LMFDB - Embedded newform 966.2.h.b.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.b.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} +(6.80060 + 4.76989i) 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	$-0.684337\pi$
$5$	−2.44752			−1.09456			−0.547282	+	0.836948i	$0.684337\pi$
$6$	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	$-0.439833\pi$
$11$	1.24636			0.375792			0.187896	+	0.982189i	$0.439833\pi$
$12$	−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	$-0.473794\pi$
$17$	0.678121			0.164468			0.0822342	+	0.996613i	$0.473794\pi$
$18$	2.14942	−	2.09285i	0.506622	−	0.493289i
$19$		−	1.06726i		−	0.244846i	−0.992478	−	0.122423i	$-0.960934\pi$
$19$		−	1.06726i		−	0.244846i	0.992478	−	0.122423i	$-0.0390664\pi$
$20$	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	$0.107139\pi$
$37$			4.01789i			0.660536i	−0.943887	+	0.330268i	$0.892861\pi$
$38$	−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	$-0.689766\pi$
$43$		−	10.8525i		−	1.65499i	0.561476	−	0.827493i	$-0.310234\pi$
$44$	−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	$-0.254811\pi$
$53$	10.1388			1.39268			0.696338	+	0.717714i	$0.254811\pi$
$54$	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	$0.163743\pi$
$61$			7.68567i			0.984050i	−0.870581	+	0.492025i	$0.836257\pi$
$62$		−	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	$0.142137\pi$
$67$			7.06957i			0.863686i	−0.901949	+	0.431843i	$0.857863\pi$
$68$	−0.678121			−0.0822342
$69$	6.80060	+	4.76989i	0.818696	+	0.574227i
$70$	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	$-0.948573\pi$
$79$		−	2.85953i		−	0.321722i	0.986977	−	0.160861i	$-0.0514271\pi$
$80$	−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	$-0.562438\pi$
$83$	−3.55124			−0.389800			−0.194900	+	0.980823i	$0.562438\pi$
$84$	−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	$-0.470775\pi$
$89$	1.72988			0.183367			0.0916833	+	0.995788i	$0.470775\pi$
$90$	−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	$0.0614741\pi$
$97$			3.78055i			0.383857i	−0.981409	+	0.191928i	$0.938526\pi$
$98$			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	$0.0665425\pi$
$103$			4.21240i			0.415060i	−0.978229	+	0.207530i	$0.933458\pi$
$104$			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	$-0.578971\pi$
$107$	−5.08016			−0.491117			−0.245559	+	0.969382i	$0.578971\pi$
$108$	−1.89207	−	4.83943i	−0.182065	−	0.465674i
$109$			20.6152i			1.97458i	0.158926	+	0.987290i	$0.449197\pi$
$109$			20.6152i			1.97458i	−0.158926	+	0.987290i	$0.550803\pi$
$110$			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	$-0.837244\pi$
$113$	−18.5411			−1.74420			−0.872102	+	0.489324i	$0.837244\pi$
$114$	−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	$-0.246259\pi$
$137$	16.7463			1.43074			0.715368	+	0.698748i	$0.246259\pi$
$138$	4.76989	−	6.80060i	0.406040	−	0.578906i
$139$	−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	$-0.724758\pi$
$149$	−15.8409			−1.29774			−0.648869	+	0.760900i	$0.724758\pi$
$150$	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	$-0.963491\pi$
$157$		−	2.86796i		−	0.228888i	0.993430	−	0.114444i	$-0.0365087\pi$
$158$	−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	$-0.670175\pi$
$181$		−	23.1527i		−	1.72092i	0.509515	−	0.860462i	$-0.329825\pi$
$182$	−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	$-0.372007\pi$
$191$	10.8172			0.782707			0.391353	+	0.920240i	$0.372007\pi$
$192$	−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	$-0.859109\pi$
$199$		−	12.0842i		−	0.856623i	0.903631	−	0.428312i	$-0.140891\pi$
$200$			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
$207$	7.63964	+	12.1916i	0.530992	+	0.847377i
$208$	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	$-0.389912\pi$
$227$	10.2150			0.677994			0.338997	+	0.940787i	$0.389912\pi$
$228$	−0.718778	+	1.70308i	−0.0476022	+	0.112789i
$229$		−	11.2623i		−	0.744235i	−0.928186	−	0.372118i	$-0.878632\pi$
$229$		−	11.2623i		−	0.744235i	0.928186	−	0.372118i	$-0.121368\pi$
$230$	−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	$-0.982171\pi$
$241$		−	1.73816i		−	0.111964i	0.998432	−	0.0559822i	$-0.0178290\pi$
$242$			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	$-0.420341\pi$
$251$	7.84707			0.495303			0.247651	+	0.968849i	$0.420341\pi$
$252$	−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	$-0.349075\pi$
$263$	14.8089			0.913155			0.456577	+	0.889684i	$0.349075\pi$
$264$	−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
$276$	−6.80060	−	4.76989i	−0.409348	−	0.287114i
$277$	−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	$-0.743194\pi$
$281$	−23.1943			−1.38365			−0.691827	+	0.722063i	$0.743194\pi$
$282$	−10.9465	−	4.61992i	−0.651854	−	0.275112i
$283$			21.2771i			1.26479i	0.774646	+	0.632395i	$0.217928\pi$
$283$			21.2771i			1.26479i	−0.774646	+	0.632395i	$0.782072\pi$
$284$		−	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	$-0.598054\pi$
$293$	−10.3798			−0.606394			−0.303197	+	0.952928i	$0.598054\pi$
$294$	−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	$-0.892588\pi$
$313$		−	11.7147i		−	0.662152i	0.943604	−	0.331076i	$-0.107412\pi$
$314$	−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	$-0.929844\pi$
$337$		−	8.02671i		−	0.437243i	0.975810	−	0.218621i	$-0.0701560\pi$
$338$		−	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
$345$	−16.6446	−	11.6744i	−0.896115	−	0.628528i
$346$	−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	$-0.303486\pi$
$359$	21.9369			1.15778			0.578891	+	0.815405i	$0.303486\pi$
$360$	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	$-0.881974\pi$
$367$		−	13.8833i		−	0.724702i	0.932042	−	0.362351i	$-0.118026\pi$
$368$	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	$0.323116\pi$
$373$			32.8144i			1.69907i	−0.527536	+	0.849533i	$0.676884\pi$
$374$		−	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	$0.260674\pi$
$379$			28.4394i			1.46083i	−0.683002	+	0.730416i	$0.739326\pi$
$380$		−	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	$-0.577998\pi$
$383$	−9.49524			−0.485184			−0.242592	+	0.970128i	$0.577998\pi$
$384$	−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	$-0.519908\pi$
$389$	−2.46547			−0.125004			−0.0625021	+	0.998045i	$0.519908\pi$
$390$	−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	$-0.327928\pi$
$401$	20.6111			1.02927			0.514634	+	0.857410i	$0.327928\pi$
$402$	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
$414$	12.1916	−	7.63964i	0.599186	−	0.375468i
$415$	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	$-0.472274\pi$
$419$	3.56141			0.173986			0.0869932	+	0.996209i	$0.472274\pi$
$420$	1.64836	−	3.90563i	0.0804316	−	0.190575i
$421$			3.06440i			0.149350i	0.997208	+	0.0746748i	$0.0237919\pi$
$421$			3.06440i			0.149350i	−0.997208	+	0.0746748i	$0.976208\pi$
$422$			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	$-0.679777\pi$
$431$	−22.2236			−1.07047			−0.535236	+	0.844703i	$0.679777\pi$
$432$	1.89207	+	4.83943i	0.0910324	+	0.232837i
$433$		−	39.0727i		−	1.87771i	−0.344306	−	0.938857i	$-0.611886\pi$
$433$		−	39.0727i		−	1.87771i	0.344306	−	0.938857i	$-0.388114\pi$
$434$	−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	$0.167203\pi$
$457$			21.4399i			1.00292i	−0.865182	+	0.501459i	$0.832797\pi$
$458$	−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	$-0.453694\pi$
$467$	6.26525			0.289921			0.144961	+	0.989437i	$0.453694\pi$
$468$	−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	$-0.771569\pi$
$479$	−32.9762			−1.50672			−0.753361	+	0.657607i	$0.771569\pi$
$480$	−1.64836	+	3.90563i	−0.0752369	+	0.178267i
$481$			16.4681i			0.750880i
$482$	−1.73816			−0.0791708
$483$	4.76989	−	6.80060i	0.217037	−	0.309438i
$484$	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	$-0.583954\pi$
$503$	−11.6938			−0.521402			−0.260701	+	0.965420i	$0.583954\pi$
$504$	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	$-0.662098\pi$
$521$	−22.2556			−0.975037			−0.487518	+	0.873113i	$0.662098\pi$
$522$	−0.255099	−	0.261994i	−0.0111654	−	0.0114672i
$523$		−	35.2887i		−	1.54307i	−0.636189	−	0.771533i	$-0.719490\pi$
$523$		−	35.2887i		−	1.54307i	0.636189	−	0.771533i	$-0.280510\pi$
$524$			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
$552$	−4.76989	+	6.80060i	−0.203020	+	0.289453i
$553$	−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	$-0.604712\pi$
$557$	−15.2491			−0.646124			−0.323062	+	0.946378i	$0.604712\pi$
$558$	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	$-0.689648\pi$
$563$	−26.6304			−1.12234			−0.561168	+	0.827702i	$0.689648\pi$
$564$	−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	$-0.672597\pi$
$569$	−24.6193			−1.03210			−0.516048	+	0.856560i	$0.672597\pi$
$570$	4.16832	+	1.75922i	0.174592	+	0.0736857i
$571$			27.5098i			1.15125i	0.817714	+	0.575624i	$0.195241\pi$
$571$			27.5098i			1.15125i	−0.817714	+	0.575624i	$0.804759\pi$
$572$	−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	$0.141257\pi$
$613$			21.2604i			0.858698i	−0.903139	+	0.429349i	$0.858743\pi$
$614$			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	$-0.464113\pi$
$617$	5.58908			0.225008			0.112504	+	0.993651i	$0.464113\pi$
$618$	6.72195	+	2.83697i	0.270396	+	0.114120i
$619$			44.0173i			1.76920i	0.466348	+	0.884601i	$0.345569\pi$
$619$			44.0173i			1.76920i	−0.466348	+	0.884601i	$0.654431\pi$
$620$	23.0849			0.927113
$621$	3.98014	+	24.6000i	0.159717	+	0.987163i
$622$	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	$-0.602544\pi$
$631$		−	47.6549i		−	1.89711i	0.316609	−	0.948556i	$-0.397456\pi$
$632$	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	$-0.711287\pi$
$641$	−31.1966			−1.23219			−0.616097	+	0.787671i	$0.711287\pi$
$642$	−3.42139	+	8.10667i	−0.135031	+	0.319945i
$643$		−	0.314769i		−	0.0124133i	−0.999981	−	0.00620664i	$-0.998024\pi$
$643$		−	0.314769i		−	0.0124133i	0.999981	−	0.00620664i	$-0.00197565\pi$
$644$	−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	$-0.669900\pi$
$659$	−26.1213			−1.01754			−0.508771	+	0.860902i	$0.669900\pi$
$660$	4.86783	+	2.05445i	0.189480	+	0.0799694i
$661$		−	18.2937i		−	0.711543i	−0.934573	−	0.355771i	$-0.884218\pi$
$661$		−	18.2937i		−	0.711543i	0.934573	−	0.355771i	$-0.115782\pi$
$662$		−	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	$-0.841015\pi$
$677$	−45.6813			−1.75568			−0.877838	+	0.478957i	$0.841015\pi$
$678$	−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
$690$	−11.6744	+	16.6446i	−0.444437	+	0.633649i
$691$	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	$-0.766638\pi$
$701$	−39.3484			−1.48617			−0.743085	+	0.669197i	$0.766638\pi$
$702$	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	$-0.828807\pi$
$709$		−	27.2802i		−	1.02453i	0.858828	−	0.512264i	$-0.171193\pi$
$710$	−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	$0.0973917\pi$
$727$			16.2432i			0.602427i	−0.953557	+	0.301214i	$0.902608\pi$
$728$	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	$-0.871989\pi$
$733$		−	21.1938i		−	0.782811i	0.920218	−	0.391405i	$-0.128011\pi$
$734$	−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	$-0.517399\pi$
$743$	−2.97839			−0.109266			−0.0546332	+	0.998506i	$0.517399\pi$
$744$	−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	$0.0499268\pi$
$751$			8.56153i			0.312415i	−0.987724	+	0.156207i	$0.950073\pi$
$752$		−	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	$-0.838274\pi$
$757$		−	26.7707i		−	0.972999i	0.873681	−	0.486499i	$-0.161726\pi$
$758$	28.4394			1.03296
$759$	8.47601	+	5.94501i	0.307660	+	0.215790i
$760$	−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	$-0.801594\pi$
$769$		−	32.3745i		−	1.16746i	0.811949	−	0.583728i	$-0.198406\pi$
$770$	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	$-0.431078\pi$
$773$	11.9462			0.429674			0.214837	+	0.976650i	$0.431078\pi$
$774$	−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	$0.329502\pi$
$787$			48.2489i			1.71989i	−0.510388	+	0.859944i	$0.670498\pi$
$788$		−	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	$-0.409595\pi$
$797$	15.8214			0.560424			0.280212	+	0.959938i	$0.409595\pi$
$798$	−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	$-0.176281\pi$
$827$	48.9185			1.70106			0.850531	+	0.525925i	$0.176281\pi$
$828$	−7.63964	−	12.1916i	−0.265496	−	0.423689i
$829$	−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	$-0.441624\pi$
$839$	10.5647			0.364734			0.182367	+	0.983231i	$0.441624\pi$
$840$	−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	$-0.347435\pi$
$881$	27.3758			0.922313			0.461156	+	0.887319i	$0.347435\pi$
$882$	−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
$897$	27.8736	+	19.5503i	0.930671	+	0.652766i
$898$	−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	$-0.857439\pi$
$907$		−	26.0835i		−	0.866088i	0.901373	−	0.433044i	$-0.142561\pi$
$908$	−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	$-0.721452\pi$
$911$	−38.6903			−1.28187			−0.640933	+	0.767597i	$0.721452\pi$
$912$	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	$-0.856642\pi$
$919$		−	26.3922i		−	0.870599i	0.900286	−	0.435299i	$-0.143358\pi$
$920$	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	$0.0963343\pi$
$937$			18.2465i			0.596089i	−0.954552	+	0.298044i	$0.903666\pi$
$938$		−	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	$-0.342590\pi$
$941$	29.1179			0.949215			0.474608	+	0.880198i	$0.342590\pi$
$942$	−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	$-0.724123\pi$
$953$	−39.9684			−1.29470			−0.647351	+	0.762192i	$0.724123\pi$
$954$	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
$966$	−6.80060	−	4.76989i	−0.218806	−	0.153469i
$967$	−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	$-0.314638\pi$
$971$	34.2752			1.09994			0.549972	+	0.835183i	$0.314638\pi$
$972$	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	$-0.838510\pi$
$977$	−54.6399			−1.74808			−0.874042	+	0.485850i	$0.838510\pi$
$978$	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	$-0.802476\pi$
$983$	−51.0151			−1.62713			−0.813565	+	0.581475i	$0.802476\pi$
$984$	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.b.827.11	yes	24
3.2	odd	2		966.2.h.a.827.23	yes	24
23.22	odd	2		966.2.h.a.827.11	✓	24
69.68	even	2	inner	966.2.h.b.827.23	yes	24

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

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} +(6.80060 + 4.76989i) 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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