$381$	−31.0648	−	13.1108i	−1.59150	−	0.671686i
$382$			10.8172i			0.553457i
$383$	9.49524			0.485184			0.242592	−	0.970128i	$-0.422002\pi$
$383$	9.49524			0.485184			0.242592	+	0.970128i	$0.422002\pi$
$384$	−0.673481	+	1.59575i	−0.0343684	+	0.0814329i
$385$		−	3.05050i		−	0.155468i
$386$			20.0319i			1.01960i
$387$	−23.3265	+	22.7126i	−1.18575	+	1.15454i
$388$			3.78055i			0.191928i
$389$	2.46547			0.125004			0.0625021	−	0.998045i	$-0.480092\pi$
$389$	2.46547			0.125004			0.0625021	+	0.998045i	$0.480092\pi$
$390$	6.75611	−	16.0080i	0.342109	−	0.810596i
$391$	3.17914	−	0.685238i	0.160776	−	0.0346540i
$392$		−	1.00000i		−	0.0505076i
$393$	7.09722	−	16.8162i	0.358008	−	0.848266i
$394$	17.3395			0.873552
$395$			6.99875i			0.352145i
$396$	2.60845	+	2.67895i	0.131079	+	0.134622i
$397$	−9.07851			−0.455637			−0.227819	−	0.973704i	$-0.573159\pi$
$397$	−9.07851			−0.455637			−0.227819	+	0.973704i	$0.573159\pi$
$398$	12.0842			0.605724
$399$	−1.70308	−	0.718778i	−0.0852606	−	0.0359839i
$400$	0.990347			0.0495174
$401$	−20.6111			−1.02927			−0.514634	−	0.857410i	$-0.672072\pi$
$401$	−20.6111			−1.02927			−0.514634	+	0.857410i	$0.672072\pi$
$402$	−11.2813	−	4.76122i	−0.562659	−	0.237468i
$403$	38.6588			1.92573
$404$			5.63445i			0.280325i
$405$	−0.587359	+	22.0198i	−0.0291861	+	1.09417i
$406$		−	0.121891i		−	0.00604934i
$407$			5.00774i			0.248225i
$408$	0.456701	−	1.08211i	0.0226101	−	0.0535726i
$409$	3.71087			0.183491			0.0917454	−	0.995783i	$-0.470755\pi$
$409$	3.71087			0.183491			0.0917454	+	0.995783i	$0.470755\pi$
$410$	−17.0279			−0.840949
$411$	−26.7230	−	11.2783i	−1.31815	−	0.556319i
$412$			4.21240i			0.207530i
$413$	−4.05242			−0.199406
$414$	−7.96201	+	11.9836i	−0.391311	+	0.588961i
$415$	8.69174			0.426661
$416$		−	4.09869i		−	0.200955i
$417$	−32.2204	−	13.5985i	−1.57784	−	0.665922i
$418$	−1.33019			−0.0650617
$419$	−3.56141			−0.173986			−0.0869932	−	0.996209i	$-0.527726\pi$
$419$	−3.56141			−0.173986			−0.0869932	+	0.996209i	$0.527726\pi$
$420$	1.64836	−	3.90563i	0.0804316	−	0.190575i
$421$		−	3.06440i		−	0.149350i	−0.997208	−	0.0746748i	$-0.976208\pi$
$421$		−	3.06440i		−	0.149350i	0.997208	−	0.0746748i	$-0.0237919\pi$
$422$			8.13866i			0.396184i
$423$	14.7445	−	14.3565i	0.716902	−	0.698035i
$424$		−	10.1388i		−	0.492385i
$425$	−0.671575			−0.0325762
$426$	8.07574	+	3.40834i	0.391271	+	0.165134i
$427$	7.68567			0.371936
$428$	−5.08016			−0.245559
$429$	−8.15183	−	3.44045i	−0.393574	−	0.166106i
$430$	26.5616			1.28092
$431$	22.2236			1.07047			0.535236	−	0.844703i	$-0.320223\pi$
$431$	22.2236			1.07047			0.535236	+	0.844703i	$0.320223\pi$
$432$	1.89207	+	4.83943i	0.0910324	+	0.232837i
$433$			39.0727i			1.87771i	0.344306	+	0.938857i	$0.388114\pi$
$433$			39.0727i			1.87771i	−0.344306	+	0.938857i	$0.611886\pi$
$434$	9.43198			0.452749
$435$	0.200920	−	0.476061i	0.00963336	−	0.0228254i
$436$			20.6152i			0.987290i
$437$	−1.07846	−	5.00348i	−0.0515897	−	0.239349i
$438$	1.97807	−	4.68685i	0.0945158	−	0.223947i
$439$	9.64952			0.460546			0.230273	−	0.973126i	$-0.426038\pi$
$439$	9.64952			0.460546			0.230273	+	0.973126i	$0.426038\pi$
$440$		−	3.05050i		−	0.145427i
$441$	−2.09285	−	2.14942i	−0.0996594	−	0.102353i
$442$			2.77941i			0.132203i
$443$			12.5345i			0.595534i	0.954639	+	0.297767i	$0.0962419\pi$
$443$			12.5345i			0.595534i	−0.954639	+	0.297767i	$0.903758\pi$
$444$	−2.70597	+	6.41155i	−0.128420	+	0.304279i
$445$	−4.23391			−0.200706
$446$		−	17.0807i		−	0.808793i
$447$	25.2782	+	10.6686i	1.19562	+	0.504605i
$448$		−	1.00000i		−	0.0472456i
$449$		−	37.5031i		−	1.76988i	−0.465706	−	0.884939i	$-0.654200\pi$
$449$		−	37.5031i		−	1.76988i	0.465706	−	0.884939i	$-0.345800\pi$
$450$	2.12867	−	2.07265i	0.100346	−	0.0977055i
$451$			8.67121i			0.408312i
$452$	−18.5411			−0.872102
$453$	1.15339	+	0.486783i	0.0541909	+	0.0228710i
$454$			10.2150i			0.479414i
$455$			10.0316i			0.470290i
$456$	−1.70308	−	0.718778i	−0.0797540	−	0.0336599i
$457$		−	21.4399i		−	1.00292i	−0.865182	−	0.501459i	$-0.832797\pi$
$457$		−	21.4399i		−	1.00292i	0.865182	−	0.501459i	$-0.167203\pi$
$458$	11.2623			0.526254
$459$	−1.28305	−	3.28172i	−0.0598879	−	0.153177i
$460$	11.4744	−	2.47321i	0.534995	−	0.115314i
$461$		−	13.1851i		−	0.614093i	−0.951694	−	0.307047i	$-0.900659\pi$
$461$		−	13.1851i		−	0.614093i	0.951694	−	0.307047i	$-0.0993408\pi$
$462$	−1.98889	−	0.839401i	−0.0925313	−	0.0390525i
$463$	10.0041			0.464930			0.232465	−	0.972605i	$-0.425321\pi$
$463$	10.0041			0.464930			0.232465	+	0.972605i	$0.425321\pi$
$464$		−	0.121891i		−	0.00565864i
$465$	36.8378	+	15.5473i	1.70831	+	0.720987i
$466$	−18.0033			−0.833986
$467$	−6.26525			−0.289921			−0.144961	−	0.989437i	$-0.546306\pi$
$467$	−6.26525			−0.289921			−0.144961	+	0.989437i	$0.546306\pi$
$468$	−8.57794	−	8.80980i	−0.396515	−	0.407233i
$469$	7.06957			0.326443
$470$	−16.7894			−0.774438
$471$	−1.93152	+	4.57655i	−0.0889996	+	0.210877i
$472$	−4.05242			−0.186528
$473$		−	13.5261i		−	0.621931i
$474$	4.56310	+	1.92584i	0.209590	+	0.0884566i
$475$			1.05696i			0.0484965i
$476$			0.678121i			0.0310816i
$477$	−21.2190	−	21.7926i	−0.971553	−	0.997814i
$478$	27.7414			1.26886
$479$	32.9762			1.50672			0.753361	−	0.657607i	$-0.228431\pi$
$479$	32.9762			1.50672			0.753361	+	0.657607i	$0.228431\pi$
$480$	1.64836	−	3.90563i	0.0752369	−	0.178267i
$481$		−	16.4681i		−	0.750880i
$482$	1.73816			0.0791708
$483$	1.54489	−	8.16170i	0.0702950	−	0.371370i
$484$	9.44658			0.429390
$485$		−	9.25296i		−	0.420155i
$486$	14.1950	+	6.44212i	0.643900	+	0.292221i
$487$	28.2063			1.27815			0.639075	−	0.769145i	$-0.279317\pi$
$487$	28.2063			1.27815			0.639075	+	0.769145i	$0.279317\pi$
$488$	7.68567			0.347914
$489$	0.966461	+	0.407891i	0.0437049	+	0.0184455i
$490$			2.44752i			0.110568i
$491$		−	14.4289i		−	0.651166i	−0.945513	−	0.325583i	$-0.894439\pi$
$491$		−	14.4289i		−	0.651166i	0.945513	−	0.325583i	$-0.105561\pi$
$492$	−4.68555	+	11.1020i	−0.211241	+	0.500516i
$493$			0.0826568i			0.00372267i
$494$	4.37436			0.196812
$495$	−6.38422	−	6.55678i	−0.286949	−	0.294706i
$496$	9.43198			0.423508
$497$	−5.06078			−0.227007
$498$	2.39170	−	5.66690i	0.107174	−	0.253940i
$499$	8.21278			0.367654			0.183827	−	0.982959i	$-0.441151\pi$
$499$	8.21278			0.367654			0.183827	+	0.982959i	$0.441151\pi$
$500$	9.81370			0.438882
$501$	−5.07230	+	12.0184i	−0.226614	+	0.536941i
$502$			7.84707i			0.350232i
$503$	11.6938			0.521402			0.260701	−	0.965420i	$-0.416046\pi$
$503$	11.6938			0.521402			0.260701	+	0.965420i	$0.416046\pi$
$504$	−2.09285	−	2.14942i	−0.0932228	−	0.0957426i
$505$		−	13.7904i		−	0.613666i
$506$	−1.25944	−	5.84315i	−0.0559891	−	0.259760i
$507$	6.06271	+	2.55874i	0.269255	+	0.113638i
$508$	19.4672			0.863718
$509$		−	12.4405i		−	0.551414i	−0.961242	−	0.275707i	$-0.911088\pi$
$509$		−	12.4405i		−	0.551414i	0.961242	−	0.275707i	$-0.0889120\pi$
$510$	−1.11779	+	2.64849i	−0.0494964	+	0.117277i
$511$			2.93708i			0.129929i
$512$		−	1.00000i		−	0.0441942i
$513$	−5.16492	+	2.01933i	−0.228037	+	0.0891557i
$514$	2.12103			0.0935547
$515$		−	10.3099i		−	0.454310i
$516$	7.30893	−	17.3179i	0.321758	−	0.762376i
$517$			8.54976i			0.376018i
$518$		−	4.01789i		−	0.176536i
$519$	12.0987	−	28.6668i	0.531074	−	1.25833i
$520$			10.0316i			0.439916i
$521$	22.2556			0.975037			0.487518	−	0.873113i	$-0.337902\pi$
$521$	22.2556			0.975037			0.487518	+	0.873113i	$0.337902\pi$
$522$	−0.255099	−	0.261994i	−0.0111654	−	0.0114672i
$523$			35.2887i			1.54307i	0.636189	+	0.771533i	$0.280510\pi$
$523$			35.2887i			1.54307i	−0.636189	+	0.771533i	$0.719490\pi$
$524$			10.5381i			0.460360i
$525$	−0.666980	+	1.58035i	−0.0291094	+	0.0689721i
$526$			14.8089i			0.645698i
$527$	−6.39602			−0.278615
$528$	−1.98889	−	0.839401i	−0.0865551	−	0.0365302i
$529$	20.9578	−	9.47474i	0.911209	−	0.411945i
$530$			24.8150i			1.07789i
$531$	−8.71034	+	8.48109i	−0.377996	+	0.368048i
$532$	1.06726			0.0462715
$533$		−	28.5155i		−	1.23514i
$534$	−1.16504	+	2.76045i	−0.0504162	+	0.119457i
$535$	12.4338			0.537559
$536$	7.06957			0.305359
$537$	2.14058	−	5.07190i	0.0923727	−	0.218869i
$538$	15.3557			0.662032
$539$	1.24636			0.0536846
$540$	−4.63089	−	11.8446i	−0.199282	−	0.509710i
$541$	15.3186			0.658599			0.329299	−	0.944226i	$-0.393187\pi$
$541$	15.3186			0.658599			0.329299	+	0.944226i	$0.393187\pi$
$542$			2.20898i			0.0948837i
$543$	−15.5929	+	36.9459i	−0.669154	+	1.58550i
$544$			0.678121i			0.0290742i
$545$		−	50.4562i		−	2.16130i
$546$	6.54050	+	2.76039i	0.279907	+	0.118134i
$547$	22.1925			0.948883			0.474441	−	0.880287i	$-0.342650\pi$
$547$	22.1925			0.948883			0.474441	+	0.880287i	$0.342650\pi$
$548$	16.7463			0.715368
$549$	16.5197	−	16.0849i	0.705044	−	0.686489i
$550$			1.23433i			0.0526321i
$551$	0.130089			0.00554198
$552$	1.54489	−	8.16170i	0.0657549	−	0.347385i
$553$	−2.85953			−0.121599
$554$			2.06261i			0.0876318i
$555$	6.62291	−	15.6924i	0.281127	−	0.666105i
$556$	20.1914			0.856305
$557$	15.2491			0.646124			0.323062	−	0.946378i	$-0.395288\pi$
$557$	15.2491			0.646124			0.323062	+	0.946378i	$0.395288\pi$
$558$	20.2732	−	19.7397i	0.858235	−	0.835647i
$559$			44.4810i			1.88134i
$560$			2.44752i			0.103427i
$561$	1.34870	+	0.569216i	0.0569424	+	0.0240323i
$562$		−	23.1943i		−	0.978392i
$563$	26.6304			1.12234			0.561168	−	0.827702i	$-0.310352\pi$
$563$	26.6304			1.12234			0.561168	+	0.827702i	$0.310352\pi$
$564$	−4.61992	+	10.9465i	−0.194534	+	0.460930i
$565$	45.3798			1.90914
$566$	−21.2771			−0.894342
$567$	−8.99680	−	0.239981i	−0.377830	−	0.0100783i
$568$	−5.06078			−0.212345
$569$	24.6193			1.03210			0.516048	−	0.856560i	$-0.327403\pi$
$569$	24.6193			1.03210			0.516048	+	0.856560i	$0.327403\pi$
$570$	4.16832	+	1.75922i	0.174592	+	0.0736857i
$571$		−	27.5098i		−	1.15125i	−0.817714	−	0.575624i	$-0.804759\pi$
$571$		−	27.5098i		−	1.15125i	0.817714	−	0.575624i	$-0.195241\pi$
$572$	5.10846			0.213595
$573$	−17.2616	−	7.28519i	−0.721114	−	0.304343i
$574$		−	6.95722i		−	0.290389i
$575$	−4.64291	+	1.00074i	−0.193623	+	0.0417338i
$576$	−2.09285	−	2.14942i	−0.0872020	−	0.0895590i
$577$	−25.2188			−1.04987			−0.524935	−	0.851142i	$-0.675911\pi$
$577$	−25.2188			−1.04987			−0.524935	+	0.851142i	$0.675911\pi$
$578$			16.5402i			0.687980i
$579$	−31.9660	−	13.4911i	−1.32846	−	0.560671i
$580$			0.298330i			0.0123875i
$581$			3.55124i			0.147330i
$582$	−6.03282	−	2.54613i	−0.250068	−	0.105540i
$583$	12.6367			0.523357
$584$			2.93708i			0.121537i
$585$	20.9947	+	21.5621i	0.868022	+	0.891485i
$586$		−	10.3798i		−	0.428786i
$587$			47.2146i			1.94875i	0.224923	+	0.974377i	$0.427787\pi$
$587$			47.2146i			1.94875i	−0.224923	+	0.974377i	$0.572213\pi$
$588$	1.59575	+	0.673481i	0.0658077	+	0.0277739i
$589$			10.0664i			0.414777i
$590$	9.91837			0.408333
$591$	−11.6778	+	27.6696i	−0.480362	+	1.13817i
$592$		−	4.01789i		−	0.165134i
$593$		−	25.5110i		−	1.04761i	−0.851838	−	0.523805i	$-0.824512\pi$
$593$		−	25.5110i		−	1.04761i	0.851838	−	0.523805i	$-0.175488\pi$
$594$	−6.03168	+	2.35821i	−0.247483	+	0.0967585i
$595$		−	1.65971i		−	0.0680416i
$596$	−15.8409			−0.648869
$597$	−8.13845	+	19.2833i	−0.333084	+	0.789213i
$598$	4.14171	+	19.2154i	0.169367	+	0.785774i
$599$		−	19.2297i		−	0.785705i	−0.919601	−	0.392853i	$-0.871488\pi$
$599$		−	19.2297i		−	0.785705i	0.919601	−	0.392853i	$-0.128512\pi$
$600$	−0.666980	+	1.58035i	−0.0272293	+	0.0645175i
$601$	−14.3657			−0.585989			−0.292994	−	0.956114i	$-0.594652\pi$
$601$	−14.3657			−0.585989			−0.292994	+	0.956114i	$0.594652\pi$
$602$			10.8525i			0.442314i
$603$	15.1955	−	14.7955i	0.618807	−	0.602521i
$604$	−0.722786			−0.0294097
$605$	−23.1207			−0.939989
$606$	−8.99119	−	3.79470i	−0.365242	−	0.154149i
$607$	−29.0122			−1.17757			−0.588785	−	0.808290i	$-0.700393\pi$
$607$	−29.0122			−1.17757			−0.588785	+	0.808290i	$0.700393\pi$
$608$	1.06726			0.0432830
$609$	0.194508	+	0.0820912i	0.00788185	+	0.00332650i
$610$	−18.8108			−0.761628
$611$		−	28.1161i		−	1.13746i
$612$	1.41920	+	1.45756i	0.0573679	+	0.0589185i
$613$		−	21.2604i		−	0.858698i	−0.903139	−	0.429349i	$-0.858743\pi$
$613$		−	21.2604i		−	0.858698i	0.903139	−	0.429349i	$-0.141257\pi$
$614$			3.39629i			0.137063i
$615$	11.4680	−	27.1723i	0.462433	−	1.09569i
$616$	1.24636			0.0502174
$617$	−5.58908			−0.225008			−0.112504	−	0.993651i	$-0.535887\pi$
$617$	−5.58908			−0.225008			−0.112504	+	0.993651i	$0.535887\pi$
$618$	−6.72195	−	2.83697i	−0.270396	−	0.114120i
$619$		−	44.0173i		−	1.76920i	−0.466348	−	0.884601i	$-0.654431\pi$
$619$		−	44.0173i		−	1.76920i	0.466348	−	0.884601i	$-0.345569\pi$
$620$	−23.0849			−0.927113
$621$	−13.7606	−	20.7761i	−0.552193	−	0.833716i
$622$	3.21288			0.128825
$623$		−	1.72988i		−	0.0693061i
$624$	6.54050	+	2.76039i	0.261829	+	0.110504i
$625$	−28.9709			−1.15884
$626$	11.7147			0.468212
$627$	0.895858	−	2.12265i	0.0357771	−	0.0847706i
$628$		−	2.86796i		−	0.114444i
$629$			2.72461i			0.108637i
$630$	5.12228	+	5.26074i	0.204077	+	0.209593i
$631$			47.6549i			1.89711i	0.316609	+	0.948556i	$0.397456\pi$
$631$			47.6549i			1.89711i	−0.316609	+	0.948556i	$0.602544\pi$
$632$	−2.85953			−0.113746
$633$	−12.9873	−	5.48123i	−0.516198	−	0.217859i
$634$	−8.78183			−0.348771
$635$	−47.6463			−1.89079
$636$	16.1791	+	6.82831i	0.641542	+	0.270760i
$637$	−4.09869			−0.162396
$638$	0.151920			0.00601458
$639$	−10.8777	+	10.5914i	−0.430316	+	0.418991i
$640$			2.44752i			0.0967467i
$641$	31.1966			1.23219			0.616097	−	0.787671i	$-0.288713\pi$
$641$	31.1966			1.23219			0.616097	+	0.787671i	$0.288713\pi$
$642$	3.42139	−	8.10667i	0.135031	−	0.319945i
$643$			0.314769i			0.0124133i	0.999981	+	0.00620664i	$0.00197565\pi$
$643$			0.314769i			0.0124133i	−0.999981	+	0.00620664i	$0.998024\pi$
$644$	1.01050	+	4.68817i	0.0398191	+	0.184740i
$645$	−17.8887	+	42.3858i	−0.704369	+	1.66894i
$646$	−0.723730			−0.0284748
$647$			31.2494i			1.22854i	0.789096	+	0.614270i	$0.210550\pi$
$647$			31.2494i			1.22854i	−0.789096	+	0.614270i	$0.789450\pi$
$648$	−8.99680	−	0.239981i	−0.353428	−	0.00942736i
$649$		−	5.05078i		−	0.198261i
$650$		−	4.05913i		−	0.159212i
$651$	−6.35225	+	15.0511i	−0.248964	+	0.589899i
$652$	−0.605646			−0.0237189
$653$			32.6276i			1.27682i	0.769697	+	0.638409i	$0.220407\pi$
$653$			32.6276i			1.27682i	−0.769697	+	0.638409i	$0.779593\pi$
$654$	−32.8968	−	13.8840i	−1.28637	−	0.542906i
$655$		−	25.7922i		−	1.00779i
$656$		−	6.95722i		−	0.271634i
$657$	6.14686	+	6.31301i	0.239812	+	0.246294i
$658$		−	6.85977i		−	0.267422i
$659$	26.1213			1.01754			0.508771	−	0.860902i	$-0.330100\pi$
$659$	26.1213			1.01754			0.508771	+	0.860902i	$0.330100\pi$
$660$	4.86783	+	2.05445i	0.189480	+	0.0799694i
$661$			18.2937i			0.711543i	0.934573	+	0.355771i	$0.115782\pi$
$661$			18.2937i			0.711543i	−0.934573	+	0.355771i	$0.884218\pi$
$662$		−	2.73961i		−	0.106478i
$663$	−4.43525	−	1.87188i	−0.172251	−	0.0726978i
$664$			3.55124i			0.137815i
$665$	−2.61213			−0.101294
$666$	−8.40882	−	8.63611i	−0.325835	−	0.334642i
$667$	0.123170	+	0.571445i	0.00476917	+	0.0221264i
$668$		−	7.53147i		−	0.291401i
$669$	27.2565	+	11.5035i	1.05380	+	0.444751i
$670$	−17.3029			−0.668470
$671$			9.57914i			0.369798i
$672$	1.59575	+	0.673481i	0.0615575	+	0.0259801i
$673$	2.42693			0.0935514			0.0467757	−	0.998905i	$-0.485105\pi$
$673$	2.42693			0.0935514			0.0467757	+	0.998905i	$0.485105\pi$
$674$	8.02671			0.309177
$675$	1.87381	+	4.79271i	0.0721230	+	0.184472i
$676$	−3.79928			−0.146126
$677$	45.6813			1.75568			0.877838	−	0.478957i	$-0.158985\pi$
$677$	45.6813			1.75568			0.877838	+	0.478957i	$0.158985\pi$
$678$	12.4871	−	29.5871i	0.479564	−	1.13628i
$679$	3.78055			0.145084
$680$		−	1.65971i		−	0.0636471i
$681$	−16.3006	−	6.87961i	−0.624641	−	0.263627i
$682$			11.7557i			0.450148i
$683$			45.0515i			1.72385i	0.507039	+	0.861923i	$0.330740\pi$
$683$			45.0515i			1.72385i	−0.507039	+	0.861923i	$0.669260\pi$
$684$	2.29398	−	2.23361i	0.0877126	−	0.0854041i
$685$	−40.9869			−1.56603
$686$	−1.00000			−0.0381802
$687$	−7.58496	+	17.9719i	−0.289384	+	0.685670i
$688$			10.8525i			0.413747i
$689$	−41.5560			−1.58316
$690$	−3.78115	+	19.9759i	−0.143946	+	0.760470i
$691$	12.0530			0.458516			0.229258	−	0.973366i	$-0.426370\pi$
$691$	12.0530			0.458516			0.229258	+	0.973366i	$0.426370\pi$
$692$			17.9644i			0.682906i
$693$	2.67895	−	2.60845i	0.101765	−	0.0990867i
$694$	6.63663			0.251923
$695$	−49.4188			−1.87456
$696$	0.194508	+	0.0820912i	0.00737279	+	0.00311166i
$697$			4.71783i			0.178701i
$698$		−	16.9467i		−	0.641440i
$699$	12.1249	−	28.7288i	0.458604	−	1.08662i
$700$		−	0.990347i		−	0.0374316i
$701$	39.3484			1.48617			0.743085	−	0.669197i	$-0.233362\pi$
$701$	39.3484			1.48617			0.743085	+	0.669197i	$0.233362\pi$
$702$	19.8353	−	7.75503i	0.748636	−	0.292695i
$703$	4.28812			0.161730
$704$	1.24636			0.0469741
$705$	11.3074	−	26.7917i	0.425859	−	1.00904i
$706$	−17.5013			−0.658668
$707$	5.63445			0.211905
$708$	2.72923	−	6.46665i	0.102571	−	0.243032i
$709$			27.2802i			1.02453i	0.858828	+	0.512264i	$0.171193\pi$
$709$			27.2802i			1.02453i	−0.858828	+	0.512264i	$0.828807\pi$
$710$	12.3863			0.464851
$711$	−6.14632	+	5.98455i	−0.230505	+	0.224438i
$712$		−	1.72988i		−	0.0648299i
$713$	−44.2187	+	9.53097i	−1.65600	+	0.356937i
$714$	−1.08211	−	0.456701i	−0.0404970	−	0.0170916i
$715$	−12.5030			−0.467587
$716$			3.17838i			0.118782i
$717$	−18.6833	+	44.2684i	−0.697741	+	1.65323i
$718$			21.9369i			0.818676i
$719$			15.9674i			0.595483i	0.954646	+	0.297742i	$0.0962334\pi$
$719$			15.9674i			0.595483i	−0.954646	+	0.297742i	$0.903767\pi$
$720$	5.12228	+	5.26074i	0.190896	+	0.196056i
$721$	4.21240			0.156878
$722$		−	17.8610i		−	0.664716i
$723$	−1.17061	+	2.77366i	−0.0435356	+	0.103154i
$724$		−	23.1527i		−	0.860462i
$725$		−	0.120714i		−	0.00448322i
$726$	−6.36209	+	15.0744i	−0.236119	+	0.559463i
$727$		−	16.2432i		−	0.602427i	−0.953557	−	0.301214i	$-0.902608\pi$
$727$		−	16.2432i		−	0.602427i	0.953557	−	0.301214i	$-0.0973917\pi$
$728$	−4.09869			−0.151908
$729$	−19.8401	+	18.3131i	−0.734819	+	0.678263i
$730$		−	7.18856i		−	0.266061i
$731$		−	7.35929i		−	0.272193i
$732$	−5.17615	+	12.2644i	−0.191316	+	0.453306i
$733$			21.1938i			0.782811i	0.920218	+	0.391405i	$0.128011\pi$
$733$			21.1938i			0.782811i	−0.920218	+	0.391405i	$0.871989\pi$
$734$	13.8833			0.512442
$735$	−3.90563	−	1.64836i	−0.144061	−	0.0608006i
$736$	1.01050	+	4.68817i	0.0372473	+	0.172808i
$737$			8.81125i			0.324567i
$738$	−14.5604	−	14.9540i	−0.535975	−	0.550463i
$739$	−54.0353			−1.98772			−0.993861	−	0.110637i	$-0.964711\pi$
$739$	−54.0353			−1.98772			−0.993861	+	0.110637i	$0.964711\pi$
$740$			9.83385i			0.361499i
$741$	−2.94605	+	6.98040i	−0.108226	+	0.256431i
$742$	−10.1388			−0.372208
$743$	2.97839			0.109266			0.0546332	−	0.998506i	$-0.482601\pi$
$743$	2.97839			0.109266			0.0546332	+	0.998506i	$0.482601\pi$
$744$	−6.35225	+	15.0511i	−0.232885	+	0.551800i
$745$	38.7709			1.42046
$746$	−32.8144			−1.20142
$747$	7.43221	+	7.63310i	0.271930	+	0.279281i
$748$	−0.845184			−0.0309030
$749$			5.08016i			0.185625i
$750$	−6.60934	+	15.6602i	−0.241339	+	0.571831i
$751$		−	8.56153i		−	0.312415i	−0.987724	−	0.156207i	$-0.950073\pi$
$751$		−	8.56153i		−	0.312415i	0.987724	−	0.156207i	$-0.0499268\pi$
$752$		−	6.85977i		−	0.250150i
$753$	−12.5220	−	5.28485i	−0.456326	−	0.192591i
$754$	−0.499593			−0.0181941
$755$	1.76903			0.0643817
$756$	4.83943	−	1.89207i	0.176008	−	0.0688141i
$757$			26.7707i			0.972999i	0.873681	+	0.486499i	$0.161726\pi$
$757$			26.7707i			0.972999i	−0.873681	+	0.486499i	$0.838274\pi$
$758$	−28.4394			−1.03296
$759$	10.1724	+	1.92549i	0.369236	+	0.0698910i
$760$	−2.61213			−0.0947521
$761$		−	25.4730i		−	0.923394i	−0.887038	−	0.461697i	$-0.847241\pi$
$761$		−	25.4730i		−	0.923394i	0.887038	−	0.461697i	$-0.152759\pi$
$762$	−13.1108	+	31.0648i	−0.474954	+	1.12536i
$763$	20.6152			0.746321
$764$	10.8172			0.391353
$765$	−3.47353	−	3.56742i	−0.125586	−	0.128980i
$766$		−	9.49524i		−	0.343077i
$767$			16.6096i			0.599739i
$768$	1.59575	+	0.673481i	0.0575817	+	0.0243021i
$769$			32.3745i			1.16746i	0.811949	+	0.583728i	$0.198406\pi$
$769$			32.3745i			1.16746i	−0.811949	+	0.583728i	$0.801594\pi$
$770$	−3.05050			−0.109932
$771$	−1.42847	+	3.38464i	−0.0514453	+	0.121895i
$772$	20.0319			0.720964
$773$	−11.9462			−0.429674			−0.214837	−	0.976650i	$-0.568922\pi$
$773$	−11.9462			−0.429674			−0.214837	+	0.976650i	$0.568922\pi$
$774$	22.7126	+	23.3265i	0.816386	+	0.838453i
$775$	9.34093			0.335536
$776$	3.78055			0.135714
$777$	6.41155	+	2.70597i	0.230013	+	0.0970761i
$778$		−	2.46547i		−	0.0883913i
$779$	7.42515			0.266033
$780$	−16.0080	−	6.75611i	−0.573178	−	0.241907i
$781$		−	6.30756i		−	0.225702i
$782$	−0.685238	−	3.17914i	−0.0245041	−	0.113686i
$783$	0.589882	−	0.230627i	0.0210807	−	0.00824192i
$784$	−1.00000			−0.0357143
$785$			7.01939i			0.250533i
$786$	−16.8162	−	7.09722i	−0.599815	−	0.253150i
$787$		−	48.2489i		−	1.71989i	−0.510388	−	0.859944i	$-0.670498\pi$
$787$		−	48.2489i		−	1.71989i	0.510388	−	0.859944i	$-0.329502\pi$
$788$		−	17.3395i		−	0.617695i
$789$	−23.6313	−	9.97350i	−0.841296	−	0.355066i
$790$	6.99875			0.249004
$791$			18.5411i			0.659247i
$792$	2.67895	−	2.60845i	0.0951924	−	0.0926871i
$793$		−	31.5012i		−	1.11864i
$794$			9.07851i			0.322184i
$795$	−39.5986	−	16.7124i	−1.40442	−	0.592728i
$796$		−	12.0842i		−	0.428312i
$797$	−15.8214			−0.560424			−0.280212	−	0.959938i	$-0.590405\pi$
$797$	−15.8214			−0.560424			−0.280212	+	0.959938i	$0.590405\pi$
$798$	−0.718778	+	1.70308i	−0.0254445	+	0.0602883i
$799$			4.65175i			0.164567i
$800$		−	0.990347i		−	0.0350141i
$801$	−3.62037	−	3.71823i	−0.127919	−	0.131377i
$802$			20.6111i			0.727802i
$803$	−3.66067			−0.129182
$804$	−4.76122	+	11.2813i	−0.167915	+	0.397860i
$805$	−2.47321	−	11.4744i	−0.0871690	−	0.404419i
$806$		−	38.6588i		−	1.36170i
$807$	−10.3418	+	24.5039i	−0.364048	+	0.862579i
$808$	5.63445			0.198219
$809$			0.459633i			0.0161598i	0.999967	+	0.00807991i	$0.00257194\pi$
$809$			0.459633i			0.0161598i	−0.999967	+	0.00807991i	$0.997428\pi$
$810$	22.0198	+	0.587359i	0.773698	+	0.0206377i
$811$	43.6018			1.53107			0.765533	−	0.643396i	$-0.222475\pi$
$811$	43.6018			1.53107			0.765533	+	0.643396i	$0.222475\pi$
$812$	−0.121891			−0.00427753
$813$	−3.52498	−	1.48770i	−0.123626	−	0.0521761i
$814$	5.00774			0.175521
$815$	1.48233			0.0519237
$816$	−1.08211	−	0.456701i	−0.0378815	−	0.0159877i
$817$	−11.5824			−0.405217
$818$		−	3.71087i		−	0.129748i
$819$	−8.80980	+	8.57794i	−0.307839	+	0.299737i
$820$			17.0279i			0.594641i
$821$		−	8.40288i		−	0.293262i	−0.989191	−	0.146631i	$-0.953157\pi$
$821$		−	8.40288i		−	0.293262i	0.989191	−	0.146631i	$-0.0468431\pi$
$822$	−11.2783	+	26.7230i	−0.393377	+	0.932071i
$823$	24.3535			0.848910			0.424455	−	0.905449i	$-0.360466\pi$
$823$	24.3535			0.848910			0.424455	+	0.905449i	$0.360466\pi$
$824$	4.21240			0.146746
$825$	−1.96969	−	0.831299i	−0.0685757	−	0.0289421i
$826$			4.05242i			0.141002i
$827$	−48.9185			−1.70106			−0.850531	−	0.525925i	$-0.823719\pi$
$827$	−48.9185			−1.70106			−0.850531	+	0.525925i	$0.823719\pi$
$828$	11.9836	+	7.96201i	0.416459	+	0.276699i
$829$	−10.6185			−0.368795			−0.184398	−	0.982852i	$-0.559033\pi$
$829$	−10.6185			−0.368795			−0.184398	+	0.982852i	$0.559033\pi$
$830$		−	8.69174i		−	0.301695i
$831$	−3.29141	−	1.38913i	−0.114178	−	0.0481883i
$832$	−4.09869			−0.142097
$833$	0.678121			0.0234955
$834$	−13.5985	+	32.2204i	−0.470878	+	1.11570i
$835$			18.4334i			0.637915i
$836$			1.33019i			0.0460056i
$837$	17.8460	+	45.6454i	0.616848	+	1.57773i
$838$			3.56141i			0.123027i
$839$	−10.5647			−0.364734			−0.182367	−	0.983231i	$-0.558376\pi$
$839$	−10.5647			−0.364734			−0.182367	+	0.983231i	$0.558376\pi$
$840$	−3.90563	−	1.64836i	−0.134757	−	0.0568737i
$841$	28.9851			0.999488
$842$	−3.06440			−0.105606
$843$	37.0123	+	15.6209i	1.27477	+	0.538013i
$844$	8.13866			0.280144
$845$	9.29882			0.319889
$846$	−14.3565	−	14.7445i	−0.493585	−	0.506926i
$847$		−	9.44658i		−	0.324588i
$848$	−10.1388			−0.348169
$849$	14.3297	−	33.9529i	0.491794	−	1.16526i
$850$			0.671575i			0.0230348i
$851$	4.06005	+	18.8365i	0.139177	+	0.645707i
$852$	3.40834	−	8.07574i	0.116768	−	0.276670i
$853$	−0.389839			−0.0133478			−0.00667392	−	0.999978i	$-0.502124\pi$
$853$	−0.389839			−0.0133478			−0.00667392	+	0.999978i	$0.502124\pi$
$854$		−	7.68567i		−	0.262998i
$855$	−5.61456	+	5.46680i	−0.192014	+	0.186961i
$856$			5.08016i			0.173636i
$857$		−	25.6473i		−	0.876096i	−0.898952	−	0.438048i	$-0.855670\pi$
$857$		−	25.6473i		−	0.876096i	0.898952	−	0.438048i	$-0.144330\pi$
$858$	−3.44045	+	8.15183i	−0.117455	+	0.278299i
$859$	−49.9824			−1.70538			−0.852689	−	0.522419i	$-0.825030\pi$
$859$	−49.9824			−1.70538			−0.852689	+	0.522419i	$0.825030\pi$
$860$		−	26.5616i		−	0.905744i
$861$	11.1020	+	4.68555i	0.378355	+	0.159683i
$862$		−	22.2236i		−	0.756937i
$863$			13.5043i			0.459693i	0.973227	+	0.229846i	$0.0738224\pi$
$863$			13.5043i			0.459693i	−0.973227	+	0.229846i	$0.926178\pi$
$864$	4.83943	−	1.89207i	0.164641	−	0.0643697i
$865$		−	43.9683i		−	1.49497i
$866$	39.0727			1.32774
$867$	−26.3940	−	11.1395i	−0.896386	−	0.378316i
$868$		−	9.43198i		−	0.320142i
$869$		−	3.56401i		−	0.120901i
$870$	−0.476061	−	0.200920i	−0.0161400	−	0.00681181i
$871$		−	28.9760i		−	0.981815i
$872$	20.6152			0.698120
$873$	8.12597	−	7.91211i	0.275023	−	0.267784i
$874$	−5.00348	+	1.07846i	−0.169245	+	0.0364794i
$875$		−	9.81370i		−	0.331764i
$876$	−4.68685	−	1.97807i	−0.158354	−	0.0668327i
$877$	−24.5964			−0.830560			−0.415280	−	0.909694i	$-0.636316\pi$
$877$	−24.5964			−0.830560			−0.415280	+	0.909694i	$0.636316\pi$
$878$		−	9.64952i		−	0.325655i
$879$	16.5636	+	6.99059i	0.558676	+	0.235787i
$880$	−3.05050			−0.102832
$881$	−27.3758			−0.922313			−0.461156	−	0.887319i	$-0.652565\pi$
$881$	−27.3758			−0.922313			−0.461156	+	0.887319i	$0.652565\pi$
$882$	−2.14942	+	2.09285i	−0.0723746	+	0.0704698i
$883$	−0.479158			−0.0161250			−0.00806248	−	0.999967i	$-0.502566\pi$
$883$	−0.479158			−0.0161250			−0.00806248	+	0.999967i	$0.502566\pi$
$884$	2.77941			0.0934817
$885$	−6.67983	+	15.8273i	−0.224540	+	0.532027i
$886$	12.5345			0.421106
$887$			37.4226i			1.25653i	0.778000	+	0.628264i	$0.216234\pi$
$887$			37.4226i			1.25653i	−0.778000	+	0.628264i	$0.783766\pi$
$888$	6.41155	+	2.70597i	0.215157	+	0.0908064i
$889$		−	19.4672i		−	0.652909i
$890$			4.23391i			0.141921i
$891$	0.299104	−	11.2133i	0.0100204	−	0.375659i
$892$	−17.0807			−0.571903
$893$	7.32115			0.244993
$894$	10.6686	−	25.2782i	0.356810	−	0.845428i
$895$		−	7.77914i		−	0.260028i
$896$	−1.00000			−0.0334077
$897$	−33.4523	−	6.33203i	−1.11694	−	0.211420i
$898$	−37.5031			−1.25149
$899$		−	1.14967i		−	0.0383437i
$900$	−2.07265	−	2.12867i	−0.0690882	−	0.0709556i
$901$	6.87536			0.229051
$902$	8.67121			0.288720
$903$	−17.3179	−	7.30893i	−0.576302	−	0.243226i
$904$			18.5411i			0.616669i
$905$			56.6665i			1.88366i
$906$	0.486783	−	1.15339i	0.0161723	−	0.0383187i
$907$			26.0835i			0.866088i	0.901373	+	0.433044i	$0.142561\pi$
$907$			26.0835i			0.866088i	−0.901373	+	0.433044i	$0.857439\pi$
$908$	10.2150			0.338997
$909$	12.1108	−	11.7921i	0.401689	−	0.391118i
$910$	10.0316			0.332545
$911$	38.6903			1.28187			0.640933	−	0.767597i	$-0.278548\pi$
$911$	38.6903			1.28187			0.640933	+	0.767597i	$0.278548\pi$
$912$	−0.718778	+	1.70308i	−0.0238011	+	0.0563946i
$913$	−4.42614			−0.146484
$914$	−21.4399			−0.709170
$915$	12.6687	−	30.0174i	0.418815	−	0.992345i
$916$		−	11.2623i		−	0.372118i
$917$	10.5381			0.347999
$918$	−3.28172	+	1.28305i	−0.108313	+	0.0423471i
$919$			26.3922i			0.870599i	0.900286	+	0.435299i	$0.143358\pi$
$919$			26.3922i			0.870599i	−0.900286	+	0.435299i	$0.856642\pi$
$920$	−2.47321	−	11.4744i	−0.0815392	−	0.378299i
$921$	−5.41963	−	2.28733i	−0.178583	−	0.0753702i
$922$	−13.1851			−0.434230
$923$			20.7426i			0.682750i
$924$	−0.839401	+	1.98889i	−0.0276143	+	0.0654295i
$925$		−	3.97910i		−	0.130832i
$926$		−	10.0041i		−	0.328756i
$927$	9.05420	−	8.81591i	0.297379	−	0.289553i
$928$	−0.121891			−0.00400126
$929$		−	40.0029i		−	1.31245i	−0.754564	−	0.656226i	$-0.772152\pi$
$929$		−	40.0029i		−	1.31245i	0.754564	−	0.656226i	$-0.227848\pi$
$930$	15.5473	−	36.8378i	0.509815	−	1.20796i
$931$		−	1.06726i		−	0.0349780i
$932$			18.0033i			0.589717i
$933$	−2.16381	+	5.12696i	−0.0708400	+	0.167849i
$934$			6.26525i			0.205005i
$935$	2.06860			0.0676506
$936$	−8.80980	+	8.57794i	−0.287957	+	0.280379i
$937$		−	18.2465i		−	0.596089i	−0.954552	−	0.298044i	$-0.903666\pi$
$937$		−	18.2465i		−	0.596089i	0.954552	−	0.298044i	$-0.0963343\pi$
$938$		−	7.06957i		−	0.230830i
$939$	−7.88960	+	18.6937i	−0.257467	+	0.610046i
$940$			16.7894i			0.547610i
$941$	−29.1179			−0.949215			−0.474608	−	0.880198i	$-0.657410\pi$
$941$	−29.1179			−0.949215			−0.474608	+	0.880198i	$0.657410\pi$
$942$	4.57655	+	1.93152i	0.149112	+	0.0629322i
$943$	7.03023	+	32.6166i	0.228936	+	1.06214i
$944$			4.05242i			0.131895i
$945$	−11.8446	+	4.63089i	−0.385304	+	0.150643i
$946$	−13.5261			−0.439772
$947$			8.21685i			0.267012i	0.991048	+	0.133506i	$0.0426235\pi$
$947$			8.21685i			0.267012i	−0.991048	+	0.133506i	$0.957377\pi$
$948$	1.92584	−	4.56310i	0.0625483	−	0.148202i
$949$	12.0382			0.390776
$950$	1.05696			0.0342922
$951$	5.91440	−	14.0136i	0.191787	−	0.454423i
$952$	0.678121			0.0219780
$953$	39.9684			1.29470			0.647351	−	0.762192i	$-0.275877\pi$
$953$	39.9684			1.29470			0.647351	+	0.762192i	$0.275877\pi$
$954$	−21.7926	+	21.2190i	−0.705561	+	0.686992i
$955$	−26.4754			−0.856723
$956$		−	27.7414i		−	0.897222i
$957$	−0.102315	+	0.242427i	−0.00330739	+	0.00783655i
$958$		−	32.9762i		−	1.06541i
$959$		−	16.7463i		−	0.540767i
$960$	−3.90563	−	1.64836i	−0.126054	−	0.0532005i
$961$	57.9622			1.86975
$962$	−16.4681			−0.530952
$963$	10.6320	+	10.9194i	0.342611	+	0.351872i
$964$		−	1.73816i		−	0.0559822i
$965$	−49.0285			−1.57828
$966$	−8.16170	−	1.54489i	−0.262598	−	0.0497060i
$967$	−43.9116			−1.41210			−0.706051	−	0.708161i	$-0.749525\pi$
$967$	−43.9116			−1.41210			−0.706051	+	0.708161i	$0.749525\pi$
$968$		−	9.44658i		−	0.303625i
$969$	0.487418	−	1.15489i	0.0156581	−	0.0371005i
$970$	−9.25296			−0.297095
$971$	−34.2752			−1.09994			−0.549972	−	0.835183i	$-0.685362\pi$
$971$	−34.2752			−1.09994			−0.549972	+	0.835183i	$0.685362\pi$
$972$	6.44212	−	14.1950i	0.206631	−	0.455306i
$973$		−	20.1914i		−	0.647306i
$974$		−	28.2063i		−	0.903788i
$975$	6.47736	+	2.73375i	0.207442	+	0.0875499i
$976$		−	7.68567i		−	0.246012i
$977$	54.6399			1.74808			0.874042	−	0.485850i	$-0.161490\pi$
$977$	54.6399			1.74808			0.874042	+	0.485850i	$0.161490\pi$
$978$	0.407891	−	0.966461i	0.0130429	−	0.0309040i
$979$	2.15605			0.0689078
$980$	2.44752			0.0781831
$981$	44.3107	−	43.1445i	1.41473	−	1.37750i
$982$	−14.4289			−0.460444
$983$	51.0151			1.62713			0.813565	−	0.581475i	$-0.197524\pi$
$983$	51.0151			1.62713			0.813565	+	0.581475i	$0.197524\pi$
$984$	11.1020	+	4.68555i	0.353919	+	0.149370i
$985$			42.4388i			1.35221i
$986$	0.0826568			0.00263233
$987$	10.9465	+	4.61992i	0.348431	+	0.147054i
$988$		−	4.37436i		−	0.139167i
$989$	−10.9664	−	50.8782i	−0.348710	−	1.61783i
$990$	−6.55678	+	6.38422i	−0.208388	+	0.202904i
$991$	11.8804			0.377393			0.188696	−	0.982035i	$-0.439574\pi$
$991$	11.8804			0.377393			0.188696	+	0.982035i	$0.439574\pi$
$992$		−	9.43198i		−	0.299466i
$993$	4.37174	+	1.84507i	0.138733	+	0.0585517i
$994$			5.06078i			0.160518i
$995$			29.5762i			0.937628i
$996$	−5.66690	−	2.39170i	−0.179563	−	0.0757838i
$997$	4.50823			0.142777			0.0713886	−	0.997449i	$-0.477257\pi$
$997$	4.50823			0.142777			0.0713886	+	0.997449i	$0.477257\pi$
$998$		−	8.21278i		−	0.259971i
$999$	19.4443	−	7.60214i	0.615189	−	0.240521i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	966.2.h.a.827.11	✓	24
3.2	odd	2		966.2.h.b.827.23	yes	24
23.22	odd	2		966.2.h.b.827.11	yes	24
69.68	even	2	inner	966.2.h.a.827.23	yes	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
966.2.h.a.827.11	✓	24	1.1	even	1	trivial
966.2.h.a.827.23	yes	24	69.68	even	2	inner
966.2.h.b.827.11	yes	24	23.22	odd	2
966.2.h.b.827.23	yes	24	3.2	odd	2

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:	\( N \)	\(=\)	\( 966 = 2 \cdot 3 \cdot 7 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	966.h (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-1.00000i q^{2} +(1.59575 + 0.673481i) q^{3} -1.00000 q^{4} +2.44752 q^{5} +(0.673481 - 1.59575i) q^{6} +1.00000i q^{7} +1.00000i q^{8} +(2.09285 + 2.14942i) q^{9} +O(q^{10})\)	\(q-1.00000i q^{2} +(1.59575 + 0.673481i) q^{3} -1.00000 q^{4} +2.44752 q^{5} +(0.673481 - 1.59575i) q^{6} +1.00000i q^{7} +1.00000i q^{8} +(2.09285 + 2.14942i) q^{9} -2.44752i q^{10} -1.24636 q^{11} +(-1.59575 - 0.673481i) q^{12} +4.09869 q^{13} +1.00000 q^{14} +(3.90563 + 1.64836i) q^{15} +1.00000 q^{16} -0.678121 q^{17} +(2.14942 - 2.09285i) q^{18} +1.06726i q^{19} -2.44752 q^{20} +(-0.673481 + 1.59575i) q^{21} +1.24636i q^{22} +(-4.68817 + 1.01050i) q^{23} +(-0.673481 + 1.59575i) q^{24} +0.990347 q^{25} -4.09869i q^{26} +(1.89207 + 4.83943i) q^{27} -1.00000i q^{28} -0.121891i q^{29} +(1.64836 - 3.90563i) q^{30} +9.43198 q^{31} -1.00000i q^{32} +(-1.98889 - 0.839401i) q^{33} +0.678121i q^{34} +2.44752i q^{35} +(-2.09285 - 2.14942i) q^{36} -4.01789i q^{37} +1.06726 q^{38} +(6.54050 + 2.76039i) q^{39} +2.44752i q^{40} -6.95722i q^{41} +(1.59575 + 0.673481i) q^{42} +10.8525i q^{43} +1.24636 q^{44} +(5.12228 + 5.26074i) q^{45} +(1.01050 + 4.68817i) q^{46} -6.85977i q^{47} +(1.59575 + 0.673481i) q^{48} -1.00000 q^{49} -0.990347i q^{50} +(-1.08211 - 0.456701i) q^{51} -4.09869 q^{52} -10.1388 q^{53} +(4.83943 - 1.89207i) q^{54} -3.05050 q^{55} -1.00000 q^{56} +(-0.718778 + 1.70308i) q^{57} -0.121891 q^{58} +4.05242i q^{59} +(-3.90563 - 1.64836i) q^{60} -7.68567i q^{61} -9.43198i q^{62} +(-2.14942 + 2.09285i) q^{63} -1.00000 q^{64} +10.0316 q^{65} +(-0.839401 + 1.98889i) q^{66} -7.06957i q^{67} +0.678121 q^{68} +(-8.16170 - 1.54489i) q^{69} +2.44752 q^{70} +5.06078i q^{71} +(-2.14942 + 2.09285i) q^{72} +2.93708 q^{73} -4.01789 q^{74} +(1.58035 + 0.666980i) q^{75} -1.06726i q^{76} -1.24636i q^{77} +(2.76039 - 6.54050i) q^{78} +2.85953i q^{79} +2.44752 q^{80} +(-0.239981 + 8.99680i) q^{81} -6.95722 q^{82} +3.55124 q^{83} +(0.673481 - 1.59575i) q^{84} -1.65971 q^{85} +10.8525 q^{86} +(0.0820912 - 0.194508i) q^{87} -1.24636i q^{88} -1.72988 q^{89} +(5.26074 - 5.12228i) q^{90} +4.09869i q^{91} +(4.68817 - 1.01050i) q^{92} +(15.0511 + 6.35225i) q^{93} -6.85977 q^{94} +2.61213i q^{95} +(0.673481 - 1.59575i) q^{96} -3.78055i q^{97} +1.00000i q^{98} +(-2.60845 - 2.67895i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 4 q^{3} - 24 q^{4} - 4 q^{5} - 4 q^{9}+O(q^{10}) \) 24 * q + 4 * q^3 - 24 * q^4 - 4 * q^5 - 4 * q^9	\( 24 q + 4 q^{3} - 24 q^{4} - 4 q^{5} - 4 q^{9} - 4 q^{12} + 8 q^{13} + 24 q^{14} - 4 q^{15} + 24 q^{16} + 32 q^{17} + 4 q^{18} + 4 q^{20} - 8 q^{23} - 12 q^{25} + 16 q^{27} - 4 q^{30} - 16 q^{31} + 20 q^{33} + 4 q^{36} - 8 q^{39} + 4 q^{42} + 24 q^{45} - 4 q^{46} + 4 q^{48} - 24 q^{49} + 24 q^{51} - 8 q^{52} + 24 q^{53} - 12 q^{54} + 16 q^{55} - 24 q^{56} + 4 q^{57} + 4 q^{58} + 4 q^{60} - 4 q^{63} - 24 q^{64} - 12 q^{66} - 32 q^{68} - 24 q^{69} - 4 q^{70} - 4 q^{72} - 32 q^{73} - 16 q^{74} + 48 q^{75} + 12 q^{78} - 4 q^{80} - 8 q^{81} - 8 q^{82} + 16 q^{83} - 16 q^{85} + 16 q^{86} + 20 q^{87} + 24 q^{89} - 28 q^{90} + 8 q^{92} + 16 q^{93} + 8 q^{94} - 48 q^{99}+O(q^{100}) \) 24 * q + 4 * q^3 - 24 * q^4 - 4 * q^5 - 4 * q^9 - 4 * q^12 + 8 * q^13 + 24 * q^14 - 4 * q^15 + 24 * q^16 + 32 * q^17 + 4 * q^18 + 4 * q^20 - 8 * q^23 - 12 * q^25 + 16 * q^27 - 4 * q^30 - 16 * q^31 + 20 * q^33 + 4 * q^36 - 8 * q^39 + 4 * q^42 + 24 * q^45 - 4 * q^46 + 4 * q^48 - 24 * q^49 + 24 * q^51 - 8 * q^52 + 24 * q^53 - 12 * q^54 + 16 * q^55 - 24 * q^56 + 4 * q^57 + 4 * q^58 + 4 * q^60 - 4 * q^63 - 24 * q^64 - 12 * q^66 - 32 * q^68 - 24 * q^69 - 4 * q^70 - 4 * q^72 - 32 * q^73 - 16 * q^74 + 48 * q^75 + 12 * q^78 - 4 * q^80 - 8 * q^81 - 8 * q^82 + 16 * q^83 - 16 * q^85 + 16 * q^86 + 20 * q^87 + 24 * q^89 - 28 * q^90 + 8 * q^92 + 16 * q^93 + 8 * q^94 - 48 * q^99

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