LMFDB - Embedded newform 189.2.f.b.127.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [189,2,Mod(64,189)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

chi = DirichletCharacter(H, H._module([2, 0]))

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

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

chi := DirichletCharacter("189.64");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 189 = 3^{3} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	189.f (of order $3$, degree $2$, not minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$1.50917259820$
Analytic rank:	$0$
Dimension:	$6$
Relative dimension:	$3$ over $\Q(\zeta_{3})$
Coefficient field:	$\Q(\zeta_{18})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - x^{3} + 1 $ x^6 - x^3 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{4}]$
Coefficient ring index:	$ 3 $
Twist minimal:	no (minimal twist has level 63)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			127.3
Root			$-0.766044 - 0.642788i$ of defining polynomial
Character	$\chi$	$=$	189.127
Dual form			189.2.f.b.64.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.26604 - 2.19285i) q^{2} +(-2.20574 - 3.82045i) q^{4} +(-0.439693 - 0.761570i) q^{5} +(-0.500000 + 0.866025i) q^{7} -6.10607 q^{8} -2.22668 q^{10} +(1.93969 - 3.35965i) q^{11} +(2.72668 + 4.72275i) q^{13} +(1.26604 + 2.19285i) q^{14} +(-3.31908 + 5.74881i) q^{16} -1.65270 q^{17} +2.41147 q^{19} +(-1.93969 + 3.35965i) q^{20} +(-4.91147 - 8.50692i) q^{22} +(1.58125 + 2.73881i) q^{23} +(2.11334 - 3.66041i) q^{25} +13.8084 q^{26} +4.41147 q^{28} +(-3.02481 + 5.23913i) q^{29} +(2.27719 + 3.94421i) q^{31} +(2.29813 + 3.98048i) q^{32} +(-2.09240 + 3.62414i) q^{34} +0.879385 q^{35} -4.55438 q^{37} +(3.05303 - 5.28801i) q^{38} +(2.68479 + 4.65020i) q^{40} +(-0.592396 - 1.02606i) q^{41} +(-0.0923963 + 0.160035i) q^{43} -17.1138 q^{44} +8.00774 q^{46} +(-0.511144 + 0.885328i) q^{47} +(-0.500000 - 0.866025i) q^{49} +(-5.35117 - 9.26849i) q^{50} +(12.0287 - 20.8343i) q^{52} -7.29086 q^{53} -3.41147 q^{55} +(3.05303 - 5.28801i) q^{56} +(7.65910 + 13.2660i) q^{58} +(3.33022 + 5.76811i) q^{59} +(1.29813 - 2.24843i) q^{61} +11.5321 q^{62} -1.63816 q^{64} +(2.39780 - 4.15312i) q^{65} +(1.47906 + 2.56180i) q^{67} +(3.64543 + 6.31407i) q^{68} +(1.11334 - 1.92836i) q^{70} +3.68004 q^{71} -12.7811 q^{73} +(-5.76604 + 9.98708i) q^{74} +(-5.31908 - 9.21291i) q^{76} +(1.93969 + 3.35965i) q^{77} +(2.97906 - 5.15988i) q^{79} +5.83750 q^{80} -3.00000 q^{82} +(-0.109470 + 0.189608i) q^{83} +(0.726682 + 1.25865i) q^{85} +(0.233956 + 0.405223i) q^{86} +(-11.8439 + 20.5142i) q^{88} -11.0273 q^{89} -5.45336 q^{91} +(6.97565 - 12.0822i) q^{92} +(1.29426 + 2.24173i) q^{94} +(-1.06031 - 1.83651i) q^{95} +(-6.25150 + 10.8279i) q^{97} -2.53209 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q + 3 q^{2} - 3 q^{4} + 3 q^{5} - 3 q^{7} - 12 q^{8} + 6 q^{11} + 3 q^{13} + 3 q^{14} - 3 q^{16} - 12 q^{17} - 6 q^{19} - 6 q^{20} - 9 q^{22} + 12 q^{23} + 6 q^{25} + 6 q^{26} + 6 q^{28} + 9 q^{29} + 3 q^{31}+ \cdots - 6 q^{98}+O(q^{100}) $ 6 * q + 3 * q^2 - 3 * q^4 + 3 * q^5 - 3 * q^7 - 12 * q^8 + 6 * q^11 + 3 * q^13 + 3 * q^14 - 3 * q^16 - 12 * q^17 - 6 * q^19 - 6 * q^20 - 9 * q^22 + 12 * q^23 + 6 * q^25 + 6 * q^26 + 6 * q^28 + 9 * q^29 + 3 * q^31 - 9 * q^34 - 6 * q^35 - 6 * q^37 + 6 * q^38 + 9 * q^40 + 3 * q^43 - 30 * q^44 + 3 * q^47 - 3 * q^49 - 6 * q^50 + 21 * q^52 - 12 * q^53 + 6 * q^56 + 9 * q^58 - 3 * q^59 - 6 * q^61 + 60 * q^62 + 24 * q^64 + 15 * q^65 + 12 * q^67 + 6 * q^68 - 18 * q^71 - 42 * q^73 - 30 * q^74 - 15 * q^76 + 6 * q^77 + 21 * q^79 + 30 * q^80 - 18 * q^82 - 18 * q^83 - 9 * q^85 + 6 * q^86 - 27 * q^88 - 24 * q^89 - 6 * q^91 + 3 * q^92 + 18 * q^94 - 12 * q^95 + 3 * q^97 - 6 * q^98

Character values

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

$n$	$29$	$136$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$1$

Coefficient data

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

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

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

$2$	1.26604	−	2.19285i	0.895229	−	1.55058i	0.0617072	−	0.998094i	$-0.480346\pi$
$2$	1.26604	−	2.19285i	0.895229	−	1.55058i	0.833521	−	0.552487i	$-0.186321\pi$
$3$		0			0
$3$		0			0
$4$	−2.20574	−	3.82045i	−1.10287	−	1.91022i
$5$	−0.439693	−	0.761570i	−0.196637	−	0.340584i	0.750799	−	0.660530i	$-0.229669\pi$
$5$	−0.439693	−	0.761570i	−0.196637	−	0.340584i	−0.947436	+	0.319946i	$0.896335\pi$
$6$		0			0
$7$	−0.500000	+	0.866025i	−0.188982	+	0.327327i
$7$	−0.500000	+	0.866025i	−0.188982	+	0.327327i
$8$	−6.10607			−2.15882
$9$		0			0
$10$	−2.22668			−0.704139
$11$	1.93969	−	3.35965i	0.584839	−	1.01297i	−0.410056	−	0.912060i	$-0.634491\pi$
$11$	1.93969	−	3.35965i	0.584839	−	1.01297i	0.994895	−	0.100911i	$-0.0321758\pi$
$12$		0			0
$13$	2.72668	+	4.72275i	0.756245	+	1.30986i	0.944753	+	0.327784i	$0.106302\pi$
$13$	2.72668	+	4.72275i	0.756245	+	1.30986i	−0.188507	+	0.982072i	$0.560365\pi$
$14$	1.26604	+	2.19285i	0.338365	+	0.586065i
$15$		0			0
$16$	−3.31908	+	5.74881i	−0.829769	+	1.43720i
$17$	−1.65270			−0.400840			−0.200420	−	0.979710i	$-0.564231\pi$
$17$	−1.65270			−0.400840			−0.200420	+	0.979710i	$0.564231\pi$
$18$		0			0
$19$	2.41147			0.553230			0.276615	−	0.960981i	$-0.410787\pi$
$19$	2.41147			0.553230			0.276615	+	0.960981i	$0.410787\pi$
$20$	−1.93969	+	3.35965i	−0.433728	+	0.751240i
$21$		0			0
$22$	−4.91147	−	8.50692i	−1.04713	−	1.81368i
$23$	1.58125	+	2.73881i	0.329714	+	0.571081i	0.982455	−	0.186500i	$-0.0597144\pi$
$23$	1.58125	+	2.73881i	0.329714	+	0.571081i	−0.652741	+	0.757581i	$0.726381\pi$
$24$		0			0
$25$	2.11334	−	3.66041i	0.422668	−	0.732083i
$26$	13.8084			2.70805
$27$		0			0
$28$	4.41147			0.833690
$29$	−3.02481	+	5.23913i	−0.561694	+	0.972883i	0.435655	+	0.900114i	$0.356517\pi$
$29$	−3.02481	+	5.23913i	−0.561694	+	0.972883i	−0.997349	+	0.0727688i	$0.976816\pi$
$30$		0			0
$31$	2.27719	+	3.94421i	0.408995	+	0.708400i	0.994777	−	0.102068i	$-0.0325459\pi$
$31$	2.27719	+	3.94421i	0.408995	+	0.708400i	−0.585782	+	0.810468i	$0.699213\pi$
$32$	2.29813	+	3.98048i	0.406256	+	0.703657i
$33$		0			0
$34$	−2.09240	+	3.62414i	−0.358843	+	0.621534i
$35$	0.879385			0.148643
$36$		0			0
$37$	−4.55438			−0.748735			−0.374368	−	0.927280i	$-0.622140\pi$
$37$	−4.55438			−0.748735			−0.374368	+	0.927280i	$0.622140\pi$
$38$	3.05303	−	5.28801i	0.495267	−	0.857828i
$39$		0			0
$40$	2.68479	+	4.65020i	0.424503	+	0.735261i
$41$	−0.592396	−	1.02606i	−0.0925168	−	0.160244i	0.816053	−	0.577977i	$-0.196158\pi$
$41$	−0.592396	−	1.02606i	−0.0925168	−	0.160244i	−0.908570	+	0.417734i	$0.862825\pi$
$42$		0			0
$43$	−0.0923963	+	0.160035i	−0.0140903	+	0.0244051i	−0.872985	−	0.487748i	$-0.837819\pi$
$43$	−0.0923963	+	0.160035i	−0.0140903	+	0.0244051i	0.858894	+	0.512153i	$0.171152\pi$
$44$	−17.1138			−2.58000
$45$		0			0
$46$	8.00774			1.18068
$47$	−0.511144	+	0.885328i	−0.0745581	+	0.129138i	−0.900894	−	0.434039i	$-0.857088\pi$
$47$	−0.511144	+	0.885328i	−0.0745581	+	0.129138i	0.826336	+	0.563178i	$0.190421\pi$
$48$		0			0
$49$	−0.500000	−	0.866025i	−0.0714286	−	0.123718i
$50$	−5.35117	−	9.26849i	−0.756769	−	1.31076i
$51$		0			0
$52$	12.0287	−	20.8343i	1.66808	−	2.88920i
$53$	−7.29086			−1.00148			−0.500738	−	0.865599i	$-0.666938\pi$
$53$	−7.29086			−1.00148			−0.500738	+	0.865599i	$0.666938\pi$
$54$		0			0
$55$	−3.41147			−0.460003
$56$	3.05303	−	5.28801i	0.407979	−	0.706640i
$57$		0			0
$58$	7.65910	+	13.2660i	1.00569	+	1.74190i
$59$	3.33022	+	5.76811i	0.433558	+	0.750944i	0.997177	−	0.0750906i	$-0.0239246\pi$
$59$	3.33022	+	5.76811i	0.433558	+	0.750944i	−0.563619	+	0.826035i	$0.690591\pi$
$60$		0			0
$61$	1.29813	−	2.24843i	0.166209	−	0.287882i	−0.770875	−	0.636986i	$-0.780181\pi$
$61$	1.29813	−	2.24843i	0.166209	−	0.287882i	0.937084	+	0.349104i	$0.113514\pi$
$62$	11.5321			1.46458
$63$		0			0
$64$	−1.63816			−0.204769
$65$	2.39780	−	4.15312i	0.297411	−	0.515131i
$66$		0			0
$67$	1.47906	+	2.56180i	0.180695	+	0.312974i	0.942118	−	0.335283i	$-0.108832\pi$
$67$	1.47906	+	2.56180i	0.180695	+	0.312974i	−0.761422	+	0.648256i	$0.775499\pi$
$68$	3.64543	+	6.31407i	0.442073	+	0.765693i
$69$		0			0
$70$	1.11334	−	1.92836i	0.133070	−	0.230483i
$71$	3.68004			0.436741			0.218370	−	0.975866i	$-0.429926\pi$
$71$	3.68004			0.436741			0.218370	+	0.975866i	$0.429926\pi$
$72$		0			0
$73$	−12.7811			−1.49591			−0.747955	−	0.663750i	$-0.768964\pi$
$73$	−12.7811			−1.49591			−0.747955	+	0.663750i	$0.768964\pi$
$74$	−5.76604	+	9.98708i	−0.670289	+	1.16097i
$75$		0			0
$76$	−5.31908	−	9.21291i	−0.610140	−	1.05679i
$77$	1.93969	+	3.35965i	0.221048	+	0.382867i
$78$		0			0
$79$	2.97906	−	5.15988i	0.335170	−	0.580531i	−0.648348	−	0.761345i	$-0.724540\pi$
$79$	2.97906	−	5.15988i	0.335170	−	0.580531i	0.983517	+	0.180813i	$0.0578729\pi$
$80$	5.83750			0.652652
$81$		0			0
$82$	−3.00000			−0.331295
$83$	−0.109470	+	0.189608i	−0.0120159	+	0.0208122i	−0.871971	−	0.489558i	$-0.837158\pi$
$83$	−0.109470	+	0.189608i	−0.0120159	+	0.0208122i	0.859955	+	0.510370i	$0.170492\pi$
$84$		0			0
$85$	0.726682	+	1.25865i	0.0788197	+	0.136520i
$86$	0.233956	+	0.405223i	0.0252281	+	0.0436963i
$87$		0			0
$88$	−11.8439	+	20.5142i	−1.26256	+	2.18682i
$89$	−11.0273			−1.16890			−0.584448	−	0.811431i	$-0.698689\pi$
$89$	−11.0273			−1.16890			−0.584448	+	0.811431i	$0.698689\pi$
$90$		0			0
$91$	−5.45336			−0.571668
$92$	6.97565	−	12.0822i	0.727262	−	1.25965i
$93$		0			0
$94$	1.29426	+	2.24173i	0.133493	+	0.231217i
$95$	−1.06031	−	1.83651i	−0.108785	−	0.188422i
$96$		0			0
$97$	−6.25150	+	10.8279i	−0.634743	+	1.09941i	0.351826	+	0.936065i	$0.385561\pi$
$97$	−6.25150	+	10.8279i	−0.634743	+	1.09941i	−0.986569	+	0.163342i	$0.947773\pi$
$98$	−2.53209			−0.255780
$99$		0			0
$100$	−18.6459			−1.86459
$101$	−4.85844	+	8.41507i	−0.483433	+	0.837330i	−0.999819	−	0.0190255i	$-0.993944\pi$
$101$	−4.85844	+	8.41507i	−0.483433	+	0.837330i	0.516386	+	0.856356i	$0.327277\pi$
$102$		0			0
$103$	−3.29813	−	5.71253i	−0.324975	−	0.562873i	0.656533	−	0.754298i	$-0.272022\pi$
$103$	−3.29813	−	5.71253i	−0.324975	−	0.562873i	−0.981507	+	0.191425i	$0.938689\pi$
$104$	−16.6493	−	28.8374i	−1.63260	−	2.82774i
$105$		0			0
$106$	−9.23055	+	15.9878i	−0.896550	+	1.55287i
$107$	−2.38919			−0.230971			−0.115486	−	0.993309i	$-0.536842\pi$
$107$	−2.38919			−0.230971			−0.115486	+	0.993309i	$0.536842\pi$
$108$		0			0
$109$	3.95811			0.379118			0.189559	−	0.981869i	$-0.439294\pi$
$109$	3.95811			0.379118			0.189559	+	0.981869i	$0.439294\pi$
$110$	−4.31908	+	7.48086i	−0.411808	+	0.713272i
$111$		0			0
$112$	−3.31908	−	5.74881i	−0.313623	−	0.543212i
$113$	8.22668	+	14.2490i	0.773901	+	1.34044i	0.935410	+	0.353565i	$0.115031\pi$
$113$	8.22668	+	14.2490i	0.773901	+	1.34044i	−0.161509	+	0.986871i	$0.551636\pi$
$114$		0			0
$115$	1.39053	−	2.40847i	0.129668	−	0.224591i
$116$	26.6878			2.47790
$117$		0			0
$118$	16.8648			1.55253
$119$	0.826352	−	1.43128i	0.0757515	−	0.131206i
$120$		0			0
$121$	−2.02481	−	3.50708i	−0.184074	−	0.318826i
$122$	−3.28699	−	5.69323i	−0.297590	−	0.515441i
$123$		0			0
$124$	10.0458	−	17.3998i	0.902136	−	1.56255i
$125$	−8.11381			−0.725721
$126$		0			0
$127$	17.6536			1.56651			0.783253	−	0.621702i	$-0.213559\pi$
$127$	17.6536			1.56651			0.783253	+	0.621702i	$0.213559\pi$
$128$	−6.67024	+	11.5532i	−0.589572	+	1.02117i
$129$		0			0
$130$	−6.07145	−	10.5161i	−0.532502	−	0.922320i
$131$	−9.59879	−	16.6256i	−0.838650	−	1.45259i	−0.891023	−	0.453958i	$-0.850012\pi$
$131$	−9.59879	−	16.6256i	−0.838650	−	1.45259i	0.0523729	−	0.998628i	$-0.483322\pi$
$132$		0			0
$133$	−1.20574	+	2.08840i	−0.104551	+	0.181087i
$134$	7.49020			0.647055
$135$		0			0
$136$	10.0915			0.865341
$137$	9.07785	−	15.7233i	0.775573	−	1.34333i	−0.158899	−	0.987295i	$-0.550794\pi$
$137$	9.07785	−	15.7233i	0.775573	−	1.34333i	0.934472	−	0.356037i	$-0.115872\pi$
$138$		0			0
$139$	−11.0287	−	19.1022i	−0.935441	−	1.62023i	−0.773846	−	0.633374i	$-0.781670\pi$
$139$	−11.0287	−	19.1022i	−0.935441	−	1.62023i	−0.161595	−	0.986857i	$-0.551664\pi$
$140$	−1.93969	−	3.35965i	−0.163934	−	0.283942i
$141$		0			0
$142$	4.65910	−	8.06980i	0.390983	−	0.677202i
$143$	21.1557			1.76913
$144$		0			0
$145$	5.31996			0.441798
$146$	−16.1814	+	28.0270i	−1.33918	+	2.31953i
$147$		0			0
$148$	10.0458	+	17.3998i	0.825756	+	1.43025i
$149$	−7.57785	−	13.1252i	−0.620802	−	1.07526i	−0.989337	−	0.145646i	$-0.953474\pi$
$149$	−7.57785	−	13.1252i	−0.620802	−	1.07526i	0.368535	−	0.929614i	$-0.379859\pi$
$150$		0			0
$151$	9.47818	−	16.4167i	0.771323	−	1.33597i	−0.165515	−	0.986207i	$-0.552929\pi$
$151$	9.47818	−	16.4167i	0.771323	−	1.33597i	0.936838	−	0.349764i	$-0.113738\pi$
$152$	−14.7246			−1.19432
$153$		0			0
$154$	9.82295			0.791556
$155$	2.00253	−	3.46848i	0.160847	−	0.278595i
$156$		0			0
$157$	9.02869	+	15.6381i	0.720568	+	1.24806i	0.960773	+	0.277337i	$0.0894520\pi$
$157$	9.02869	+	15.6381i	0.720568	+	1.24806i	−0.240205	+	0.970722i	$0.577215\pi$
$158$	−7.54323	−	13.0653i	−0.600107	−	1.03942i
$159$		0			0
$160$	2.02094	−	3.50038i	0.159770	−	0.276729i
$161$	−3.16250			−0.249240
$162$		0			0
$163$	0.958111			0.0750450			0.0375225	−	0.999296i	$-0.488053\pi$
$163$	0.958111			0.0750450			0.0375225	+	0.999296i	$0.488053\pi$
$164$	−2.61334	+	4.52644i	−0.204068	+	0.353456i
$165$		0			0
$166$	0.277189	+	0.480105i	0.0215140	+	0.0372634i
$167$	9.91921	+	17.1806i	0.767572	+	1.32947i	0.938876	+	0.344255i	$0.111869\pi$
$167$	9.91921	+	17.1806i	0.767572	+	1.32947i	−0.171304	+	0.985218i	$0.554798\pi$
$168$		0			0
$169$	−8.36959	+	14.4965i	−0.643814	+	1.11512i
$170$	3.68004			0.282247
$171$		0			0
$172$	0.815207			0.0621590
$173$	11.3414	−	19.6438i	0.862268	−	1.49349i	−0.00746626	−	0.999972i	$-0.502377\pi$
$173$	11.3414	−	19.6438i	0.862268	−	1.49349i	0.869734	−	0.493520i	$-0.164290\pi$
$174$		0			0
$175$	2.11334	+	3.66041i	0.159754	+	0.276701i
$176$	12.8760	+	22.3019i	0.970564	+	1.68107i
$177$		0			0
$178$	−13.9611	+	24.1813i	−1.04643	+	1.81247i
$179$	7.34730			0.549163			0.274581	−	0.961564i	$-0.411461\pi$
$179$	7.34730			0.549163			0.274581	+	0.961564i	$0.411461\pi$
$180$		0			0
$181$	−3.44562			−0.256111			−0.128056	−	0.991767i	$-0.540874\pi$
$181$	−3.44562			−0.256111			−0.128056	+	0.991767i	$0.540874\pi$
$182$	−6.90420	+	11.9584i	−0.511773	+	0.886417i
$183$		0			0
$184$	−9.65523	−	16.7233i	−0.711793	−	1.23286i
$185$	2.00253	+	3.46848i	0.147229	+	0.255008i
$186$		0			0
$187$	−3.20574	+	5.55250i	−0.234427	+	0.406039i
$188$	4.50980			0.328911
$189$		0			0
$190$	−5.36959			−0.389551
$191$	2.82888	−	4.89976i	0.204690	−	0.354534i	−0.745344	−	0.666680i	$-0.767715\pi$
$191$	2.82888	−	4.89976i	0.204690	−	0.354534i	0.950034	+	0.312146i	$0.101048\pi$
$192$		0			0
$193$	−4.79813	−	8.31061i	−0.345377	−	0.598211i	0.640045	−	0.768337i	$-0.278916\pi$
$193$	−4.79813	−	8.31061i	−0.345377	−	0.598211i	−0.985422	+	0.170127i	$0.945582\pi$
$194$	15.8293	+	27.4172i	1.13648	+	1.96844i
$195$		0			0
$196$	−2.20574	+	3.82045i	−0.157553	+	0.272889i
$197$	−8.31996			−0.592772			−0.296386	−	0.955068i	$-0.595782\pi$
$197$	−8.31996			−0.592772			−0.296386	+	0.955068i	$0.595782\pi$
$198$		0			0
$199$	6.59627			0.467597			0.233798	−	0.972285i	$-0.424884\pi$
$199$	6.59627			0.467597			0.233798	+	0.972285i	$0.424884\pi$
$200$	−12.9042	+	22.3507i	−0.912465	+	1.58044i
$201$		0			0
$202$	12.3020	+	21.3077i	0.865566	+	1.49920i
$203$	−3.02481	−	5.23913i	−0.212300	−	0.367715i
$204$		0			0
$205$	−0.520945	+	0.902302i	−0.0363843	+	0.0630195i
$206$	−16.7023			−1.16371
$207$		0			0
$208$	−36.2003			−2.51004
$209$	4.67752	−	8.10170i	0.323551	−	0.560406i
$210$		0			0
$211$	1.68479	+	2.91815i	0.115986	+	0.200893i	0.918173	−	0.396179i	$-0.129664\pi$
$211$	1.68479	+	2.91815i	0.115986	+	0.200893i	−0.802188	+	0.597072i	$0.796331\pi$
$212$	16.0817	+	27.8544i	1.10450	+	1.91304i
$213$		0			0
$214$	−3.02481	+	5.23913i	−0.206772	+	0.358140i
$215$	0.162504			0.0110827
$216$		0			0
$217$	−4.55438			−0.309171
$218$	5.01114	−	8.67956i	0.339398	−	0.587854i
$219$		0			0
$220$	7.52481	+	13.0334i	0.507323	+	0.878709i
$221$	−4.50640	−	7.80531i	−0.303133	−	0.525042i
$222$		0			0
$223$	3.13816	−	5.43545i	0.210146	−	0.363984i	−0.741614	−	0.670827i	$-0.765939\pi$
$223$	3.13816	−	5.43545i	0.210146	−	0.363984i	0.951760	+	0.306843i	$0.0992726\pi$
$224$	−4.59627			−0.307101
$225$		0			0
$226$	41.6614			2.77127
$227$	−3.08125	+	5.33688i	−0.204510	+	0.354221i	−0.949976	−	0.312322i	$-0.898893\pi$
$227$	−3.08125	+	5.33688i	−0.204510	+	0.354221i	0.745467	+	0.666543i	$0.232227\pi$
$228$		0			0
$229$	−11.6925	−	20.2521i	−0.772664	−	1.33829i	−0.936098	−	0.351740i	$-0.885590\pi$
$229$	−11.6925	−	20.2521i	−0.772664	−	1.33829i	0.163434	−	0.986554i	$-0.447743\pi$
$230$	−3.52094	−	6.09845i	−0.232164	−	0.402120i
$231$		0			0
$232$	18.4697	−	31.9905i	1.21260	−	2.10028i
$233$	8.52528			0.558510			0.279255	−	0.960217i	$-0.409913\pi$
$233$	8.52528			0.558510			0.279255	+	0.960217i	$0.409913\pi$
$234$		0			0
$235$	0.898986			0.0586434
$236$	14.6912	−	25.4459i	0.956315	−	1.65639i
$237$		0			0
$238$	−2.09240	−	3.62414i	−0.135630	−	0.234918i
$239$	7.28106	+	12.6112i	0.470973	+	0.815748i	0.999449	−	0.0331997i	$-0.0105697\pi$
$239$	7.28106	+	12.6112i	0.470973	+	0.815748i	−0.528476	+	0.848948i	$0.677236\pi$
$240$		0			0
$241$	2.70187	−	4.67977i	0.174043	−	0.301451i	−0.765787	−	0.643094i	$-0.777650\pi$
$241$	2.70187	−	4.67977i	0.174043	−	0.301451i	0.939830	+	0.341644i	$0.110984\pi$
$242$	−10.2540			−0.659154
$243$		0			0
$244$	−11.4534			−0.733226
$245$	−0.439693	+	0.761570i	−0.0280909	+	0.0486549i
$246$		0			0
$247$	6.57532	+	11.3888i	0.418378	+	0.724651i
$248$	−13.9047	−	24.0836i	−0.882947	−	1.52931i
$249$		0			0
$250$	−10.2724	+	17.7924i	−0.649686	+	1.12529i
$251$	12.0669			0.761654			0.380827	−	0.924646i	$-0.375639\pi$
$251$	12.0669			0.761654			0.380827	+	0.924646i	$0.375639\pi$
$252$		0			0
$253$	12.2686			0.771318
$254$	22.3503	−	38.7118i	1.40238	−	2.42900i
$255$		0			0
$256$	15.2515	+	26.4164i	0.953219	+	1.65102i
$257$	5.28312	+	9.15063i	0.329552	+	0.570801i	0.982423	−	0.186668i	$-0.0597690\pi$
$257$	5.28312	+	9.15063i	0.329552	+	0.570801i	−0.652871	+	0.757469i	$0.726436\pi$
$258$		0			0
$259$	2.27719	−	3.94421i	0.141498	−	0.245081i
$260$	−21.1557			−1.31202
$261$		0			0
$262$	−48.6100			−3.00314
$263$	−14.1766	+	24.5547i	−0.874169	+	1.51411i	−0.0165240	+	0.999863i	$0.505260\pi$
$263$	−14.1766	+	24.5547i	−0.874169	+	1.51411i	−0.857645	+	0.514242i	$0.828073\pi$
$264$		0			0
$265$	3.20574	+	5.55250i	0.196927	+	0.341087i
$266$	3.05303	+	5.28801i	0.187193	+	0.324229i
$267$		0			0
$268$	6.52481	−	11.3013i	0.398567	−	0.690337i
$269$	−7.48339			−0.456271			−0.228135	−	0.973629i	$-0.573263\pi$
$269$	−7.48339			−0.456271			−0.228135	+	0.973629i	$0.573263\pi$
$270$		0			0
$271$	13.6382			0.828459			0.414229	−	0.910172i	$-0.364051\pi$
$271$	13.6382			0.828459			0.414229	+	0.910172i	$0.364051\pi$
$272$	5.48545	−	9.50108i	0.332604	−	0.576088i
$273$		0			0
$274$	−22.9859	−	39.8128i	−1.38863	−	2.40518i
$275$	−8.19846	−	14.2002i	−0.494386	−	0.856302i
$276$		0			0
$277$	3.07532	−	5.32661i	0.184778	−	0.320045i	−0.758724	−	0.651413i	$-0.774177\pi$
$277$	3.07532	−	5.32661i	0.184778	−	0.320045i	0.943502	+	0.331368i	$0.107510\pi$
$278$	−55.8512			−3.34973
$279$		0			0
$280$	−5.36959			−0.320894
$281$	1.65611	−	2.86846i	0.0987951	−	0.171118i	−0.812391	−	0.583113i	$-0.801835\pi$
$281$	1.65611	−	2.86846i	0.0987951	−	0.171118i	0.911186	+	0.411995i	$0.135168\pi$
$282$		0			0
$283$	−14.5116	−	25.1348i	−0.862626	−	1.49411i	−0.869385	−	0.494134i	$-0.835485\pi$
$283$	−14.5116	−	25.1348i	−0.862626	−	1.49411i	0.00675974	−	0.999977i	$-0.497848\pi$
$284$	−8.11721	−	14.0594i	−0.481668	−	0.834273i
$285$		0			0
$286$	26.7841	−	46.3913i	1.58377	−	2.74318i
$287$	1.18479			0.0699361
$288$		0			0
$289$	−14.2686			−0.839328
$290$	6.73530	−	11.6659i	0.395510	−	0.685044i
$291$		0			0
$292$	28.1917	+	48.8294i	1.64979	+	2.85752i
$293$	−4.20961	−	7.29125i	−0.245928	−	0.425960i	0.716464	−	0.697624i	$-0.245759\pi$
$293$	−4.20961	−	7.29125i	−0.245928	−	0.425960i	−0.962392	+	0.271664i	$0.912426\pi$
$294$		0			0
$295$	2.92855	−	5.07239i	0.170507	−	0.295326i
$296$	27.8093			1.61638
$297$		0			0
$298$	−38.3756			−2.22304
$299$	−8.62314	+	14.9357i	−0.498689	+	0.863755i
$300$		0			0
$301$	−0.0923963	−	0.160035i	−0.00532563	−	0.00922427i
$302$	−23.9996	−	41.5685i	−1.38102	−	2.39200i
$303$		0			0
$304$	−8.00387	+	13.8631i	−0.459053	+	0.795104i
$305$	−2.28312			−0.130731
$306$		0			0
$307$	−12.6878			−0.724130			−0.362065	−	0.932153i	$-0.617928\pi$
$307$	−12.6878			−0.724130			−0.362065	+	0.932153i	$0.617928\pi$
$308$	8.55690	−	14.8210i	0.487575	−	0.844504i
$309$		0			0
$310$	−5.07057	−	8.78249i	−0.287989	−	0.498812i
$311$	−8.24510	−	14.2809i	−0.467537	−	0.809797i	0.531775	−	0.846886i	$-0.321525\pi$
$311$	−8.24510	−	14.2809i	−0.467537	−	0.809797i	−0.999312	+	0.0370881i	$0.988192\pi$
$312$		0			0
$313$	−14.2592	+	24.6977i	−0.805980	+	1.39600i	0.109648	+	0.993970i	$0.465028\pi$
$313$	−14.2592	+	24.6977i	−0.805980	+	1.39600i	−0.915628	+	0.402027i	$0.868306\pi$
$314$	45.7229			2.58029
$315$		0			0
$316$	−26.2841			−1.47859
$317$	−12.9474	+	22.4256i	−0.727200	+	1.25955i	0.230862	+	0.972987i	$0.425846\pi$
$317$	−12.9474	+	22.4256i	−0.727200	+	1.25955i	−0.958062	+	0.286561i	$0.907488\pi$
$318$		0			0
$319$	11.7344	+	20.3246i	0.657002	+	1.13796i
$320$	0.720285	+	1.24757i	0.0402652	+	0.0697413i
$321$		0			0
$322$	−4.00387	+	6.93491i	−0.223127	+	0.386467i
$323$	−3.98545			−0.221756
$324$		0			0
$325$	23.0496			1.27856
$326$	1.21301	−	2.10100i	0.0671825	−	0.116363i
$327$		0			0
$328$	3.61721	+	6.26519i	0.199727	+	0.345937i
$329$	−0.511144	−	0.885328i	−0.0281803	−	0.0488097i
$330$		0			0
$331$	−4.10947	+	7.11781i	−0.225877	+	0.391230i	−0.956582	−	0.291463i	$-0.905858\pi$
$331$	−4.10947	+	7.11781i	−0.225877	+	0.391230i	0.730705	+	0.682693i	$0.239191\pi$
$332$	0.965852			0.0530080
$333$		0			0
$334$	50.2327			2.74861
$335$	1.30066	−	2.25281i	0.0710626	−	0.123084i
$336$		0			0
$337$	−2.28564	−	3.95885i	−0.124507	−	0.215652i	0.797033	−	0.603936i	$-0.206402\pi$
$337$	−2.28564	−	3.95885i	−0.124507	−	0.215652i	−0.921540	+	0.388283i	$0.873068\pi$
$338$	21.1925	+	36.7065i	1.15272	+	1.99657i
$339$		0			0
$340$	3.20574	−	5.55250i	0.173856	−	0.301127i
$341$	17.6682			0.956786
$342$		0			0
$343$	1.00000			0.0539949
$344$	0.564178	−	0.977185i	0.0304184	−	0.0526863i
$345$		0			0
$346$	−28.7173	−	49.7399i	−1.54385	−	2.67403i
$347$	11.2331	+	19.4563i	0.603023	+	1.04447i	0.992361	+	0.123372i	$0.0393707\pi$
$347$	11.2331	+	19.4563i	0.603023	+	1.04447i	−0.389337	+	0.921095i	$0.627296\pi$
$348$		0			0
$349$	−13.0496	+	22.6026i	−0.698531	+	1.20989i	0.270445	+	0.962735i	$0.412829\pi$
$349$	−13.0496	+	22.6026i	−0.698531	+	1.20989i	−0.968976	+	0.247155i	$0.920504\pi$
$350$	10.7023			0.572064
$351$		0			0
$352$	17.8307			0.950379
$353$	−0.177519	+	0.307471i	−0.00944836	+	0.0163650i	−0.870711	−	0.491795i	$-0.836341\pi$
$353$	−0.177519	+	0.307471i	−0.00944836	+	0.0163650i	0.861263	+	0.508160i	$0.169674\pi$
$354$		0			0
$355$	−1.61809	−	2.80261i	−0.0858792	−	0.148747i
$356$	24.3234	+	42.1294i	1.28914	+	2.23285i
$357$		0			0
$358$	9.30200	−	16.1115i	0.491626	−	0.851522i
$359$	−5.45605			−0.287959			−0.143980	−	0.989581i	$-0.545990\pi$
$359$	−5.45605			−0.287959			−0.143980	+	0.989581i	$0.545990\pi$
$360$		0			0
$361$	−13.1848			−0.693936
$362$	−4.36231	+	7.55574i	−0.229278	+	0.397121i
$363$		0			0
$364$	12.0287	+	20.8343i	0.630474	+	1.09201i
$365$	5.61974	+	9.73367i	0.294150	+	0.509484i
$366$		0			0
$367$	−5.46198	+	9.46043i	−0.285113	+	0.493830i	−0.972637	−	0.232332i	$-0.925364\pi$
$367$	−5.46198	+	9.46043i	−0.285113	+	0.493830i	0.687523	+	0.726162i	$0.258698\pi$
$368$	−20.9932			−1.09435
$369$		0			0
$370$	10.1411			0.527213
$371$	3.64543	−	6.31407i	0.189261	−	0.327810i
$372$		0			0
$373$	−0.865715	−	1.49946i	−0.0448250	−	0.0776392i	0.842742	−	0.538317i	$-0.180940\pi$
$373$	−0.865715	−	1.49946i	−0.0448250	−	0.0776392i	−0.887567	+	0.460678i	$0.847606\pi$
$374$	8.11721	+	14.0594i	0.419731	+	0.726995i
$375$		0			0
$376$	3.12108	−	5.40587i	0.160957	−	0.278787i
$377$	−32.9908			−1.69911
$378$		0			0
$379$	−12.1334			−0.623251			−0.311626	−	0.950205i	$-0.600873\pi$
$379$	−12.1334			−0.623251			−0.311626	+	0.950205i	$0.600873\pi$
$380$	−4.67752	+	8.10170i	−0.239952	+	0.415608i
$381$		0			0
$382$	−7.16297	−	12.4066i	−0.366489	−	0.634778i
$383$	−4.35591	−	7.54467i	−0.222577	−	0.385514i	0.733013	−	0.680215i	$-0.238113\pi$
$383$	−4.35591	−	7.54467i	−0.222577	−	0.385514i	−0.955590	+	0.294700i	$0.904780\pi$
$384$		0			0
$385$	1.70574	−	2.95442i	0.0869324	−	0.150571i
$386$	−24.2986			−1.23677
$387$		0			0
$388$	55.1566			2.80015
$389$	1.82160	−	3.15511i	0.0923590	−	0.159970i	−0.816144	−	0.577848i	$-0.803893\pi$
$389$	1.82160	−	3.15511i	0.0923590	−	0.159970i	0.908503	+	0.417878i	$0.137226\pi$
$390$		0			0
$391$	−2.61334	−	4.52644i	−0.132162	−	0.228912i
$392$	3.05303	+	5.28801i	0.154201	+	0.267085i
$393$		0			0
$394$	−10.5334	+	18.2444i	−0.530667	+	0.919142i
$395$	−5.23947			−0.263627
$396$		0			0
$397$	−15.4456			−0.775194			−0.387597	−	0.921829i	$-0.626695\pi$
$397$	−15.4456			−0.775194			−0.387597	+	0.921829i	$0.626695\pi$
$398$	8.35117	−	14.4646i	0.418606	−	0.725047i
$399$		0			0
$400$	14.0287	+	24.2984i	0.701434	+	1.21492i
$401$	9.21095	+	15.9538i	0.459973	+	0.796697i	0.998959	−	0.0456182i	$-0.0145258\pi$
$401$	9.21095	+	15.9538i	0.459973	+	0.796697i	−0.538986	+	0.842315i	$0.681192\pi$
$402$		0			0
$403$	−12.4183	+	21.5092i	−0.618601	+	1.07145i
$404$	42.8658			2.13265
$405$		0			0
$406$	−15.3182			−0.760230
$407$	−8.83409	+	15.3011i	−0.437890	+	0.758447i
$408$		0			0
$409$	14.3182	+	24.7999i	0.707989	+	1.22627i	0.965602	+	0.260025i	$0.0837309\pi$
$409$	14.3182	+	24.7999i	0.707989	+	1.22627i	−0.257612	+	0.966248i	$0.582936\pi$
$410$	1.31908	+	2.28471i	0.0651446	+	0.112834i
$411$		0			0
$412$	−14.5496	+	25.2007i	−0.716809	+	1.24155i
$413$	−6.66044			−0.327739
$414$		0			0
$415$	0.192533			0.00945109
$416$	−12.5326	+	21.7070i	−0.614459	+	1.06427i
$417$		0			0
$418$	−11.8439	−	20.5142i	−0.579304	−	1.00338i
$419$	−17.3478	−	30.0472i	−0.847494	−	1.46790i	−0.883438	−	0.468548i	$-0.844777\pi$
$419$	−17.3478	−	30.0472i	−0.847494	−	1.46790i	0.0359442	−	0.999354i	$-0.488556\pi$
$420$		0			0
$421$	13.7010	−	23.7308i	0.667745	−	1.15657i	−0.310788	−	0.950479i	$-0.600593\pi$
$421$	13.7010	−	23.7308i	0.667745	−	1.15657i	0.978533	−	0.206090i	$-0.0660738\pi$
$422$	8.53209			0.415336
$423$		0			0
$424$	44.5185			2.16201
$425$	−3.49273	+	6.04958i	−0.169422	+	0.293448i
$426$		0			0
$427$	1.29813	+	2.24843i	0.0628211	+	0.108809i
$428$	5.26991	+	9.12776i	0.254731	+	0.441207i
$429$		0			0
$430$	0.205737	−	0.356347i	0.00992152	−	0.0171846i
$431$	−26.5921			−1.28090			−0.640449	−	0.768000i	$-0.721252\pi$
$431$	−26.5921			−1.28090			−0.640449	+	0.768000i	$0.721252\pi$
$432$		0			0
$433$	37.1830			1.78690			0.893451	−	0.449160i	$-0.148277\pi$
$433$	37.1830			1.78690			0.893451	+	0.449160i	$0.148277\pi$
$434$	−5.76604	+	9.98708i	−0.276779	+	0.479395i
$435$		0			0
$436$	−8.73055	−	15.1218i	−0.418118	−	0.724201i
$437$	3.81315	+	6.60457i	0.182408	+	0.315939i
$438$		0			0
$439$	−12.5373	+	21.7152i	−0.598373	+	1.03641i	0.394689	+	0.918815i	$0.370853\pi$
$439$	−12.5373	+	21.7152i	−0.598373	+	1.03641i	−0.993061	+	0.117597i	$0.962481\pi$
$440$	20.8307			0.993064
$441$		0			0
$442$	−22.8212			−1.08549
$443$	1.02229	−	1.77066i	0.0485704	−	0.0841264i	−0.840718	−	0.541473i	$-0.817867\pi$
$443$	1.02229	−	1.77066i	0.0485704	−	0.0841264i	0.889288	+	0.457347i	$0.151200\pi$
$444$		0			0
$445$	4.84864	+	8.39809i	0.229848	+	0.398108i
$446$	−7.94609	−	13.7630i	−0.376258	−	0.651698i
$447$		0			0
$448$	0.819078	−	1.41868i	0.0386978	−	0.0670265i
$449$	10.2344			0.482992			0.241496	−	0.970402i	$-0.422362\pi$
$449$	10.2344			0.482992			0.241496	+	0.970402i	$0.422362\pi$
$450$		0			0
$451$	−4.59627			−0.216430
$452$	36.2918	−	62.8592i	1.70702	−	2.95665i
$453$		0			0
$454$	7.80200	+	13.5135i	0.366166	+	0.634218i
$455$	2.39780	+	4.15312i	0.112411	+	0.194701i
$456$		0			0
$457$	21.2973	−	36.8879i	0.996244	−	1.72554i	0.423129	−	0.906070i	$-0.360932\pi$
$457$	21.2973	−	36.8879i	0.996244	−	1.72554i	0.573115	−	0.819475i	$-0.305735\pi$
$458$	−59.2131			−2.76684
$459$		0			0
$460$	−12.2686			−0.572025
$461$	0.252374	−	0.437124i	0.0117542	−	0.0203589i	−0.860088	−	0.510145i	$-0.829592\pi$
$461$	0.252374	−	0.437124i	0.0117542	−	0.0203589i	0.871843	+	0.489786i	$0.162925\pi$
$462$		0			0
$463$	−1.34002	−	2.32099i	−0.0622761	−	0.107865i	0.833206	−	0.552962i	$-0.186503\pi$
$463$	−1.34002	−	2.32099i	−0.0622761	−	0.107865i	−0.895482	+	0.445097i	$0.853169\pi$
$464$	−20.0792	−	34.7782i	−0.932153	−	1.61454i
$465$		0			0
$466$	10.7934	−	18.6947i	0.499994	−	0.866015i
$467$	31.4165			1.45378			0.726892	−	0.686752i	$-0.240964\pi$
$467$	31.4165			1.45378			0.726892	+	0.686752i	$0.240964\pi$
$468$		0			0
$469$	−2.95811			−0.136593
$470$	1.13816	−	1.97134i	0.0524992	−	0.0909313i
$471$		0			0
$472$	−20.3346	−	35.2205i	−0.935974	−	1.62115i
$473$	0.358441	+	0.620838i	0.0164811	+	0.0285461i
$474$		0			0
$475$	5.09627	−	8.82699i	0.233833	−	0.405010i
$476$	−7.29086			−0.334176
$477$		0			0
$478$	36.8726			1.68651
$479$	−8.22028	+	14.2380i	−0.375594	+	0.650549i	−0.990416	−	0.138118i	$-0.955895\pi$
$479$	−8.22028	+	14.2380i	−0.375594	+	0.650549i	0.614821	+	0.788666i	$0.289228\pi$
$480$		0			0
$481$	−12.4183	−	21.5092i	−0.566227	−	0.980735i
$482$	−6.84137	−	11.8496i	−0.311616	−	0.539734i
$483$		0			0
$484$	−8.93242	+	15.4714i	−0.406019	+	0.703246i
$485$	10.9949			0.499255
$486$		0			0
$487$	−2.97535			−0.134826			−0.0674129	−	0.997725i	$-0.521474\pi$
$487$	−2.97535			−0.134826			−0.0674129	+	0.997725i	$0.521474\pi$
$488$	−7.92649	+	13.7291i	−0.358815	+	0.621486i
$489$		0			0
$490$	1.11334	+	1.92836i	0.0502956	+	0.0871146i
$491$	−13.2430	−	22.9376i	−0.597650	−	1.03516i	−0.993167	−	0.116702i	$-0.962768\pi$
$491$	−13.2430	−	22.9376i	−0.597650	−	1.03516i	0.395517	−	0.918459i	$-0.370565\pi$
$492$		0			0
$493$	4.99912	−	8.65873i	0.225149	−	0.389970i
$494$	33.2986			1.49817
$495$		0			0
$496$	−30.2327			−1.35749
$497$	−1.84002	+	3.18701i	−0.0825363	+	0.142957i
$498$		0			0
$499$	6.72193	+	11.6427i	0.300915	+	0.521200i	0.976343	−	0.216225i	$-0.0693746\pi$
$499$	6.72193	+	11.6427i	0.300915	+	0.521200i	−0.675428	+	0.737426i	$0.736041\pi$
$500$	17.8969	+	30.9984i	0.800375	+	1.38629i
$501$		0			0
$502$	15.2772	−	26.4609i	0.681854	−	1.18101i
$503$	22.6631			1.01050			0.505250	−	0.862973i	$-0.331400\pi$
$503$	22.6631			1.01050			0.505250	+	0.862973i	$0.331400\pi$
$504$		0			0
$505$	8.54488			0.380242
$506$	15.5326	−	26.9032i	0.690506	−	1.19599i
$507$		0			0
$508$	−38.9393	−	67.4448i	−1.72765	−	2.99238i
$509$	4.77379	+	8.26844i	0.211594	+	0.366492i	0.952214	−	0.305433i	$-0.0988011\pi$
$509$	4.77379	+	8.26844i	0.211594	+	0.366492i	−0.740619	+	0.671925i	$0.765468\pi$
$510$		0			0
$511$	6.39053	−	11.0687i	0.282700	−	0.489651i
$512$	50.5553			2.23425
$513$		0			0
$514$	26.7547			1.18010
$515$	−2.90033	+	5.02352i	−0.127804	+	0.221363i
$516$		0			0
$517$	1.98293	+	3.43453i	0.0872090	+	0.151050i
$518$	−5.76604	−	9.98708i	−0.253345	−	0.438807i
$519$		0			0
$520$	−14.6411	+	25.3592i	−0.642057	+	1.11208i
$521$	3.11287			0.136377			0.0681887	−	0.997672i	$-0.478278\pi$
$521$	3.11287			0.136377			0.0681887	+	0.997672i	$0.478278\pi$
$522$		0			0
$523$	−16.1489			−0.706142			−0.353071	−	0.935597i	$-0.614863\pi$
$523$	−16.1489			−0.706142			−0.353071	+	0.935597i	$0.614863\pi$
$524$	−42.3448	+	73.3434i	−1.84984	+	3.20402i
$525$		0			0
$526$	35.8965	+	62.1746i	1.56516	+	2.71094i
$527$	−3.76352	−	6.51860i	−0.163941	−	0.283955i
$528$		0			0
$529$	6.49928	−	11.2571i	0.282578	−	0.489439i
$530$	16.2344			0.705178
$531$		0			0
$532$	10.6382			0.461223
$533$	3.23055	−	5.59548i	0.139931	−	0.242367i
$534$		0			0
$535$	1.05051	+	1.81953i	0.0454174	+	0.0786652i
$536$	−9.03121	−	15.6425i	−0.390089	−	0.675654i
$537$		0			0
$538$	−9.47431	+	16.4100i	−0.408466	+	0.707485i
$539$	−3.87939			−0.167097
$540$		0			0
$541$	−5.01548			−0.215632			−0.107816	−	0.994171i	$-0.534386\pi$
$541$	−5.01548			−0.215632			−0.107816	+	0.994171i	$0.534386\pi$
$542$	17.2665	−	29.9065i	0.741660	−	1.28459i
$543$		0			0
$544$	−3.79813	−	6.57856i	−0.162844	−	0.282053i
$545$	−1.74035	−	3.01438i	−0.0745485	−	0.129122i
$546$		0			0
$547$	−8.23901	+	14.2704i	−0.352275	+	0.610157i	−0.986648	−	0.162870i	$-0.947925\pi$
$547$	−8.23901	+	14.2704i	−0.352275	+	0.610157i	0.634373	+	0.773027i	$0.281258\pi$
$548$	−80.0934			−3.42142
$549$		0			0
$550$	−41.5185			−1.77035
$551$	−7.29426	+	12.6340i	−0.310746	+	0.538228i
$552$		0			0
$553$	2.97906	+	5.15988i	0.126682	+	0.219420i
$554$	−7.78699	−	13.4875i	−0.330837	−	0.573027i
$555$		0			0
$556$	−48.6528	+	84.2691i	−2.06334	+	3.57380i
$557$	34.5631			1.46448			0.732242	−	0.681045i	$-0.238474\pi$
$557$	34.5631			1.46448			0.732242	+	0.681045i	$0.238474\pi$
$558$		0			0
$559$	−1.00774			−0.0426229
$560$	−2.91875	+	5.05542i	−0.123340	+	0.213630i
$561$		0			0
$562$	−4.19341	−	7.26320i	−0.176888	−	0.306380i
$563$	−18.6052	−	32.2251i	−0.784115	−	1.35813i	−0.929526	−	0.368756i	$-0.879784\pi$
$563$	−18.6052	−	32.2251i	−0.784115	−	1.35813i	0.145411	−	0.989371i	$-0.453550\pi$
$564$		0			0
$565$	7.23442	−	12.5304i	0.304354	−	0.527157i
$566$	−73.4894			−3.08899
$567$		0			0
$568$	−22.4706			−0.942845
$569$	0.202333	−	0.350452i	0.00848226	−	0.0146917i	−0.861753	−	0.507328i	$-0.830633\pi$
$569$	0.202333	−	0.350452i	0.00848226	−	0.0146917i	0.870235	+	0.492636i	$0.163967\pi$
$570$		0			0
$571$	18.8897	+	32.7178i	0.790507	+	1.36920i	0.925653	+	0.378373i	$0.123516\pi$
$571$	18.8897	+	32.7178i	0.790507	+	1.36920i	−0.135146	+	0.990826i	$0.543150\pi$
$572$	−46.6639	−	80.8243i	−1.95112	−	3.37943i
$573$		0			0
$574$	1.50000	−	2.59808i	0.0626088	−	0.108442i
$575$	13.3669			0.557438
$576$		0			0
$577$	−2.21120			−0.0920535			−0.0460267	−	0.998940i	$-0.514656\pi$
$577$	−2.21120			−0.0920535			−0.0460267	+	0.998940i	$0.514656\pi$
$578$	−18.0646	+	31.2889i	−0.751390	+	1.30145i
$579$		0			0
$580$	−11.7344	−	20.3246i	−0.487245	−	0.843934i
$581$	−0.109470	−	0.189608i	−0.00454160	−	0.00786628i
$582$		0			0
$583$	−14.1420	+	24.4947i	−0.585703	+	1.01447i
$584$	78.0420			3.22940
$585$		0			0
$586$	−21.3182			−0.880647
$587$	12.1049	−	20.9663i	0.499622	−	0.865371i	−0.500378	−	0.865807i	$-0.666806\pi$
$587$	12.1049	−	20.9663i	0.499622	−	0.865371i	1.00000		0.000436347i	$0.000138894\pi$
$588$		0			0
$589$	5.49138	+	9.51135i	0.226268	+	0.391908i
$590$	−7.41534	−	12.8438i	−0.305285	−	0.528769i
$591$		0			0
$592$	15.1163	−	26.1823i	0.621277	−	1.07608i
$593$	−12.2385			−0.502577			−0.251288	−	0.967912i	$-0.580854\pi$
$593$	−12.2385			−0.502577			−0.251288	+	0.967912i	$0.580854\pi$
$594$		0			0
$595$	−1.45336			−0.0595821
$596$	−33.4295	+	57.9016i	−1.36932	+	2.37174i
$597$		0			0
$598$	21.8346	+	37.8186i	0.892882	+	1.54652i
$599$	19.8084	+	34.3092i	0.809349	+	1.40183i	0.913315	+	0.407253i	$0.133513\pi$
$599$	19.8084	+	34.3092i	0.809349	+	1.40183i	−0.103966	+	0.994581i	$0.533153\pi$
$600$		0			0
$601$	15.0039	−	25.9875i	0.612021	−	1.06005i	−0.378879	−	0.925446i	$-0.623690\pi$
$601$	15.0039	−	25.9875i	0.612021	−	1.06005i	0.990899	−	0.134605i	$-0.0429764\pi$
$602$	−0.467911			−0.0190706
$603$		0			0
$604$	−83.6255			−3.40267
$605$	−1.78059	+	3.08408i	−0.0723914	+	0.125386i
$606$		0			0
$607$	9.74216	+	16.8739i	0.395422	+	0.684891i	0.993155	−	0.116804i	$-0.0372650\pi$
$607$	9.74216	+	16.8739i	0.395422	+	0.684891i	−0.597733	+	0.801695i	$0.703932\pi$
$608$	5.54189	+	9.59883i	0.224753	+	0.389284i
$609$		0			0
$610$	−2.89053	+	5.00654i	−0.117034	+	0.202709i
$611$	−5.57491			−0.225537
$612$		0			0
$613$	−18.5276			−0.748325			−0.374162	−	0.927363i	$-0.622070\pi$
$613$	−18.5276			−0.748325			−0.374162	+	0.927363i	$0.622070\pi$
$614$	−16.0633	+	27.8225i	−0.648262	+	1.12282i
$615$		0			0
$616$	−11.8439	−	20.5142i	−0.477204	−	0.826542i
$617$	13.9201	+	24.1103i	0.560402	+	0.970644i	0.997461	+	0.0712118i	$0.0226866\pi$
$617$	13.9201	+	24.1103i	0.560402	+	0.970644i	−0.437059	+	0.899433i	$0.643980\pi$
$618$		0			0
$619$	22.4907	−	38.9550i	0.903976	−	1.56573i	0.0816906	−	0.996658i	$-0.473968\pi$
$619$	22.4907	−	38.9550i	0.903976	−	1.56573i	0.822286	−	0.569075i	$-0.192699\pi$
$620$	−17.6682			−0.709571
$621$		0			0
$622$	−41.7547			−1.67421
$623$	5.51367	−	9.54996i	0.220901	−	0.382611i
$624$		0			0
$625$	−6.99912	−	12.1228i	−0.279965	−	0.484913i
$626$	36.1057	+	62.5368i	1.44307	+	2.49947i
$627$		0			0
$628$	39.8298	−	68.9873i	1.58938	−	2.75289i
$629$	7.52704			0.300123
$630$		0			0
$631$	9.43613			0.375646			0.187823	−	0.982203i	$-0.439857\pi$
$631$	9.43613			0.375646			0.187823	+	0.982203i	$0.439857\pi$
$632$	−18.1903	+	31.5065i	−0.723572	+	1.25326i
$633$		0			0
$634$	32.7841	+	56.7836i	1.30202	+	2.25517i
$635$	−7.76217	−	13.4445i	−0.308032	−	0.533528i
$636$		0			0
$637$	2.72668	−	4.72275i	0.108035	−	0.187122i
$638$	59.4252			2.35267
$639$		0			0
$640$	11.7314			0.463725
$641$	18.6951	−	32.3808i	0.738410	−	1.27896i	−0.214800	−	0.976658i	$-0.568910\pi$
$641$	18.6951	−	32.3808i	0.738410	−	1.27896i	0.953211	−	0.302306i	$-0.0977566\pi$
$642$		0			0
$643$	−0.805874	−	1.39581i	−0.0317806	−	0.0550456i	0.849698	−	0.527270i	$-0.176784\pi$
$643$	−0.805874	−	1.39581i	−0.0317806	−	0.0550456i	−0.881478	+	0.472225i	$0.843451\pi$
$644$	6.97565	+	12.0822i	0.274879	+	0.476105i
$645$		0			0
$646$	−5.04576	+	8.73951i	−0.198523	+	0.343851i
$647$	41.1762			1.61880			0.809402	−	0.587255i	$-0.199791\pi$
$647$	41.1762			1.61880			0.809402	+	0.587255i	$0.199791\pi$
$648$		0			0
$649$	25.8384			1.01425
$650$	29.1819	−	50.5445i	1.14461	−	1.98252i
$651$		0			0
$652$	−2.11334	−	3.66041i	−0.0827648	−	0.143353i
$653$	1.52600	+	2.64310i	0.0597169	+	0.103433i	0.894338	−	0.447391i	$-0.147647\pi$
$653$	1.52600	+	2.64310i	0.0597169	+	0.103433i	−0.834621	+	0.550824i	$0.814314\pi$
$654$		0			0
$655$	−8.44104	+	14.6203i	−0.329819	+	0.571263i
$656$	7.86484			0.307070
$657$		0			0
$658$	−2.58853			−0.100911
$659$	20.8175	−	36.0569i	0.810934	−	1.40458i	−0.101277	−	0.994858i	$-0.532293\pi$
$659$	20.8175	−	36.0569i	0.810934	−	1.40458i	0.912211	−	0.409721i	$-0.134374\pi$
$660$		0			0
$661$	−10.1505	−	17.5812i	−0.394808	−	0.683828i	0.598269	−	0.801296i	$-0.295856\pi$
$661$	−10.1505	−	17.5812i	−0.394808	−	0.683828i	−0.993077	+	0.117468i	$0.962522\pi$
$662$	10.4055	+	18.0229i	0.404423	+	0.700481i
$663$		0			0
$664$	0.668434	−	1.15776i	0.0259403	−	0.0449298i
$665$	2.12061			0.0822339
$666$		0			0
$667$	−19.1320			−0.740793
$668$	43.7584	−	75.7917i	1.69306	−	2.93247i
$669$		0			0
$670$	−3.29339	−	5.70431i	−0.127235	−	0.220377i
$671$	−5.03596	−	8.72254i	−0.194411	−	0.336730i
$672$		0			0
$673$	0.415345	−	0.719398i	0.0160104	−	0.0277307i	−0.857909	−	0.513801i	$-0.828237\pi$
$673$	0.415345	−	0.719398i	0.0160104	−	0.0277307i	0.873920	+	0.486071i	$0.161570\pi$
$674$	−11.5749			−0.445849
$675$		0			0
$676$	73.8444			2.84017
$677$	5.43360	−	9.41127i	0.208830	−	0.361705i	−0.742516	−	0.669828i	$-0.766368\pi$
$677$	5.43360	−	9.41127i	0.208830	−	0.361705i	0.951346	+	0.308124i	$0.0997011\pi$
$678$		0			0
$679$	−6.25150	−	10.8279i	−0.239910	−	0.415537i
$680$	−4.43717	−	7.68540i	−0.170158	−	0.294722i
$681$		0			0
$682$	22.3687	−	38.7437i	0.856542	−	1.48357i
$683$	−32.6946			−1.25102			−0.625512	−	0.780215i	$-0.715110\pi$
$683$	−32.6946			−1.25102			−0.625512	+	0.780215i	$0.715110\pi$
$684$		0			0
$685$	−15.9659			−0.610024
$686$	1.26604	−	2.19285i	0.0483378	−	0.0837235i
$687$		0			0
$688$	−0.613341	−	1.06234i	−0.0233834	−	0.0405012i
$689$	−19.8799	−	34.4329i	−0.757362	−	1.31179i
$690$		0			0
$691$	−7.49912	+	12.9889i	−0.285280	+	0.494120i	−0.972677	−	0.232162i	$-0.925420\pi$
$691$	−7.49912	+	12.9889i	−0.285280	+	0.494120i	0.687397	+	0.726282i	$0.258753\pi$
$692$	−100.064			−3.80387
$693$		0			0
$694$	56.8863			2.15937
$695$	−9.69846	+	16.7982i	−0.367884	+	0.637193i
$696$		0			0
$697$	0.979055	+	1.69577i	0.0370844	+	0.0642320i
$698$	33.0428	+	57.2318i	1.25069	+	2.16626i
$699$		0			0
$700$	9.32295	−	16.1478i	0.352374	−	0.610330i
$701$	−26.4688			−0.999714			−0.499857	−	0.866108i	$-0.666614\pi$
$701$	−26.4688			−0.999714			−0.499857	+	0.866108i	$0.666614\pi$
$702$		0			0
$703$	−10.9828			−0.414223
$704$	−3.17752	+	5.50362i	−0.119757	+	0.207426i
$705$		0			0
$706$	0.449493	+	0.778544i	0.0169169	+	0.0293009i
$707$	−4.85844	−	8.41507i	−0.182720	−	0.316481i
$708$		0			0
$709$	−7.68004	+	13.3022i	−0.288430	+	0.499576i	−0.973435	−	0.228963i	$-0.926467\pi$
$709$	−7.68004	+	13.3022i	−0.288430	+	0.499576i	0.685005	+	0.728538i	$0.259800\pi$
$710$	−8.19429			−0.307526
$711$		0			0
$712$	67.3337			2.52344
$713$	−7.20162	+	12.4736i	−0.269703	+	0.467139i
$714$		0			0
$715$	−9.30200	−	16.1115i	−0.347875	−	0.602538i
$716$	−16.2062	−	28.0700i	−0.605654	−	1.04902i
$717$		0			0
$718$	−6.90760	+	11.9643i	−0.257789	+	0.446504i
$719$	−26.7306			−0.996883			−0.498442	−	0.866923i	$-0.666094\pi$
$719$	−26.7306			−0.996883			−0.498442	+	0.866923i	$0.666094\pi$
$720$		0			0
$721$	6.59627			0.245658
$722$	−16.6925	+	28.9123i	−0.621232	+	1.07600i
$723$		0			0
$724$	7.60014	+	13.1638i	0.282457	+	0.489230i
$725$	12.7849	+	22.1441i	0.474820	+	0.822413i
$726$		0			0
$727$	22.8221	−	39.5290i	0.846424	−	1.46605i	−0.0379552	−	0.999279i	$-0.512084\pi$
$727$	22.8221	−	39.5290i	0.846424	−	1.46605i	0.884379	−	0.466770i	$-0.154582\pi$
$728$	33.2986			1.23413
$729$		0			0
$730$	28.4593			1.05333
$731$	0.152704	−	0.264490i	0.00564795	−	0.00978253i
$732$		0			0
$733$	−2.98751	−	5.17452i	−0.110346	−	0.191125i	0.805564	−	0.592509i	$-0.201863\pi$
$733$	−2.98751	−	5.17452i	−0.110346	−	0.191125i	−0.915910	+	0.401384i	$0.868529\pi$
$734$	13.8302	+	23.9546i	0.510483	+	0.884182i
$735$		0			0
$736$	−7.26786	+	12.5883i	−0.267897	+	0.464011i
$737$	11.4757			0.422711
$738$		0			0
$739$	−35.5963			−1.30943			−0.654715	−	0.755876i	$-0.727211\pi$
$739$	−35.5963			−1.30943			−0.654715	+	0.755876i	$0.727211\pi$
$740$	8.83409	−	15.3011i	0.324748	−	0.562480i
$741$		0			0
$742$	−9.23055	−	15.9878i	−0.338864	−	0.586930i
$743$	−14.6544	−	25.3821i	−0.537616	−	0.931178i	−0.999032	−	0.0439943i	$-0.985992\pi$
$743$	−14.6544	−	25.3821i	−0.537616	−	0.931178i	0.461416	−	0.887184i	$-0.347342\pi$
$744$		0			0
$745$	−6.66385	+	11.5421i	−0.244145	+	0.422871i
$746$	−4.38413			−0.160515
$747$		0			0
$748$	28.2841			1.03417
$749$	1.19459	−	2.06910i	0.0436495	−	0.0756031i
$750$		0			0
$751$	8.66684	+	15.0114i	0.316258	+	0.547774i	0.979704	−	0.200450i	$-0.0642403\pi$
$751$	8.66684	+	15.0114i	0.316258	+	0.547774i	−0.663446	+	0.748224i	$0.730907\pi$
$752$	−3.39306	−	5.87695i	−0.123732	−	0.214310i
$753$		0			0
$754$	−41.7679	+	72.3440i	−1.52110	+	2.63461i
$755$	−16.6699			−0.606681
$756$		0			0
$757$	−2.77156			−0.100734			−0.0503671	−	0.998731i	$-0.516039\pi$
$757$	−2.77156			−0.100734			−0.0503671	+	0.998731i	$0.516039\pi$
$758$	−15.3614	+	26.6068i	−0.557952	+	0.966402i
$759$		0			0
$760$	6.47431	+	11.2138i	0.234848	+	0.406768i
$761$	3.75372	+	6.50163i	0.136072	+	0.235684i	0.926007	−	0.377508i	$-0.123219\pi$
$761$	3.75372	+	6.50163i	0.136072	+	0.235684i	−0.789934	+	0.613191i	$0.789885\pi$
$762$		0			0
$763$	−1.97906	+	3.42782i	−0.0716466	+	0.124096i
$764$	−24.9590			−0.902987
$765$		0			0
$766$	−22.0591			−0.797029
$767$	−18.1609	+	31.4556i	−0.655752	+	1.13580i
$768$		0			0
$769$	−1.02182	−	1.76985i	−0.0368478	−	0.0638223i	0.847013	−	0.531572i	$-0.178398\pi$
$769$	−1.02182	−	1.76985i	−0.0368478	−	0.0638223i	−0.883861	+	0.467749i	$0.845065\pi$
$770$	−4.31908	−	7.48086i	−0.155649	−	0.269592i
$771$		0			0
$772$	−21.1668	+	36.6620i	−0.761811	+	1.31950i
$773$	24.9418			0.897094			0.448547	−	0.893759i	$-0.351942\pi$
$773$	24.9418			0.897094			0.448547	+	0.893759i	$0.351942\pi$
$774$		0			0
$775$	19.2499			0.691477
$776$	38.1721	−	66.1159i	1.37030	−	2.37342i
$777$		0			0
$778$	−4.61246	−	7.98902i	−0.165365	−	0.286420i
$779$	−1.42855	−	2.47432i	−0.0511831	−	0.0886516i
$780$		0			0
$781$	7.13816	−	12.3636i	0.255423	−	0.442406i
$782$	−13.2344			−0.473262
$783$		0			0
$784$	6.63816			0.237077
$785$	7.93969	−	13.7520i	0.283380	−	0.490828i
$786$		0			0
$787$	−3.55350	−	6.15484i	−0.126669	−	0.219396i	0.795715	−	0.605671i	$-0.207095\pi$
$787$	−3.55350	−	6.15484i	−0.126669	−	0.219396i	−0.922384	+	0.386274i	$0.873762\pi$
$788$	18.3516	+	31.7860i	0.653750	+	1.13233i
$789$		0			0
$790$	−6.63341	+	11.4894i	−0.236006	+	0.408774i
$791$	−16.4534			−0.585014
$792$		0			0
$793$	14.1584			0.502779
$794$	−19.5548	+	33.8700i	−0.693975	+	1.20200i
$795$		0			0
$796$	−14.5496	−	25.2007i	−0.515698	−	0.893215i
$797$	16.8314	+	29.1528i	0.596199	+	1.03265i	0.993376	+	0.114905i	$0.0366564\pi$
$797$	16.8314	+	29.1528i	0.596199	+	1.03265i	−0.397178	+	0.917742i	$0.630010\pi$
$798$		0			0
$799$	0.844770	−	1.46318i	0.0298858	−	0.0517638i
$800$	19.4270			0.686847
$801$		0			0
$802$	46.6459			1.64712
$803$	−24.7913	+	42.9398i	−0.874867	+	1.51531i
$804$		0			0
$805$	1.39053	+	2.40847i	0.0490097	+	0.0848873i
$806$	31.4443	+	54.4632i	1.10758	+	1.91838i
$807$		0			0
$808$	29.6660	−	51.3830i	1.04364	−	1.80765i
$809$	12.8161			0.450592			0.225296	−	0.974290i	$-0.427665\pi$
$809$	12.8161			0.450592			0.225296	+	0.974290i	$0.427665\pi$
$810$		0			0
$811$	−26.1239			−0.917335			−0.458667	−	0.888608i	$-0.651673\pi$
$811$	−26.1239			−0.917335			−0.458667	+	0.888608i	$0.651673\pi$
$812$	−13.3439	+	23.1123i	−0.468279	+	0.811083i
$813$		0			0
$814$	22.3687	+	38.7437i	0.784023	+	1.35797i
$815$	−0.421274	−	0.729669i	−0.0147566	−	0.0255592i
$816$		0			0
$817$	−0.222811	+	0.385920i	−0.00779518	+	0.0135016i
$818$	72.5099			2.53525
$819$		0			0
$820$	4.59627			0.160509
$821$	13.8320	−	23.9578i	0.482741	−	0.836132i	−0.517062	−	0.855948i	$-0.672974\pi$
$821$	13.8320	−	23.9578i	0.482741	−	0.836132i	0.999804	+	0.0198153i	$0.00630781\pi$
$822$		0			0
$823$	−13.9162	−	24.1036i	−0.485089	−	0.840199i	0.514764	−	0.857332i	$-0.327879\pi$
$823$	−13.9162	−	24.1036i	−0.485089	−	0.840199i	−0.999853	+	0.0171330i	$0.994546\pi$
$824$	20.1386	+	34.8811i	0.701562	+	1.21514i
$825$		0			0
$826$	−8.43242	+	14.6054i	−0.293401	+	0.508186i
$827$	−4.65507			−0.161873			−0.0809363	−	0.996719i	$-0.525791\pi$
$827$	−4.65507			−0.161873			−0.0809363	+	0.996719i	$0.525791\pi$
$828$		0			0
$829$	−9.97359			−0.346397			−0.173199	−	0.984887i	$-0.555410\pi$
$829$	−9.97359			−0.346397			−0.173199	+	0.984887i	$0.555410\pi$
$830$	0.243756	−	0.422197i	0.00846089	−	0.0146547i
$831$		0			0
$832$	−4.46673	−	7.73660i	−0.154856	−	0.268218i
$833$	0.826352	+	1.43128i	0.0286314	+	0.0495910i
$834$		0			0
$835$	8.72281	−	15.1084i	0.301865	−	0.522846i
$836$	−41.2695			−1.42734
$837$		0			0
$838$	−87.8522			−3.03480
$839$	−3.36484	+	5.82807i	−0.116167	+	0.201207i	−0.918246	−	0.396011i	$-0.870394\pi$
$839$	−3.36484	+	5.82807i	−0.116167	+	0.201207i	0.802079	+	0.597218i	$0.203727\pi$
$840$		0			0
$841$	−3.79901	−	6.58008i	−0.131000	−	0.226899i
$842$	−34.6921	−	60.0885i	−1.19557	−	2.07079i
$843$		0			0
$844$	7.43242	−	12.8733i	0.255834	−	0.443118i
$845$	14.7202			0.506390
$846$		0			0
$847$	4.04963			0.139147
$848$	24.1989	−	41.9138i	0.830995	−	1.43932i
$849$		0			0
$850$	8.84389	+	15.3181i	0.303343	+	0.525406i
$851$	−7.20162	−	12.4736i	−0.246868	−	0.427588i
$852$		0			0
$853$	−2.89528	+	5.01477i	−0.0991324	+	0.171702i	−0.911326	−	0.411686i	$-0.864940\pi$
$853$	−2.89528	+	5.01477i	−0.0991324	+	0.171702i	0.812193	+	0.583388i	$0.198273\pi$
$854$	6.57398			0.224957
$855$		0			0
$856$	14.5885			0.498626
$857$	−17.4538	+	30.2309i	−0.596211	+	1.03267i	0.397163	+	0.917748i	$0.369995\pi$
$857$	−17.4538	+	30.2309i	−0.596211	+	1.03267i	−0.993375	+	0.114921i	$0.963339\pi$
$858$		0			0
$859$	6.30747	+	10.9249i	0.215208	+	0.372751i	0.953337	−	0.301909i	$-0.0976237\pi$
$859$	6.30747	+	10.9249i	0.215208	+	0.372751i	−0.738129	+	0.674660i	$0.764290\pi$
$860$	−0.358441	−	0.620838i	−0.0122227	−	0.0211704i
$861$		0			0
$862$	−33.6668	+	58.3127i	−1.14670	+	1.98614i
$863$	24.2053			0.823959			0.411979	−	0.911193i	$-0.364838\pi$
$863$	24.2053			0.823959			0.411979	+	0.911193i	$0.364838\pi$
$864$		0			0
$865$	−19.9469			−0.678214
$866$	47.0754	−	81.5369i	1.59969	−	2.77074i
$867$		0			0
$868$	10.0458	+	17.3998i	0.340975	+	0.590587i
$869$	−11.5569	−	20.0171i	−0.392041	−	0.679035i
$870$		0			0
$871$	−8.06583	+	13.9704i	−0.273300	+	0.473370i
$872$	−24.1685			−0.818448
$873$		0			0
$874$	19.3105			0.653186
$875$	4.05690	−	7.02676i	0.137148	−	0.237548i
$876$		0			0
$877$	0.562834	+	0.974856i	0.0190055	+	0.0329186i	0.875372	−	0.483450i	$-0.160617\pi$
$877$	0.562834	+	0.974856i	0.0190055	+	0.0329186i	−0.856366	+	0.516369i	$0.827283\pi$
$878$	31.7456	+	54.9849i	1.07136	+	1.85565i
$879$		0			0
$880$	11.3229	−	19.6119i	0.381697	−	0.661118i
$881$	4.38331			0.147678			0.0738388	−	0.997270i	$-0.476475\pi$
$881$	4.38331			0.147678			0.0738388	+	0.997270i	$0.476475\pi$
$882$		0			0
$883$	−6.88949			−0.231850			−0.115925	−	0.993258i	$-0.536983\pi$
$883$	−6.88949			−0.231850			−0.115925	+	0.993258i	$0.536983\pi$
$884$	−19.8799	+	34.4329i	−0.668632	+	1.15810i
$885$		0			0
$886$	−2.58853	−	4.48346i	−0.0869632	−	0.150625i
$887$	19.5376	+	33.8401i	0.656009	+	1.13624i	0.981640	+	0.190744i	$0.0610899\pi$
$887$	19.5376	+	33.8401i	0.656009	+	1.13624i	−0.325631	+	0.945497i	$0.605577\pi$
$888$		0			0
$889$	−8.82682	+	15.2885i	−0.296042	+	0.512760i
$890$	24.5544			0.823065
$891$		0			0
$892$	−27.6878			−0.927056
$893$	−1.23261	+	2.13495i	−0.0412478	+	0.0714432i
$894$		0			0
$895$	−3.23055	−	5.59548i	−0.107985	−	0.187036i
$896$	−6.67024	−	11.5532i	−0.222837	−	0.385965i
$897$		0			0
$898$	12.9572	−	22.4426i	0.432388	−	0.748919i
$899$	−27.5523			−0.918921
$900$		0			0
$901$	12.0496			0.401431
$902$	−5.81908	+	10.0789i	−0.193754	+	0.335592i
$903$		0			0
$904$	−50.2327	−	87.0055i	−1.67071	−	2.89376i
$905$	1.51501	+	2.62408i	0.0503608	+	0.0872275i
$906$		0			0
$907$	−21.2469	+	36.8007i	−0.705492	+	1.22195i	0.261022	+	0.965333i	$0.415941\pi$
$907$	−21.2469	+	36.8007i	−0.705492	+	1.22195i	−0.966514	+	0.256615i	$0.917393\pi$
$908$	27.1857			0.902190
$909$		0			0
$910$	12.1429			0.402533
$911$	−7.74675	+	13.4178i	−0.256661	+	0.444550i	−0.965345	−	0.260976i	$-0.915956\pi$
$911$	−7.74675	+	13.4178i	−0.256661	+	0.444550i	0.708684	+	0.705526i	$0.249289\pi$
$912$		0			0
$913$	0.424678	+	0.735564i	0.0140548	+	0.0243436i
$914$	−53.9265	−	93.4035i	−1.78373	−	3.08951i
$915$		0			0
$916$	−51.5813	+	89.3414i	−1.70429	+	2.95192i
$917$	19.1976			0.633960
$918$		0			0
$919$	6.52940			0.215385			0.107693	−	0.994184i	$-0.465654\pi$
$919$	6.52940			0.215385			0.107693	+	0.994184i	$0.465654\pi$
$920$	−8.49067	+	14.7063i	−0.279929	+	0.484851i
$921$		0			0
$922$	−0.639033	−	1.10684i	−0.0210454	−	0.0364518i
$923$	10.0343	+	17.3799i	0.330283	+	0.572068i
$924$		0			0
$925$	−9.62495	+	16.6709i	−0.316466	+	0.548136i
$926$	−6.78611			−0.223005
$927$		0			0
$928$	−27.8057			−0.912767
$929$	29.1386	−	50.4696i	0.956007	−	1.65585i	0.223961	−	0.974598i	$-0.428101\pi$
$929$	29.1386	−	50.4696i	0.956007	−	1.65585i	0.732046	−	0.681255i	$-0.238565\pi$
$930$		0			0
$931$	−1.20574	−	2.08840i	−0.0395164	−	0.0684445i
$932$	−18.8045	−	32.5704i	−0.615963	−	1.06688i
$933$		0			0
$934$	39.7747	−	68.8918i	1.30147	−	2.25421i
$935$	5.63816			0.184387
$936$		0			0
$937$	32.4175			1.05903			0.529516	−	0.848300i	$-0.322374\pi$
$937$	32.4175			1.05903			0.529516	+	0.848300i	$0.322374\pi$
$938$	−3.74510	+	6.48670i	−0.122282	+	0.211798i
$939$		0			0
$940$	−1.98293	−	3.43453i	−0.0646759	−	0.112022i
$941$	−13.6613	−	23.6621i	−0.445346	−	0.771363i	0.552730	−	0.833360i	$-0.313586\pi$
$941$	−13.6613	−	23.6621i	−0.445346	−	0.771363i	−0.998076	+	0.0619979i	$0.980253\pi$
$942$		0			0
$943$	1.87346	−	3.24492i	0.0610081	−	0.105669i
$944$	−44.2131			−1.43901
$945$		0			0
$946$	1.81521			0.0590175
$947$	−19.1065	+	33.0935i	−0.620879	+	1.07539i	0.368443	+	0.929650i	$0.379891\pi$
$947$	−19.1065	+	33.0935i	−0.620879	+	1.07539i	−0.989322	+	0.145744i	$0.953443\pi$
$948$		0			0
$949$	−34.8499	−	60.3618i	−1.13127	−	1.95943i
$950$	−12.9042	−	22.3507i	−0.418668	−	0.725153i
$951$		0			0
$952$	−5.04576	+	8.73951i	−0.163534	+	0.283249i
$953$	−58.9377			−1.90918			−0.954590	−	0.297924i	$-0.903706\pi$
$953$	−58.9377			−1.90918			−0.954590	+	0.297924i	$0.903706\pi$
$954$		0			0
$955$	−4.97535			−0.160998
$956$	32.1202	−	55.6338i	1.03884	−	1.79933i
$957$		0			0
$958$	20.8145	+	36.0518i	0.672486	+	1.16478i
$959$	9.07785	+	15.7233i	0.293139	+	0.507732i
$960$		0			0
$961$	5.12882	−	8.88338i	0.165446	−	0.286561i
$962$	−62.8887			−2.02761
$963$		0			0
$964$	−23.8384			−0.767784
$965$	−4.21941	+	7.30823i	−0.135828	+	0.235260i
$966$		0			0
$967$	−12.3594	−	21.4071i	−0.397451	−	0.688405i	0.595960	−	0.803014i	$-0.296772\pi$
$967$	−12.3594	−	21.4071i	−0.397451	−	0.688405i	−0.993411	+	0.114609i	$0.963438\pi$
$968$	12.3637	+	21.4145i	0.397383	+	0.688287i
$969$		0			0
$970$	13.9201	−	24.1103i	0.446947	−	0.774135i
$971$	−8.17623			−0.262388			−0.131194	−	0.991357i	$-0.541881\pi$
$971$	−8.17623			−0.262388			−0.131194	+	0.991357i	$0.541881\pi$
$972$		0			0
$973$	22.0574			0.707127
$974$	−3.76692	+	6.52450i	−0.120700	+	0.209058i
$975$		0			0
$976$	8.61721	+	14.9254i	0.275830	+	0.477752i
$977$	−7.92427	−	13.7252i	−0.253520	−	0.439109i	0.710973	−	0.703220i	$-0.248255\pi$
$977$	−7.92427	−	13.7252i	−0.253520	−	0.439109i	−0.964492	+	0.264111i	$0.914922\pi$
$978$		0			0
$979$	−21.3897	+	37.0480i	−0.683616	+	1.18406i
$980$	3.87939			0.123922
$981$		0			0
$982$	−67.0651			−2.14013
$983$	26.6532	−	46.1646i	0.850104	−	1.47242i	−0.0310096	−	0.999519i	$-0.509872\pi$
$983$	26.6532	−	46.1646i	0.850104	−	1.47242i	0.881114	−	0.472904i	$-0.156794\pi$
$984$		0			0
$985$	3.65822	+	6.33623i	0.116561	+	0.201889i
$986$	−12.6582	−	21.9247i	−0.403120	−	0.698224i
$987$		0			0
$988$	29.0069	−	50.2414i	0.922831	−	1.59839i
$989$	−0.584407			−0.0185831
$990$		0			0
$991$	40.2094			1.27730			0.638648	−	0.769499i	$-0.279494\pi$
$991$	40.2094			1.27730			0.638648	+	0.769499i	$0.279494\pi$
$992$	−10.4666	+	18.1286i	−0.332314	+	0.575584i
$993$		0			0
$994$	4.65910	+	8.06980i	0.147778	+	0.255958i
$995$	−2.90033	−	5.02352i	−0.0919466	−	0.159256i
$996$		0			0
$997$	−14.3601	+	24.8724i	−0.454789	+	0.787717i	−0.998676	−	0.0514412i	$-0.983619\pi$
$997$	−14.3601	+	24.8724i	−0.454789	+	0.787717i	0.543887	+	0.839158i	$0.316952\pi$
$998$	34.0411			1.07755
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	189.2.f.b.127.3		6
3.2	odd	2		63.2.f.a.43.1	yes	6
4.3	odd	2		3024.2.r.k.2017.1		6
7.2	even	3		1323.2.h.c.802.1		6
7.3	odd	6		1323.2.g.e.667.3		6
7.4	even	3		1323.2.g.d.667.3		6
7.5	odd	6		1323.2.h.b.802.1		6
7.6	odd	2		1323.2.f.d.883.3		6
9.2	odd	6		567.2.a.h.1.3		3
9.4	even	3	inner	189.2.f.b.64.3		6
9.5	odd	6		63.2.f.a.22.1	✓	6
9.7	even	3		567.2.a.c.1.1		3
12.11	even	2		1008.2.r.h.673.3		6
21.2	odd	6		441.2.h.d.214.3		6
21.5	even	6		441.2.h.e.214.3		6
21.11	odd	6		441.2.g.c.79.1		6
21.17	even	6		441.2.g.b.79.1		6
21.20	even	2		441.2.f.c.295.1		6
36.7	odd	6		9072.2.a.bs.1.3		3
36.11	even	6		9072.2.a.ca.1.1		3
36.23	even	6		1008.2.r.h.337.3		6
36.31	odd	6		3024.2.r.k.1009.1		6
63.4	even	3		1323.2.h.c.226.1		6
63.5	even	6		441.2.g.b.67.1		6
63.13	odd	6		1323.2.f.d.442.3		6
63.20	even	6		3969.2.a.q.1.3		3
63.23	odd	6		441.2.g.c.67.1		6
63.31	odd	6		1323.2.h.b.226.1		6
63.32	odd	6		441.2.h.d.373.3		6
63.34	odd	6		3969.2.a.l.1.1		3
63.40	odd	6		1323.2.g.e.361.3		6
63.41	even	6		441.2.f.c.148.1		6
63.58	even	3		1323.2.g.d.361.3		6
63.59	even	6		441.2.h.e.373.3		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
63.2.f.a.22.1	✓	6	9.5	odd	6
63.2.f.a.43.1	yes	6	3.2	odd	2
189.2.f.b.64.3		6	9.4	even	3	inner
189.2.f.b.127.3		6	1.1	even	1	trivial
441.2.f.c.148.1		6	63.41	even	6
441.2.f.c.295.1		6	21.20	even	2
441.2.g.b.67.1		6	63.5	even	6
441.2.g.b.79.1		6	21.17	even	6
441.2.g.c.67.1		6	63.23	odd	6
441.2.g.c.79.1		6	21.11	odd	6
441.2.h.d.214.3		6	21.2	odd	6
441.2.h.d.373.3		6	63.32	odd	6
441.2.h.e.214.3		6	21.5	even	6
441.2.h.e.373.3		6	63.59	even	6
567.2.a.c.1.1		3	9.7	even	3
567.2.a.h.1.3		3	9.2	odd	6
1008.2.r.h.337.3		6	36.23	even	6
1008.2.r.h.673.3		6	12.11	even	2
1323.2.f.d.442.3		6	63.13	odd	6
1323.2.f.d.883.3		6	7.6	odd	2
1323.2.g.d.361.3		6	63.58	even	3
1323.2.g.d.667.3		6	7.4	even	3
1323.2.g.e.361.3		6	63.40	odd	6
1323.2.g.e.667.3		6	7.3	odd	6
1323.2.h.b.226.1		6	63.31	odd	6
1323.2.h.b.802.1		6	7.5	odd	6
1323.2.h.c.226.1		6	63.4	even	3
1323.2.h.c.802.1		6	7.2	even	3
3024.2.r.k.1009.1		6	36.31	odd	6
3024.2.r.k.2017.1		6	4.3	odd	2
3969.2.a.l.1.1		3	63.34	odd	6
3969.2.a.q.1.3		3	63.20	even	6
9072.2.a.bs.1.3		3	36.7	odd	6
9072.2.a.ca.1.1		3	36.11	even	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 189 = 3^{3} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	189.f (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(1.26604 - 2.19285i) q^{2} +(-2.20574 - 3.82045i) q^{4} +(-0.439693 - 0.761570i) q^{5} +(-0.500000 + 0.866025i) q^{7} -6.10607 q^{8} -2.22668 q^{10} +(1.93969 - 3.35965i) q^{11} +(2.72668 + 4.72275i) q^{13} +(1.26604 + 2.19285i) q^{14} +(-3.31908 + 5.74881i) q^{16} -1.65270 q^{17} +2.41147 q^{19} +(-1.93969 + 3.35965i) q^{20} +(-4.91147 - 8.50692i) q^{22} +(1.58125 + 2.73881i) q^{23} +(2.11334 - 3.66041i) q^{25} +13.8084 q^{26} +4.41147 q^{28} +(-3.02481 + 5.23913i) q^{29} +(2.27719 + 3.94421i) q^{31} +(2.29813 + 3.98048i) q^{32} +(-2.09240 + 3.62414i) q^{34} +0.879385 q^{35} -4.55438 q^{37} +(3.05303 - 5.28801i) q^{38} +(2.68479 + 4.65020i) q^{40} +(-0.592396 - 1.02606i) q^{41} +(-0.0923963 + 0.160035i) q^{43} -17.1138 q^{44} +8.00774 q^{46} +(-0.511144 + 0.885328i) q^{47} +(-0.500000 - 0.866025i) q^{49} +(-5.35117 - 9.26849i) q^{50} +(12.0287 - 20.8343i) q^{52} -7.29086 q^{53} -3.41147 q^{55} +(3.05303 - 5.28801i) q^{56} +(7.65910 + 13.2660i) q^{58} +(3.33022 + 5.76811i) q^{59} +(1.29813 - 2.24843i) q^{61} +11.5321 q^{62} -1.63816 q^{64} +(2.39780 - 4.15312i) q^{65} +(1.47906 + 2.56180i) q^{67} +(3.64543 + 6.31407i) q^{68} +(1.11334 - 1.92836i) q^{70} +3.68004 q^{71} -12.7811 q^{73} +(-5.76604 + 9.98708i) q^{74} +(-5.31908 - 9.21291i) q^{76} +(1.93969 + 3.35965i) q^{77} +(2.97906 - 5.15988i) q^{79} +5.83750 q^{80} -3.00000 q^{82} +(-0.109470 + 0.189608i) q^{83} +(0.726682 + 1.25865i) q^{85} +(0.233956 + 0.405223i) q^{86} +(-11.8439 + 20.5142i) q^{88} -11.0273 q^{89} -5.45336 q^{91} +(6.97565 - 12.0822i) q^{92} +(1.29426 + 2.24173i) q^{94} +(-1.06031 - 1.83651i) q^{95} +(-6.25150 + 10.8279i) q^{97} -2.53209 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q + 3 q^{2} - 3 q^{4} + 3 q^{5} - 3 q^{7} - 12 q^{8} + 6 q^{11} + 3 q^{13} + 3 q^{14} - 3 q^{16} - 12 q^{17} - 6 q^{19} - 6 q^{20} - 9 q^{22} + 12 q^{23} + 6 q^{25} + 6 q^{26} + 6 q^{28} + 9 q^{29} + 3 q^{31}+ \cdots - 6 q^{98}+O(q^{100}) \) 6 * q + 3 * q^2 - 3 * q^4 + 3 * q^5 - 3 * q^7 - 12 * q^8 + 6 * q^11 + 3 * q^13 + 3 * q^14 - 3 * q^16 - 12 * q^17 - 6 * q^19 - 6 * q^20 - 9 * q^22 + 12 * q^23 + 6 * q^25 + 6 * q^26 + 6 * q^28 + 9 * q^29 + 3 * q^31 - 9 * q^34 - 6 * q^35 - 6 * q^37 + 6 * q^38 + 9 * q^40 + 3 * q^43 - 30 * q^44 + 3 * q^47 - 3 * q^49 - 6 * q^50 + 21 * q^52 - 12 * q^53 + 6 * q^56 + 9 * q^58 - 3 * q^59 - 6 * q^61 + 60 * q^62 + 24 * q^64 + 15 * q^65 + 12 * q^67 + 6 * q^68 - 18 * q^71 - 42 * q^73 - 30 * q^74 - 15 * q^76 + 6 * q^77 + 21 * q^79 + 30 * q^80 - 18 * q^82 - 18 * q^83 - 9 * q^85 + 6 * q^86 - 27 * q^88 - 24 * q^89 - 6 * q^91 + 3 * q^92 + 18 * q^94 - 12 * q^95 + 3 * q^97 - 6 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more