LMFDB - Embedded newform 1323.2.g.e.667.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1323,2,Mod(361,1323)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1323, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([2, 4]))

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

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

chi := DirichletCharacter("1323.361");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1323 = 3^{3} \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1323.g (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:	$10.5642081874$
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			667.3
Root			$-0.766044 + 0.642788i$ of defining polynomial
Character	$\chi$	$=$	1323.667
Dual form			1323.2.g.e.361.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.26604 + 2.19285i) q^{2} +(-2.20574 + 3.82045i) q^{4} -0.879385 q^{5} -6.10607 q^{8} +O(q^{10})$	\(q+(1.26604 + 2.19285i) q^{2} +(-2.20574 + 3.82045i) q^{4} -0.879385 q^{5} -6.10607 q^{8} +(-1.11334 - 1.92836i) q^{10} -3.87939 q^{11} +(-2.72668 - 4.72275i) q^{13} +(-3.31908 - 5.74881i) q^{16} +(-0.826352 - 1.43128i) q^{17} +(1.20574 - 2.08840i) q^{19} +(1.93969 - 3.35965i) q^{20} +(-4.91147 - 8.50692i) q^{22} -3.16250 q^{23} -4.22668 q^{25} +(6.90420 - 11.9584i) q^{26} +(-3.02481 + 5.23913i) q^{29} +(-2.27719 + 3.94421i) q^{31} +(2.29813 - 3.98048i) q^{32} +(2.09240 - 3.62414i) q^{34} +(2.27719 - 3.94421i) q^{37} +6.10607 q^{38} +5.36959 q^{40} +(0.592396 + 1.02606i) q^{41} +(-0.0923963 + 0.160035i) q^{43} +(8.55690 - 14.8210i) q^{44} +(-4.00387 - 6.93491i) q^{46} +(0.511144 + 0.885328i) q^{47} +(-5.35117 - 9.26849i) q^{50} +24.0574 q^{52} +(3.64543 + 6.31407i) q^{53} +3.41147 q^{55} -15.3182 q^{58} +(-3.33022 + 5.76811i) q^{59} +(-1.29813 - 2.24843i) q^{61} -11.5321 q^{62} -1.63816 q^{64} +(2.39780 + 4.15312i) q^{65} +(1.47906 - 2.56180i) q^{67} +7.29086 q^{68} +3.68004 q^{71} +(-6.39053 - 11.0687i) q^{73} +11.5321 q^{74} +(5.31908 + 9.21291i) q^{76} +(2.97906 + 5.15988i) q^{79} +(2.91875 + 5.05542i) q^{80} +(-1.50000 + 2.59808i) q^{82} +(0.109470 - 0.189608i) q^{83} +(0.726682 + 1.25865i) q^{85} -0.467911 q^{86} +23.6878 q^{88} +(-5.51367 + 9.54996i) q^{89} +(6.97565 - 12.0822i) q^{92} +(-1.29426 + 2.24173i) q^{94} +(-1.06031 + 1.83651i) q^{95} +(6.25150 - 10.8279i) q^{97} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q + 3 q^{2} - 3 q^{4} + 6 q^{5} - 12 q^{8}+O(q^{10}) $ 6 * q + 3 * q^2 - 3 * q^4 + 6 * q^5 - 12 * q^8	$ 6 q + 3 q^{2} - 3 q^{4} + 6 q^{5} - 12 q^{8} - 12 q^{11} - 3 q^{13} - 3 q^{16} - 6 q^{17} - 3 q^{19} + 6 q^{20} - 9 q^{22} - 24 q^{23} - 12 q^{25} + 3 q^{26} + 9 q^{29} - 3 q^{31} + 9 q^{34} + 3 q^{37} + 12 q^{38} + 18 q^{40} + 3 q^{43} + 15 q^{44} - 3 q^{47} - 6 q^{50} + 42 q^{52} + 6 q^{53} - 18 q^{58} + 3 q^{59} + 6 q^{61} - 60 q^{62} + 24 q^{64} + 15 q^{65} + 12 q^{67} + 12 q^{68} - 18 q^{71} - 21 q^{73} + 60 q^{74} + 15 q^{76} + 21 q^{79} + 15 q^{80} - 9 q^{82} + 18 q^{83} - 9 q^{85} - 12 q^{86} + 54 q^{88} - 12 q^{89} + 3 q^{92} - 18 q^{94} - 12 q^{95} - 3 q^{97}+O(q^{100}) $ 6 * q + 3 * q^2 - 3 * q^4 + 6 * q^5 - 12 * q^8 - 12 * q^11 - 3 * q^13 - 3 * q^16 - 6 * q^17 - 3 * q^19 + 6 * q^20 - 9 * q^22 - 24 * q^23 - 12 * q^25 + 3 * q^26 + 9 * q^29 - 3 * q^31 + 9 * q^34 + 3 * q^37 + 12 * q^38 + 18 * q^40 + 3 * q^43 + 15 * q^44 - 3 * q^47 - 6 * q^50 + 42 * q^52 + 6 * q^53 - 18 * q^58 + 3 * q^59 + 6 * q^61 - 60 * q^62 + 24 * q^64 + 15 * q^65 + 12 * q^67 + 12 * q^68 - 18 * q^71 - 21 * q^73 + 60 * q^74 + 15 * q^76 + 21 * q^79 + 15 * q^80 - 9 * q^82 + 18 * q^83 - 9 * q^85 - 12 * q^86 + 54 * q^88 - 12 * q^89 + 3 * q^92 - 18 * q^94 - 12 * q^95 - 3 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1323\mathbb{Z}\right)^\times$.

$n$	$785$	$1081$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{1}{3}\right)$

Coefficient data

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

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

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

$2$	1.26604	+	2.19285i	0.895229	+	1.55058i	0.833521	+	0.552487i	$0.186321\pi$
$2$	1.26604	+	2.19285i	0.895229	+	1.55058i	0.0617072	+	0.998094i	$0.480346\pi$
$3$		0			0
$3$		0			0
$4$	−2.20574	+	3.82045i	−1.10287	+	1.91022i
$5$	−0.879385			−0.393273			−0.196637	−	0.980476i	$-0.563002\pi$
$5$	−0.879385			−0.393273			−0.196637	+	0.980476i	$0.563002\pi$
$6$		0			0
$7$		0			0
$7$		0			0
$8$	−6.10607			−2.15882
$9$		0			0
$10$	−1.11334	−	1.92836i	−0.352069	−	0.609802i
$11$	−3.87939			−1.16968			−0.584839	−	0.811149i	$-0.698842\pi$
$11$	−3.87939			−1.16968			−0.584839	+	0.811149i	$0.698842\pi$
$12$		0			0
$13$	−2.72668	−	4.72275i	−0.756245	−	1.30986i	−0.944753	−	0.327784i	$-0.893698\pi$
$13$	−2.72668	−	4.72275i	−0.756245	−	1.30986i	0.188507	−	0.982072i	$-0.439635\pi$
$14$		0			0
$15$		0			0
$16$	−3.31908	−	5.74881i	−0.829769	−	1.43720i
$17$	−0.826352	−	1.43128i	−0.200420	−	0.347137i	0.748244	−	0.663424i	$-0.230897\pi$
$17$	−0.826352	−	1.43128i	−0.200420	−	0.347137i	−0.948664	+	0.316286i	$0.897564\pi$
$18$		0			0
$19$	1.20574	−	2.08840i	0.276615	−	0.479111i	−0.693926	−	0.720046i	$-0.744121\pi$
$19$	1.20574	−	2.08840i	0.276615	−	0.479111i	0.970541	+	0.240935i	$0.0774540\pi$
$20$	1.93969	−	3.35965i	0.433728	−	0.751240i
$21$		0			0
$22$	−4.91147	−	8.50692i	−1.04713	−	1.81368i
$23$	−3.16250			−0.659428			−0.329714	−	0.944081i	$-0.606952\pi$
$23$	−3.16250			−0.659428			−0.329714	+	0.944081i	$0.606952\pi$
$24$		0			0
$25$	−4.22668			−0.845336
$26$	6.90420	−	11.9584i	1.35403	−	2.34524i
$27$		0			0
$28$		0			0
$29$	−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	$-0.967454\pi$
$31$	−2.27719	+	3.94421i	−0.408995	+	0.708400i	0.585782	+	0.810468i	$0.300787\pi$
$32$	2.29813	−	3.98048i	0.406256	−	0.703657i
$33$		0			0
$34$	2.09240	−	3.62414i	0.358843	−	0.621534i
$35$		0			0
$36$		0			0
$37$	2.27719	−	3.94421i	0.374368	−	0.648424i	−0.615865	−	0.787852i	$-0.711193\pi$
$37$	2.27719	−	3.94421i	0.374368	−	0.648424i	0.990232	+	0.139428i	$0.0445265\pi$
$38$	6.10607			0.990535
$39$		0			0
$40$	5.36959			0.849006
$41$	0.592396	+	1.02606i	0.0925168	+	0.160244i	0.908570	−	0.417734i	$-0.137175\pi$
$41$	0.592396	+	1.02606i	0.0925168	+	0.160244i	−0.816053	+	0.577977i	$0.803842\pi$
$42$		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	$0.171152\pi$
$44$	8.55690	−	14.8210i	1.29000	−	2.23435i
$45$		0			0
$46$	−4.00387	−	6.93491i	−0.590338	−	1.02250i
$47$	0.511144	+	0.885328i	0.0745581	+	0.129138i	0.900894	−	0.434039i	$-0.142912\pi$
$47$	0.511144	+	0.885328i	0.0745581	+	0.129138i	−0.826336	+	0.563178i	$0.809579\pi$
$48$		0			0
$49$		0			0
$50$	−5.35117	−	9.26849i	−0.756769	−	1.31076i
$51$		0			0
$52$	24.0574			3.33616
$53$	3.64543	+	6.31407i	0.500738	+	0.867304i	1.00000		0.000852699i	$0.000271423\pi$
$53$	3.64543	+	6.31407i	0.500738	+	0.867304i	−0.499261	+	0.866451i	$0.666395\pi$
$54$		0			0
$55$	3.41147			0.460003
$56$		0			0
$57$		0			0
$58$	−15.3182			−2.01138
$59$	−3.33022	+	5.76811i	−0.433558	+	0.750944i	−0.997177	−	0.0750906i	$-0.976075\pi$
$59$	−3.33022	+	5.76811i	−0.433558	+	0.750944i	0.563619	+	0.826035i	$0.309409\pi$
$60$		0			0
$61$	−1.29813	−	2.24843i	−0.166209	−	0.287882i	0.770875	−	0.636986i	$-0.219819\pi$
$61$	−1.29813	−	2.24843i	−0.166209	−	0.287882i	−0.937084	+	0.349104i	$0.886486\pi$
$62$	−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	−0.761422	−	0.648256i	$-0.775499\pi$
$67$	1.47906	−	2.56180i	0.180695	−	0.312974i	0.942118	+	0.335283i	$0.108832\pi$
$68$	7.29086			0.884147
$69$		0			0
$70$		0			0
$71$	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
$73$	−6.39053	−	11.0687i	−0.747955	−	1.29550i	−0.948801	−	0.315873i	$-0.897703\pi$
$73$	−6.39053	−	11.0687i	−0.747955	−	1.29550i	0.200847	−	0.979623i	$-0.435631\pi$
$74$	11.5321			1.34058
$75$		0			0
$76$	5.31908	+	9.21291i	0.610140	+	1.05679i
$77$		0			0
$78$		0			0
$79$	2.97906	+	5.15988i	0.335170	+	0.580531i	0.983517	−	0.180813i	$-0.0578729\pi$
$79$	2.97906	+	5.15988i	0.335170	+	0.580531i	−0.648348	+	0.761345i	$0.724540\pi$
$80$	2.91875	+	5.05542i	0.326326	+	0.565213i
$81$		0			0
$82$	−1.50000	+	2.59808i	−0.165647	+	0.286910i
$83$	0.109470	−	0.189608i	0.0120159	−	0.0208122i	−0.859955	−	0.510370i	$-0.829508\pi$
$83$	0.109470	−	0.189608i	0.0120159	−	0.0208122i	0.871971	+	0.489558i	$0.162842\pi$
$84$		0			0
$85$	0.726682	+	1.25865i	0.0788197	+	0.136520i
$86$	−0.467911			−0.0504562
$87$		0			0
$88$	23.6878			2.52513
$89$	−5.51367	+	9.54996i	−0.584448	+	1.01229i	0.410496	+	0.911862i	$0.365356\pi$
$89$	−5.51367	+	9.54996i	−0.584448	+	1.01229i	−0.994944	+	0.100431i	$0.967978\pi$
$90$		0			0
$91$		0			0
$92$	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	$-0.614439\pi$
$97$	6.25150	−	10.8279i	0.634743	−	1.09941i	0.986569	−	0.163342i	$-0.0522275\pi$
$98$		0			0
$99$		0			0
$100$	9.32295	−	16.1478i	0.932295	−	1.61478i
$101$	−9.71688			−0.966866			−0.483433	−	0.875381i	$-0.660610\pi$
$101$	−9.71688			−0.966866			−0.483433	+	0.875381i	$0.660610\pi$
$102$		0			0
$103$	−6.59627			−0.649949			−0.324975	−	0.945723i	$-0.605356\pi$
$103$	−6.59627			−0.649949			−0.324975	+	0.945723i	$0.605356\pi$
$104$	16.6493	+	28.8374i	1.63260	+	2.82774i
$105$		0			0
$106$	−9.23055	+	15.9878i	−0.896550	+	1.55287i
$107$	1.19459	−	2.06910i	0.115486	−	0.200027i	−0.802488	−	0.596668i	$-0.796491\pi$
$107$	1.19459	−	2.06910i	0.115486	−	0.200027i	0.917974	+	0.396641i	$0.129824\pi$
$108$		0			0
$109$	−1.97906	−	3.42782i	−0.189559	−	0.328326i	0.755544	−	0.655098i	$-0.227373\pi$
$109$	−1.97906	−	3.42782i	−0.189559	−	0.328326i	−0.945103	+	0.326772i	$0.894039\pi$
$110$	4.31908	+	7.48086i	0.411808	+	0.713272i
$111$		0			0
$112$		0			0
$113$	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
$115$	2.78106			0.259335
$116$	−13.3439	−	23.1123i	−1.23895	−	2.14592i
$117$		0			0
$118$	−16.8648			−1.55253
$119$		0			0
$120$		0			0
$121$	4.04963			0.368148
$122$	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
$131$	−19.1976			−1.67730			−0.838650	−	0.544670i	$-0.816655\pi$
$131$	−19.1976			−1.67730			−0.838650	+	0.544670i	$0.816655\pi$
$132$		0			0
$133$		0			0
$134$	7.49020			0.647055
$135$		0			0
$136$	5.04576	+	8.73951i	0.432670	+	0.749407i
$137$	−18.1557			−1.55115			−0.775573	−	0.631258i	$-0.782539\pi$
$137$	−18.1557			−1.55115			−0.775573	+	0.631258i	$0.782539\pi$
$138$		0			0
$139$	11.0287	+	19.1022i	0.935441	+	1.62023i	0.773846	+	0.633374i	$0.218330\pi$
$139$	11.0287	+	19.1022i	0.935441	+	1.62023i	0.161595	+	0.986857i	$0.448336\pi$
$140$		0			0
$141$		0			0
$142$	4.65910	+	8.06980i	0.390983	+	0.677202i
$143$	10.5778	+	18.3214i	0.884564	+	1.53211i
$144$		0			0
$145$	2.65998	−	4.60722i	0.220899	−	0.382608i
$146$	16.1814	−	28.0270i	1.33918	−	2.31953i
$147$		0			0
$148$	10.0458	+	17.3998i	0.825756	+	1.43025i
$149$	15.1557			1.24160			0.620802	−	0.783968i	$-0.286807\pi$
$149$	15.1557			1.24160			0.620802	+	0.783968i	$0.286807\pi$
$150$		0			0
$151$	−18.9564			−1.54265			−0.771323	−	0.636444i	$-0.780405\pi$
$151$	−18.9564			−1.54265			−0.771323	+	0.636444i	$0.780405\pi$
$152$	−7.36231	+	12.7519i	−0.597162	+	1.03432i
$153$		0			0
$154$		0			0
$155$	2.00253	−	3.46848i	0.160847	−	0.278595i
$156$		0			0
$157$	−9.02869	+	15.6381i	−0.720568	+	1.24806i	0.240205	+	0.970722i	$0.422785\pi$
$157$	−9.02869	+	15.6381i	−0.720568	+	1.24806i	−0.960773	+	0.277337i	$0.910548\pi$
$158$	−7.54323	+	13.0653i	−0.600107	+	1.03942i
$159$		0			0
$160$	−2.02094	+	3.50038i	−0.159770	+	0.276729i
$161$		0			0
$162$		0			0
$163$	−0.479055	+	0.829748i	−0.0375225	+	0.0649909i	−0.884177	−	0.467152i	$-0.845280\pi$
$163$	−0.479055	+	0.829748i	−0.0375225	+	0.0649909i	0.846654	+	0.532143i	$0.178613\pi$
$164$	−5.22668			−0.408135
$165$		0			0
$166$	0.554378			0.0430280
$167$	−9.91921	−	17.1806i	−0.767572	−	1.32947i	−0.938876	−	0.344255i	$-0.888131\pi$
$167$	−9.91921	−	17.1806i	−0.767572	−	1.32947i	0.171304	−	0.985218i	$-0.445202\pi$
$168$		0			0
$169$	−8.36959	+	14.4965i	−0.643814	+	1.11512i
$170$	−1.84002	+	3.18701i	−0.141123	+	0.244433i
$171$		0			0
$172$	−0.407604	−	0.705990i	−0.0310795	−	0.0538313i
$173$	−11.3414	−	19.6438i	−0.862268	−	1.49349i	−0.869734	−	0.493520i	$-0.835710\pi$
$173$	−11.3414	−	19.6438i	−0.862268	−	1.49349i	0.00746626	−	0.999972i	$-0.497623\pi$
$174$		0			0
$175$		0			0
$176$	12.8760	+	22.3019i	0.970564	+	1.68107i
$177$		0			0
$178$	−27.9222			−2.09286
$179$	−3.67365	−	6.36295i	−0.274581	−	0.475589i	0.695448	−	0.718576i	$-0.255206\pi$
$179$	−3.67365	−	6.36295i	−0.274581	−	0.475589i	−0.970029	+	0.242988i	$0.921873\pi$
$180$		0			0
$181$	3.44562			0.256111			0.128056	−	0.991767i	$-0.459126\pi$
$181$	3.44562			0.256111			0.128056	+	0.991767i	$0.459126\pi$
$182$		0			0
$183$		0			0
$184$	19.3105			1.42359
$185$	−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	0.950034	−	0.312146i	$-0.101048\pi$
$191$	2.82888	+	4.89976i	0.204690	+	0.354534i	−0.745344	+	0.666680i	$0.767715\pi$
$192$		0			0
$193$	−4.79813	+	8.31061i	−0.345377	+	0.598211i	−0.985422	−	0.170127i	$-0.945582\pi$
$193$	−4.79813	+	8.31061i	−0.345377	+	0.598211i	0.640045	+	0.768337i	$0.278916\pi$
$194$	31.6587			2.27296
$195$		0			0
$196$		0			0
$197$	−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
$199$	3.29813	+	5.71253i	0.233798	+	0.404951i	0.958923	−	0.283667i	$-0.0915511\pi$
$199$	3.29813	+	5.71253i	0.233798	+	0.404951i	−0.725124	+	0.688618i	$0.758218\pi$
$200$	25.8084			1.82493
$201$		0			0
$202$	−12.3020	−	21.3077i	−0.865566	−	1.49920i
$203$		0			0
$204$		0			0
$205$	−0.520945	−	0.902302i	−0.0363843	−	0.0630195i
$206$	−8.35117	−	14.4646i	−0.581853	−	1.00780i
$207$		0			0
$208$	−18.1001	+	31.3504i	−1.25502	+	2.17376i
$209$	−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	$0.796331\pi$
$212$	−32.1634			−2.20899
$213$		0			0
$214$	6.04963			0.413544
$215$	0.0812519	−	0.140732i	0.00554133	−	0.00959787i
$216$		0			0
$217$		0			0
$218$	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	−0.951760	−	0.306843i	$-0.900727\pi$
$223$	−3.13816	+	5.43545i	−0.210146	+	0.363984i	0.741614	+	0.670827i	$0.234061\pi$
$224$		0			0
$225$		0			0
$226$	−20.8307	+	36.0798i	−1.38564	+	2.39999i
$227$	−6.16250			−0.409020			−0.204510	−	0.978865i	$-0.565560\pi$
$227$	−6.16250			−0.409020			−0.204510	+	0.978865i	$0.565560\pi$
$228$		0			0
$229$	−23.3851			−1.54533			−0.772664	−	0.634815i	$-0.781076\pi$
$229$	−23.3851			−1.54533			−0.772664	+	0.634815i	$0.781076\pi$
$230$	3.52094	+	6.09845i	0.232164	+	0.402120i
$231$		0			0
$232$	18.4697	−	31.9905i	1.21260	−	2.10028i
$233$	−4.26264	+	7.38311i	−0.279255	+	0.483684i	−0.971200	−	0.238267i	$-0.923421\pi$
$233$	−4.26264	+	7.38311i	−0.279255	+	0.483684i	0.691945	+	0.721950i	$0.256754\pi$
$234$		0			0
$235$	−0.449493	−	0.778544i	−0.0293217	−	0.0507866i
$236$	−14.6912	−	25.4459i	−0.956315	−	1.65639i
$237$		0			0
$238$		0			0
$239$	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
$241$	5.40373			0.348085			0.174043	−	0.984738i	$-0.444317\pi$
$241$	5.40373			0.348085			0.174043	+	0.984738i	$0.444317\pi$
$242$	5.12701	+	8.88024i	0.329577	+	0.570844i
$243$		0			0
$244$	11.4534			0.733226
$245$		0			0
$246$		0			0
$247$	−13.1506			−0.836755
$248$	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	$-0.624361\pi$
$251$	−12.0669			−0.761654			−0.380827	+	0.924646i	$0.624361\pi$
$252$		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
$257$	10.5662			0.659104			0.329552	−	0.944137i	$-0.393102\pi$
$257$	10.5662			0.659104			0.329552	+	0.944137i	$0.393102\pi$
$258$		0			0
$259$		0			0
$260$	−21.1557			−1.31202
$261$		0			0
$262$	−24.3050	−	42.0975i	−1.50157	−	2.60079i
$263$	28.3533			1.74834			0.874169	−	0.485622i	$-0.161407\pi$
$263$	28.3533			1.74834			0.874169	+	0.485622i	$0.161407\pi$
$264$		0			0
$265$	−3.20574	−	5.55250i	−0.196927	−	0.341087i
$266$		0			0
$267$		0			0
$268$	6.52481	+	11.3013i	0.398567	+	0.690337i
$269$	−3.74170	−	6.48081i	−0.228135	−	0.395142i	0.729120	−	0.684386i	$-0.239930\pi$
$269$	−3.74170	−	6.48081i	−0.228135	−	0.395142i	−0.957255	+	0.289244i	$0.906596\pi$
$270$		0			0
$271$	6.81908	−	11.8110i	0.414229	−	0.717467i	−0.581118	−	0.813819i	$-0.697384\pi$
$271$	6.81908	−	11.8110i	0.414229	−	0.717467i	0.995347	+	0.0963530i	$0.0307178\pi$
$272$	−5.48545	+	9.50108i	−0.332604	+	0.576088i
$273$		0			0
$274$	−22.9859	−	39.8128i	−1.38863	−	2.40518i
$275$	16.3969			0.988772
$276$		0			0
$277$	−6.15064			−0.369556			−0.184778	−	0.982780i	$-0.559157\pi$
$277$	−6.15064			−0.369556			−0.184778	+	0.982780i	$0.559157\pi$
$278$	−27.9256	+	48.3686i	−1.67487	+	2.90095i
$279$		0			0
$280$		0			0
$281$	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	−0.00675974	−	0.999977i	$-0.502152\pi$
$283$	14.5116	−	25.1348i	0.862626	−	1.49411i	0.869385	−	0.494134i	$-0.164515\pi$
$284$	−8.11721	+	14.0594i	−0.481668	+	0.834273i
$285$		0			0
$286$	−26.7841	+	46.3913i	−1.58377	+	2.74318i
$287$		0			0
$288$		0			0
$289$	7.13429	−	12.3569i	0.419664	−	0.726879i
$290$	13.4706			0.791021
$291$		0			0
$292$	56.3833			3.29958
$293$	4.20961	+	7.29125i	0.245928	+	0.425960i	0.962392	−	0.271664i	$-0.0875740\pi$
$293$	4.20961	+	7.29125i	0.245928	+	0.425960i	−0.716464	+	0.697624i	$0.754241\pi$
$294$		0			0
$295$	2.92855	−	5.07239i	0.170507	−	0.295326i
$296$	−13.9047	+	24.0836i	−0.808192	+	1.39983i
$297$		0			0
$298$	19.1878	+	33.2342i	1.11152	+	1.92521i
$299$	8.62314	+	14.9357i	0.498689	+	0.863755i
$300$		0			0
$301$		0			0
$302$	−23.9996	−	41.5685i	−1.38102	−	2.39200i
$303$		0			0
$304$	−16.0077			−0.918107
$305$	1.14156	+	1.97724i	0.0653655	+	0.113216i
$306$		0			0
$307$	12.6878			0.724130			0.362065	−	0.932153i	$-0.382072\pi$
$307$	12.6878			0.724130			0.362065	+	0.932153i	$0.382072\pi$
$308$		0			0
$309$		0			0
$310$	10.1411			0.575979
$311$	8.24510	−	14.2809i	0.467537	−	0.809797i	−0.531775	−	0.846886i	$-0.678475\pi$
$311$	8.24510	−	14.2809i	0.467537	−	0.809797i	0.999312	+	0.0370881i	$0.0118082\pi$
$312$		0			0
$313$	14.2592	+	24.6977i	0.805980	+	1.39600i	0.915628	+	0.402027i	$0.131694\pi$
$313$	14.2592	+	24.6977i	0.805980	+	1.39600i	−0.109648	+	0.993970i	$0.534972\pi$
$314$	−45.7229			−2.58029
$315$		0			0
$316$	−26.2841			−1.47859
$317$	−12.9474	−	22.4256i	−0.727200	−	1.25955i	−0.958062	−	0.286561i	$-0.907488\pi$
$317$	−12.9474	−	22.4256i	−0.727200	−	1.25955i	0.230862	−	0.972987i	$-0.425846\pi$
$318$		0			0
$319$	11.7344	−	20.3246i	0.657002	−	1.13796i
$320$	1.44057			0.0805303
$321$		0			0
$322$		0			0
$323$	−3.98545			−0.221756
$324$		0			0
$325$	11.5248	+	19.9616i	0.639282	+	1.10727i
$326$	−2.42602			−0.134365
$327$		0			0
$328$	−3.61721	−	6.26519i	−0.199727	−	0.345937i
$329$		0			0
$330$		0			0
$331$	−4.10947	−	7.11781i	−0.225877	−	0.391230i	0.730705	−	0.682693i	$-0.239191\pi$
$331$	−4.10947	−	7.11781i	−0.225877	−	0.391230i	−0.956582	+	0.291463i	$0.905858\pi$
$332$	0.482926	+	0.836452i	0.0265040	+	0.0459063i
$333$		0			0
$334$	25.1163	−	43.5028i	1.37430	−	2.38037i
$335$	−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	$0.873068\pi$
$338$	−42.3851			−2.30544
$339$		0			0
$340$	−6.41147			−0.347711
$341$	8.83409	−	15.3011i	0.478393	−	0.828601i
$342$		0			0
$343$		0			0
$344$	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	−0.389337	−	0.921095i	$-0.627296\pi$
$347$	11.2331	−	19.4563i	0.603023	−	1.04447i	0.992361	−	0.123372i	$-0.0393707\pi$
$348$		0			0
$349$	13.0496	−	22.6026i	0.698531	−	1.20989i	−0.270445	−	0.962735i	$-0.587171\pi$
$349$	13.0496	−	22.6026i	0.698531	−	1.20989i	0.968976	−	0.247155i	$-0.0794958\pi$
$350$		0			0
$351$		0			0
$352$	−8.91534	+	15.4418i	−0.475189	+	0.823052i
$353$	−0.355037			−0.0188967			−0.00944836	−	0.999955i	$-0.503008\pi$
$353$	−0.355037			−0.0188967			−0.00944836	+	0.999955i	$0.503008\pi$
$354$		0			0
$355$	−3.23618			−0.171758
$356$	−24.3234	−	42.1294i	−1.28914	−	2.23285i
$357$		0			0
$358$	9.30200	−	16.1115i	0.491626	−	0.851522i
$359$	2.72803	−	4.72508i	0.143980	−	0.249380i	−0.785012	−	0.619480i	$-0.787343\pi$
$359$	2.72803	−	4.72508i	0.143980	−	0.249380i	0.928992	+	0.370100i	$0.120677\pi$
$360$		0			0
$361$	6.59240	+	11.4184i	0.346968	+	0.600967i
$362$	4.36231	+	7.55574i	0.229278	+	0.397121i
$363$		0			0
$364$		0			0
$365$	5.61974	+	9.73367i	0.294150	+	0.509484i
$366$		0			0
$367$	−10.9240			−0.570226			−0.285113	−	0.958494i	$-0.592031\pi$
$367$	−10.9240			−0.570226			−0.285113	+	0.958494i	$0.592031\pi$
$368$	10.4966	+	18.1806i	0.547173	+	0.947731i
$369$		0			0
$370$	−10.1411			−0.527213
$371$		0			0
$372$		0			0
$373$	1.73143			0.0896500			0.0448250	−	0.998995i	$-0.485727\pi$
$373$	1.73143			0.0896500			0.0448250	+	0.998995i	$0.485727\pi$
$374$	−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
$383$	−8.71183			−0.445154			−0.222577	−	0.974915i	$-0.571447\pi$
$383$	−8.71183			−0.445154			−0.222577	+	0.974915i	$0.571447\pi$
$384$		0			0
$385$		0			0
$386$	−24.2986			−1.23677
$387$		0			0
$388$	27.5783	+	47.7670i	1.40008	+	2.42500i
$389$	−3.64321			−0.184718			−0.0923590	−	0.995726i	$-0.529441\pi$
$389$	−3.64321			−0.184718			−0.0923590	+	0.995726i	$0.529441\pi$
$390$		0			0
$391$	2.61334	+	4.52644i	0.132162	+	0.228912i
$392$		0			0
$393$		0			0
$394$	−10.5334	−	18.2444i	−0.530667	−	0.919142i
$395$	−2.61974	−	4.53752i	−0.131813	−	0.228307i
$396$		0			0
$397$	−7.72281	+	13.3763i	−0.387597	+	0.671337i	−0.992126	−	0.125246i	$-0.960028\pi$
$397$	−7.72281	+	13.3763i	−0.387597	+	0.671337i	0.604529	+	0.796583i	$0.293361\pi$
$398$	−8.35117	+	14.4646i	−0.418606	+	0.725047i
$399$		0			0
$400$	14.0287	+	24.2984i	0.701434	+	1.21492i
$401$	−18.4219			−0.919946			−0.459973	−	0.887933i	$-0.652141\pi$
$401$	−18.4219			−0.919946			−0.459973	+	0.887933i	$0.652141\pi$
$402$		0			0
$403$	24.8367			1.23720
$404$	21.4329	−	37.1228i	1.06633	−	1.84693i
$405$		0			0
$406$		0			0
$407$	−8.83409	+	15.3011i	−0.437890	+	0.758447i
$408$		0			0
$409$	−14.3182	+	24.7999i	−0.707989	+	1.22627i	0.257612	+	0.966248i	$0.417064\pi$
$409$	−14.3182	+	24.7999i	−0.707989	+	1.22627i	−0.965602	+	0.260025i	$0.916269\pi$
$410$	1.31908	−	2.28471i	0.0651446	−	0.112834i
$411$		0			0
$412$	14.5496	−	25.2007i	0.716809	−	1.24155i
$413$		0			0
$414$		0			0
$415$	−0.0962667	+	0.166739i	−0.00472554	+	0.00818488i
$416$	−25.0651			−1.22892
$417$		0			0
$418$	−23.6878			−1.15861
$419$	17.3478	+	30.0472i	0.847494	+	1.46790i	0.883438	+	0.468548i	$0.155223\pi$
$419$	17.3478	+	30.0472i	0.847494	+	1.46790i	−0.0359442	+	0.999354i	$0.511444\pi$
$420$		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	$-0.0660738\pi$
$422$	−4.26604	+	7.38901i	−0.207668	+	0.359691i
$423$		0			0
$424$	−22.2592	−	38.5541i	−1.08100	−	1.87235i
$425$	3.49273	+	6.04958i	0.169422	+	0.293448i
$426$		0			0
$427$		0			0
$428$	5.26991	+	9.12776i	0.254731	+	0.441207i
$429$		0			0
$430$	0.411474			0.0198430
$431$	13.2961	+	23.0295i	0.640449	+	1.10929i	0.985333	+	0.170645i	$0.0545852\pi$
$431$	13.2961	+	23.0295i	0.640449	+	1.10929i	−0.344883	+	0.938646i	$0.612081\pi$
$432$		0			0
$433$	−37.1830			−1.78690			−0.893451	−	0.449160i	$-0.851723\pi$
$433$	−37.1830			−1.78690			−0.893451	+	0.449160i	$0.851723\pi$
$434$		0			0
$435$		0			0
$436$	17.4611			0.836235
$437$	−3.81315	+	6.60457i	−0.182408	+	0.315939i
$438$		0			0
$439$	12.5373	+	21.7152i	0.598373	+	1.03641i	0.993061	+	0.117597i	$0.0375192\pi$
$439$	12.5373	+	21.7152i	0.598373	+	1.03641i	−0.394689	+	0.918815i	$0.629147\pi$
$440$	−20.8307			−0.993064
$441$		0			0
$442$	−22.8212			−1.08549
$443$	1.02229	+	1.77066i	0.0485704	+	0.0841264i	0.889288	−	0.457347i	$-0.151200\pi$
$443$	1.02229	+	1.77066i	0.0485704	+	0.0841264i	−0.840718	+	0.541473i	$0.817867\pi$
$444$		0			0
$445$	4.84864	−	8.39809i	0.229848	−	0.398108i
$446$	−15.8922			−0.752516
$447$		0			0
$448$		0			0
$449$	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
$451$	−2.29813	−	3.98048i	−0.108215	−	0.187434i
$452$	−72.5836			−3.41404
$453$		0			0
$454$	−7.80200	−	13.5135i	−0.366166	−	0.634218i
$455$		0			0
$456$		0			0
$457$	21.2973	+	36.8879i	0.996244	+	1.72554i	0.573115	+	0.819475i	$0.305735\pi$
$457$	21.2973	+	36.8879i	0.996244	+	1.72554i	0.423129	+	0.906070i	$0.360932\pi$
$458$	−29.6065	−	51.2800i	−1.38342	−	2.39616i
$459$		0			0
$460$	−6.13429	+	10.6249i	−0.286013	+	0.495388i
$461$	−0.252374	+	0.437124i	−0.0117542	+	0.0203589i	−0.871843	−	0.489786i	$-0.837075\pi$
$461$	−0.252374	+	0.437124i	−0.0117542	+	0.0203589i	0.860088	+	0.510145i	$0.170408\pi$
$462$		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	$0.853169\pi$
$464$	40.1584			1.86431
$465$		0			0
$466$	−21.5868			−0.999988
$467$	15.7083	−	27.2075i	0.726892	−	1.25901i	−0.231299	−	0.972883i	$-0.574298\pi$
$467$	15.7083	−	27.2075i	0.726892	−	1.25901i	0.958191	−	0.286131i	$-0.0923691\pi$
$468$		0			0
$469$		0			0
$470$	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
$476$		0			0
$477$		0			0
$478$	−18.4363	+	31.9326i	−0.843256	+	1.46056i
$479$	−16.4406			−0.751189			−0.375594	−	0.926784i	$-0.622561\pi$
$479$	−16.4406			−0.751189			−0.375594	+	0.926784i	$0.622561\pi$
$480$		0			0
$481$	−24.8367			−1.13245
$482$	6.84137	+	11.8496i	0.311616	+	0.539734i
$483$		0			0
$484$	−8.93242	+	15.4714i	−0.406019	+	0.703246i
$485$	−5.49747	+	9.52190i	−0.249627	+	0.432367i
$486$		0			0
$487$	1.48767	+	2.57673i	0.0674129	+	0.116763i	0.897762	−	0.440481i	$-0.145192\pi$
$487$	1.48767	+	2.57673i	0.0674129	+	0.116763i	−0.830349	+	0.557244i	$0.811859\pi$
$488$	7.92649	+	13.7291i	0.358815	+	0.621486i
$489$		0			0
$490$		0			0
$491$	−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
$493$	9.99825			0.450298
$494$	−16.6493	−	28.8374i	−0.749087	−	1.29746i
$495$		0			0
$496$	30.2327			1.35749
$497$		0			0
$498$		0			0
$499$	−13.4439			−0.601830			−0.300915	−	0.953651i	$-0.597292\pi$
$499$	−13.4439			−0.601830			−0.300915	+	0.953651i	$0.597292\pi$
$500$	−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	$-0.668600\pi$
$503$	−22.6631			−1.01050			−0.505250	+	0.862973i	$0.668600\pi$
$504$		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
$509$	9.54757			0.423189			0.211594	−	0.977358i	$-0.432134\pi$
$509$	9.54757			0.423189			0.211594	+	0.977358i	$0.432134\pi$
$510$		0			0
$511$		0			0
$512$	50.5553			2.23425
$513$		0			0
$514$	13.3773	+	23.1702i	0.590049	+	1.02199i
$515$	5.80066			0.255608
$516$		0			0
$517$	−1.98293	−	3.43453i	−0.0872090	−	0.151050i
$518$		0			0
$519$		0			0
$520$	−14.6411	−	25.3592i	−0.642057	−	1.11208i
$521$	1.55644	+	2.69583i	0.0681887	+	0.118106i	0.898104	−	0.439783i	$-0.144945\pi$
$521$	1.55644	+	2.69583i	0.0681887	+	0.118106i	−0.829915	+	0.557889i	$0.811611\pi$
$522$		0			0
$523$	−8.07444	+	13.9853i	−0.353071	+	0.611537i	−0.986786	−	0.162030i	$-0.948196\pi$
$523$	−8.07444	+	13.9853i	−0.353071	+	0.611537i	0.633715	+	0.773567i	$0.281529\pi$
$524$	42.3448	−	73.3434i	1.84984	−	3.20402i
$525$		0			0
$526$	35.8965	+	62.1746i	1.56516	+	2.71094i
$527$	7.52704			0.327883
$528$		0			0
$529$	−12.9986			−0.565155
$530$	8.11721	−	14.0594i	0.352589	−	0.610702i
$531$		0			0
$532$		0			0
$533$	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
$539$		0			0
$540$		0			0
$541$	2.50774	−	4.34353i	0.107816	−	0.186743i	−0.807069	−	0.590457i	$-0.798948\pi$
$541$	2.50774	−	4.34353i	0.107816	−	0.186743i	0.914885	+	0.403714i	$0.132281\pi$
$542$	34.5330			1.48332
$543$		0			0
$544$	−7.59627			−0.325687
$545$	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	$0.281258\pi$
$548$	40.0467	−	69.3629i	1.71071	−	2.96304i
$549$		0			0
$550$	20.7592	+	35.9561i	0.885177	+	1.53317i
$551$	7.29426	+	12.6340i	0.310746	+	0.538228i
$552$		0			0
$553$		0			0
$554$	−7.78699	−	13.4875i	−0.330837	−	0.573027i
$555$		0			0
$556$	−97.3055			−4.12667
$557$	−17.2815	−	29.9325i	−0.732242	−	1.26828i	−0.955923	−	0.293618i	$-0.905141\pi$
$557$	−17.2815	−	29.9325i	−0.732242	−	1.26828i	0.223681	−	0.974662i	$-0.428193\pi$
$558$		0			0
$559$	1.00774			0.0426229
$560$		0			0
$561$		0			0
$562$	8.38682			0.353777
$563$	18.6052	−	32.2251i	0.784115	−	1.35813i	−0.145411	−	0.989371i	$-0.546450\pi$
$563$	18.6052	−	32.2251i	0.784115	−	1.35813i	0.929526	−	0.368756i	$-0.120216\pi$
$564$		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	0.870235	−	0.492636i	$-0.163967\pi$
$569$	0.202333	+	0.350452i	0.00848226	+	0.0146917i	−0.861753	+	0.507328i	$0.830633\pi$
$570$		0			0
$571$	18.8897	−	32.7178i	0.790507	−	1.36920i	−0.135146	−	0.990826i	$-0.543150\pi$
$571$	18.8897	−	32.7178i	0.790507	−	1.36920i	0.925653	−	0.378373i	$-0.123516\pi$
$572$	−93.3278			−3.90223
$573$		0			0
$574$		0			0
$575$	13.3669			0.557438
$576$		0			0
$577$	−1.10560	−	1.91496i	−0.0460267	−	0.0797206i	0.842094	−	0.539330i	$-0.181323\pi$
$577$	−1.10560	−	1.91496i	−0.0460267	−	0.0797206i	−0.888121	+	0.459610i	$0.847989\pi$
$578$	36.1293			1.50278
$579$		0			0
$580$	11.7344	+	20.3246i	0.487245	+	0.843934i
$581$		0			0
$582$		0			0
$583$	−14.1420	−	24.4947i	−0.585703	−	1.01447i
$584$	39.0210	+	67.5864i	1.61470	+	2.79674i
$585$		0			0
$586$	−10.6591	+	18.4621i	−0.440323	+	0.762662i
$587$	−12.1049	+	20.9663i	−0.499622	+	0.865371i	−1.00000		0.000436347i	$-0.999861\pi$
$587$	−12.1049	+	20.9663i	−0.499622	+	0.865371i	0.500378	+	0.865807i	$0.333194\pi$
$588$		0			0
$589$	5.49138	+	9.51135i	0.226268	+	0.391908i
$590$	14.8307			0.610570
$591$		0			0
$592$	−30.2327			−1.24255
$593$	−6.11927	+	10.5989i	−0.251288	+	0.435244i	−0.963881	−	0.266334i	$-0.914188\pi$
$593$	−6.11927	+	10.5989i	−0.251288	+	0.435244i	0.712592	+	0.701578i	$0.247521\pi$
$594$		0			0
$595$		0			0
$596$	−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	−0.103966	−	0.994581i	$-0.533153\pi$
$599$	19.8084	−	34.3092i	0.809349	−	1.40183i	0.913315	−	0.407253i	$-0.133513\pi$
$600$		0			0
$601$	−15.0039	+	25.9875i	−0.612021	+	1.06005i	0.378879	+	0.925446i	$0.376310\pi$
$601$	−15.0039	+	25.9875i	−0.612021	+	1.06005i	−0.990899	+	0.134605i	$0.957024\pi$
$602$		0			0
$603$		0			0
$604$	41.8127	−	72.4218i	1.70134	−	2.94680i
$605$	−3.56118			−0.144783
$606$		0			0
$607$	19.4843			0.790844			0.395422	−	0.918499i	$-0.370598\pi$
$607$	19.4843			0.790844			0.395422	+	0.918499i	$0.370598\pi$
$608$	−5.54189	−	9.59883i	−0.224753	−	0.389284i
$609$		0			0
$610$	−2.89053	+	5.00654i	−0.117034	+	0.202709i
$611$	2.78746	−	4.82802i	0.112768	−	0.195321i
$612$		0			0
$613$	9.26382	+	16.0454i	0.374162	+	0.648068i	0.990201	−	0.139648i	$-0.0445970\pi$
$613$	9.26382	+	16.0454i	0.374162	+	0.648068i	−0.616039	+	0.787716i	$0.711264\pi$
$614$	16.0633	+	27.8225i	0.648262	+	1.12282i
$615$		0			0
$616$		0			0
$617$	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
$619$	44.9813			1.80795			0.903976	−	0.427583i	$-0.140635\pi$
$619$	44.9813			1.80795			0.903976	+	0.427583i	$0.140635\pi$
$620$	8.83409	+	15.3011i	0.354786	+	0.614507i
$621$		0			0
$622$	41.7547			1.67421
$623$		0			0
$624$		0			0
$625$	13.9982			0.559930
$626$	−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
$635$	−15.5243			−0.616065
$636$		0			0
$637$		0			0
$638$	59.4252			2.35267
$639$		0			0
$640$	5.86571	+	10.1597i	0.231863	+	0.401598i
$641$	−37.3901			−1.47682			−0.738410	−	0.674352i	$-0.764423\pi$
$641$	−37.3901			−1.47682			−0.738410	+	0.674352i	$0.764423\pi$
$642$		0			0
$643$	0.805874	+	1.39581i	0.0317806	+	0.0550456i	0.881478	−	0.472225i	$-0.156549\pi$
$643$	0.805874	+	1.39581i	0.0317806	+	0.0550456i	−0.849698	+	0.527270i	$0.823216\pi$
$644$		0			0
$645$		0			0
$646$	−5.04576	−	8.73951i	−0.198523	−	0.343851i
$647$	20.5881	+	35.6597i	0.809402	+	1.40193i	0.913278	+	0.407336i	$0.133542\pi$
$647$	20.5881	+	35.6597i	0.809402	+	1.40193i	−0.103876	+	0.994590i	$0.533125\pi$
$648$		0			0
$649$	12.9192	−	22.3767i	0.507124	−	0.878364i
$650$	−29.1819	+	50.5445i	−1.14461	+	1.98252i
$651$		0			0
$652$	−2.11334	−	3.66041i	−0.0827648	−	0.143353i
$653$	−3.05199			−0.119434			−0.0597169	−	0.998215i	$-0.519020\pi$
$653$	−3.05199			−0.119434			−0.0597169	+	0.998215i	$0.519020\pi$
$654$		0			0
$655$	16.8821			0.659637
$656$	3.93242	−	6.81115i	0.153535	−	0.265931i
$657$		0			0
$658$		0			0
$659$	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	$-0.704144\pi$
$661$	10.1505	−	17.5812i	0.394808	−	0.683828i	0.993077	+	0.117468i	$0.0374778\pi$
$662$	10.4055	−	18.0229i	0.404423	−	0.700481i
$663$		0			0
$664$	−0.668434	+	1.15776i	−0.0259403	+	0.0449298i
$665$		0			0
$666$		0			0
$667$	9.56599	−	16.5688i	0.370397	−	0.641546i
$668$	87.5167			3.38612
$669$		0			0
$670$	−6.58677			−0.254469
$671$	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	$0.161570\pi$
$674$	5.78746	−	10.0242i	0.222924	−	0.386117i
$675$		0			0
$676$	−36.9222	−	63.9511i	−1.42008	−	2.45966i
$677$	−5.43360	−	9.41127i	−0.208830	−	0.361705i	0.742516	−	0.669828i	$-0.233632\pi$
$677$	−5.43360	−	9.41127i	−0.208830	−	0.361705i	−0.951346	+	0.308124i	$0.900299\pi$
$678$		0			0
$679$		0			0
$680$	−4.43717	−	7.68540i	−0.170158	−	0.294722i
$681$		0			0
$682$	44.7374			1.71308
$683$	16.3473	+	28.3143i	0.625512	+	1.08342i	0.988442	+	0.151602i	$0.0484432\pi$
$683$	16.3473	+	28.3143i	0.625512	+	1.08342i	−0.362930	+	0.931817i	$0.618223\pi$
$684$		0			0
$685$	15.9659			0.610024
$686$		0			0
$687$		0			0
$688$	1.22668			0.0467668
$689$	19.8799	−	34.4329i	0.757362	−	1.31179i
$690$		0			0
$691$	7.49912	+	12.9889i	0.285280	+	0.494120i	0.972677	−	0.232162i	$-0.0745801\pi$
$691$	7.49912	+	12.9889i	0.285280	+	0.494120i	−0.687397	+	0.726282i	$0.741247\pi$
$692$	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
$698$	66.0856			2.50138
$699$		0			0
$700$		0			0
$701$	−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
$703$	−5.49138	−	9.51135i	−0.207111	−	0.358727i
$704$	6.35504			0.239514
$705$		0			0
$706$	−0.449493	−	0.778544i	−0.0169169	−	0.0293009i
$707$		0			0
$708$		0			0
$709$	−7.68004	−	13.3022i	−0.288430	−	0.499576i	0.685005	−	0.728538i	$-0.259800\pi$
$709$	−7.68004	−	13.3022i	−0.288430	−	0.499576i	−0.973435	+	0.228963i	$0.926467\pi$
$710$	−4.09714	−	7.09646i	−0.153763	−	0.266325i
$711$		0			0
$712$	33.6668	−	58.3127i	1.26172	−	2.18536i
$713$	7.20162	−	12.4736i	0.269703	−	0.467139i
$714$		0			0
$715$	−9.30200	−	16.1115i	−0.347875	−	0.602538i
$716$	32.4124			1.21131
$717$		0			0
$718$	13.8152			0.515579
$719$	−13.3653	+	23.1494i	−0.498442	+	0.863326i	−0.999998	−	0.00179839i	$-0.999428\pi$
$719$	−13.3653	+	23.1494i	−0.498442	+	0.863326i	0.501557	+	0.865125i	$0.332761\pi$
$720$		0			0
$721$		0			0
$722$	−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	$0.487916\pi$
$727$	−22.8221	+	39.5290i	−0.846424	+	1.46605i	−0.884379	+	0.466770i	$0.845418\pi$
$728$		0			0
$729$		0			0
$730$	−14.2297	+	24.6465i	−0.526664	+	0.912209i
$731$	0.305407			0.0112959
$732$		0			0
$733$	−5.97502			−0.220693			−0.110346	−	0.993893i	$-0.535196\pi$
$733$	−5.97502			−0.220693			−0.110346	+	0.993893i	$0.535196\pi$
$734$	−13.8302	−	23.9546i	−0.510483	−	0.884182i
$735$		0			0
$736$	−7.26786	+	12.5883i	−0.267897	+	0.464011i
$737$	−5.73783	+	9.93821i	−0.211356	+	0.366079i
$738$		0			0
$739$	17.7981	+	30.8273i	0.654715	+	1.13400i	0.981965	+	0.189062i	$0.0605447\pi$
$739$	17.7981	+	30.8273i	0.654715	+	1.13400i	−0.327250	+	0.944938i	$0.606122\pi$
$740$	−8.83409	−	15.3011i	−0.324748	−	0.562480i
$741$		0			0
$742$		0			0
$743$	−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
$745$	−13.3277			−0.488289
$746$	2.19207	+	3.79677i	0.0802573	+	0.139010i
$747$		0			0
$748$	−28.2841			−1.03417
$749$		0			0
$750$		0			0
$751$	−17.3337			−0.632515			−0.316258	−	0.948673i	$-0.602426\pi$
$751$	−17.3337			−0.632515			−0.316258	+	0.948673i	$0.602426\pi$
$752$	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
$761$	7.50744			0.272144			0.136072	−	0.990699i	$-0.456552\pi$
$761$	7.50744			0.272144			0.136072	+	0.990699i	$0.456552\pi$
$762$		0			0
$763$		0			0
$764$	−24.9590			−0.902987
$765$		0			0
$766$	−11.0296	−	19.1038i	−0.398514	−	0.690247i
$767$	36.3218			1.31150
$768$		0			0
$769$	1.02182	+	1.76985i	0.0368478	+	0.0638223i	0.883861	−	0.467749i	$-0.154935\pi$
$769$	1.02182	+	1.76985i	0.0368478	+	0.0638223i	−0.847013	+	0.531572i	$0.821602\pi$
$770$		0			0
$771$		0			0
$772$	−21.1668	−	36.6620i	−0.761811	−	1.31950i
$773$	12.4709	+	21.6002i	0.448547	+	0.776907i	0.998292	−	0.0584263i	$-0.0186083\pi$
$773$	12.4709	+	21.6002i	0.448547	+	0.776907i	−0.549744	+	0.835333i	$0.685275\pi$
$774$		0			0
$775$	9.62495	−	16.6709i	0.345738	−	0.598837i
$776$	−38.1721	+	66.1159i	−1.37030	+	2.37342i
$777$		0			0
$778$	−4.61246	−	7.98902i	−0.165365	−	0.286420i
$779$	2.85710			0.102366
$780$		0			0
$781$	−14.2763			−0.510847
$782$	−6.61721	+	11.4613i	−0.236631	+	0.409857i
$783$		0			0
$784$		0			0
$785$	7.93969	−	13.7520i	0.283380	−	0.490828i
$786$		0			0
$787$	3.55350	−	6.15484i	0.126669	−	0.219396i	−0.795715	−	0.605671i	$-0.792905\pi$
$787$	3.55350	−	6.15484i	0.126669	−	0.219396i	0.922384	+	0.386274i	$0.126238\pi$
$788$	18.3516	−	31.7860i	0.653750	−	1.13233i
$789$		0			0
$790$	6.63341	−	11.4894i	0.236006	−	0.408774i
$791$		0			0
$792$		0			0
$793$	−7.07919	+	12.2615i	−0.251389	+	0.435419i
$794$	−39.1097			−1.38795
$795$		0			0
$796$	−29.0993			−1.03140
$797$	−16.8314	−	29.1528i	−0.596199	−	1.03265i	−0.993376	−	0.114905i	$-0.963344\pi$
$797$	−16.8314	−	29.1528i	−0.596199	−	1.03265i	0.397178	−	0.917742i	$-0.369990\pi$
$798$		0			0
$799$	0.844770	−	1.46318i	0.0298858	−	0.0517638i
$800$	−9.71348	+	16.8242i	−0.343423	+	0.594827i
$801$		0			0
$802$	−23.3229	−	40.3965i	−0.823562	−	1.42645i
$803$	24.7913	+	42.9398i	0.874867	+	1.51531i
$804$		0			0
$805$		0			0
$806$	31.4443	+	54.4632i	1.10758	+	1.91838i
$807$		0			0
$808$	59.3319			2.08729
$809$	−6.40807	−	11.0991i	−0.225296	−	0.390224i	0.731112	−	0.682257i	$-0.239002\pi$
$809$	−6.40807	−	11.0991i	−0.225296	−	0.390224i	−0.956408	+	0.292033i	$0.905668\pi$
$810$		0			0
$811$	26.1239			0.917335			0.458667	−	0.888608i	$-0.348327\pi$
$811$	26.1239			0.917335			0.458667	+	0.888608i	$0.348327\pi$
$812$		0			0
$813$		0			0
$814$	−44.7374			−1.56805
$815$	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	0.999804	−	0.0198153i	$-0.00630781\pi$
$821$	13.8320	+	23.9578i	0.482741	+	0.836132i	−0.517062	+	0.855948i	$0.672974\pi$
$822$		0			0
$823$	−13.9162	+	24.1036i	−0.485089	+	0.840199i	−0.999853	−	0.0171330i	$-0.994546\pi$
$823$	−13.9162	+	24.1036i	−0.485089	+	0.840199i	0.514764	+	0.857332i	$0.327879\pi$
$824$	40.2772			1.40312
$825$		0			0
$826$		0			0
$827$	−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
$829$	−4.98680	−	8.63738i	−0.173199	−	0.299989i	0.766338	−	0.642438i	$-0.222077\pi$
$829$	−4.98680	−	8.63738i	−0.173199	−	0.299989i	−0.939536	+	0.342449i	$0.888744\pi$
$830$	−0.487511			−0.0169218
$831$		0			0
$832$	4.46673	+	7.73660i	0.154856	+	0.268218i
$833$		0			0
$834$		0			0
$835$	8.72281	+	15.1084i	0.301865	+	0.522846i
$836$	−20.6348	−	35.7404i	−0.713668	−	1.23611i
$837$		0			0
$838$	−43.9261	+	76.0822i	−1.51740	+	2.62822i
$839$	3.36484	−	5.82807i	0.116167	−	0.201207i	−0.802079	−	0.597218i	$-0.796273\pi$
$839$	3.36484	−	5.82807i	0.116167	−	0.201207i	0.918246	+	0.396011i	$0.129606\pi$
$840$		0			0
$841$	−3.79901	−	6.58008i	−0.131000	−	0.226899i
$842$	69.3842			2.39114
$843$		0			0
$844$	−14.8648			−0.511669
$845$	7.36009	−	12.7480i	0.253195	−	0.438546i
$846$		0			0
$847$		0			0
$848$	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	−0.812193	−	0.583388i	$-0.801727\pi$
$853$	2.89528	−	5.01477i	0.0991324	−	0.171702i	0.911326	+	0.411686i	$0.135060\pi$
$854$		0			0
$855$		0			0
$856$	−7.29426	+	12.6340i	−0.249313	+	0.431822i
$857$	−34.9077			−1.19242			−0.596211	−	0.802827i	$-0.703328\pi$
$857$	−34.9077			−1.19242			−0.596211	+	0.802827i	$0.703328\pi$
$858$		0			0
$859$	12.6149			0.430416			0.215208	−	0.976568i	$-0.430957\pi$
$859$	12.6149			0.430416			0.215208	+	0.976568i	$0.430957\pi$
$860$	0.358441	+	0.620838i	0.0122227	+	0.0211704i
$861$		0			0
$862$	−33.6668	+	58.3127i	−1.14670	+	1.98614i
$863$	−12.1027	+	20.9624i	−0.411979	+	0.713569i	−0.995106	−	0.0988119i	$-0.968496\pi$
$863$	−12.1027	+	20.9624i	−0.411979	+	0.713569i	0.583127	+	0.812381i	$0.301829\pi$
$864$		0			0
$865$	9.97343	+	17.2745i	0.339107	+	0.587350i
$866$	−47.0754	−	81.5369i	−1.59969	−	2.77074i
$867$		0			0
$868$		0			0
$869$	−11.5569	−	20.0171i	−0.392041	−	0.679035i
$870$		0			0
$871$	−16.1317			−0.546600
$872$	12.0842	+	20.9305i	0.409224	+	0.708797i
$873$		0			0
$874$	−19.3105			−0.653186
$875$		0			0
$876$		0			0
$877$	−1.12567			−0.0380111			−0.0190055	−	0.999819i	$-0.506050\pi$
$877$	−1.12567			−0.0380111			−0.0190055	+	0.999819i	$0.506050\pi$
$878$	−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	$-0.523525\pi$
$881$	−4.38331			−0.147678			−0.0738388	+	0.997270i	$0.523525\pi$
$882$		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
$887$	39.0752			1.31202			0.656009	−	0.754753i	$-0.272243\pi$
$887$	39.0752			1.31202			0.656009	+	0.754753i	$0.272243\pi$
$888$		0			0
$889$		0			0
$890$	24.5544			0.823065
$891$		0			0
$892$	−13.8439	−	23.9783i	−0.463528	−	0.802854i
$893$	2.46522			0.0824955
$894$		0			0
$895$	3.23055	+	5.59548i	0.107985	+	0.187036i
$896$		0			0
$897$		0			0
$898$	12.9572	+	22.4426i	0.432388	+	0.748919i
$899$	−13.7761	−	23.8610i	−0.459460	−	0.795809i
$900$		0			0
$901$	6.02481	−	10.4353i	0.200716	−	0.347650i
$902$	5.81908	−	10.0789i	0.193754	−	0.335592i
$903$		0			0
$904$	−50.2327	−	87.0055i	−1.67071	−	2.89376i
$905$	−3.03003			−0.100722
$906$		0			0
$907$	42.4938			1.41098			0.705492	−	0.708718i	$-0.250726\pi$
$907$	42.4938			1.41098			0.705492	+	0.708718i	$0.250726\pi$
$908$	13.5929	−	23.5435i	0.451095	−	0.781319i
$909$		0			0
$910$		0			0
$911$	−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
$917$		0			0
$918$		0			0
$919$	−3.26470	+	5.65463i	−0.107693	+	0.186529i	−0.914835	−	0.403828i	$-0.867680\pi$
$919$	−3.26470	+	5.65463i	−0.107693	+	0.186529i	0.807143	+	0.590357i	$0.201013\pi$
$920$	−16.9813			−0.559858
$921$		0			0
$922$	−1.27807			−0.0420909
$923$	−10.0343	−	17.3799i	−0.330283	−	0.572068i
$924$		0			0
$925$	−9.62495	+	16.6709i	−0.316466	+	0.548136i
$926$	3.39306	−	5.87695i	0.111503	−	0.193128i
$927$		0			0
$928$	13.9029	+	24.0805i	0.456384	+	0.790480i
$929$	−29.1386	−	50.4696i	−0.956007	−	1.65585i	−0.732046	−	0.681255i	$-0.761435\pi$
$929$	−29.1386	−	50.4696i	−0.956007	−	1.65585i	−0.223961	−	0.974598i	$-0.571899\pi$
$930$		0			0
$931$		0			0
$932$	−18.8045	−	32.5704i	−0.615963	−	1.06688i
$933$		0			0
$934$	79.5494			2.60294
$935$	−2.81908	−	4.88279i	−0.0921937	−	0.159684i
$936$		0			0
$937$	−32.4175			−1.05903			−0.529516	−	0.848300i	$-0.677626\pi$
$937$	−32.4175			−1.05903			−0.529516	+	0.848300i	$0.677626\pi$
$938$		0			0
$939$		0			0
$940$	3.96585			0.129352
$941$	13.6613	−	23.6621i	0.445346	−	0.771363i	−0.552730	−	0.833360i	$-0.686414\pi$
$941$	13.6613	−	23.6621i	0.445346	−	0.771363i	0.998076	+	0.0619979i	$0.0197472\pi$
$942$		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	−0.989322	−	0.145744i	$-0.953443\pi$
$947$	−19.1065	−	33.0935i	−0.620879	−	1.07539i	0.368443	−	0.929650i	$-0.379891\pi$
$948$		0			0
$949$	−34.8499	+	60.3618i	−1.13127	+	1.95943i
$950$	−25.8084			−0.837335
$951$		0			0
$952$		0			0
$953$	−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
$955$	−2.48767	−	4.30878i	−0.0804992	−	0.139429i
$956$	−64.2404			−2.07768
$957$		0			0
$958$	−20.8145	−	36.0518i	−0.672486	−	1.16478i
$959$		0			0
$960$		0			0
$961$	5.12882	+	8.88338i	0.165446	+	0.286561i
$962$	−31.4443	−	54.4632i	−1.01381	−	1.75596i
$963$		0			0
$964$	−11.9192	+	20.6447i	−0.383892	+	0.664921i
$965$	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	$0.963438\pi$
$968$	−24.7273			−0.794766
$969$		0			0
$970$	−27.8402			−0.893894
$971$	−4.08812	+	7.08082i	−0.131194	+	0.227234i	−0.924137	−	0.382061i	$-0.875214\pi$
$971$	−4.08812	+	7.08082i	−0.131194	+	0.227234i	0.792943	+	0.609296i	$0.208548\pi$
$972$		0			0
$973$		0			0
$974$	−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	−0.964492	−	0.264111i	$-0.914922\pi$
$977$	−7.92427	+	13.7252i	−0.253520	+	0.439109i	0.710973	+	0.703220i	$0.248255\pi$
$978$		0			0
$979$	21.3897	−	37.0480i	0.683616	−	1.18406i
$980$		0			0
$981$		0			0
$982$	33.5326	−	58.0801i	1.07007	−	1.85341i
$983$	53.3063			1.70021			0.850104	−	0.526615i	$-0.176539\pi$
$983$	53.3063			1.70021			0.850104	+	0.526615i	$0.176539\pi$
$984$		0			0
$985$	7.31645			0.233121
$986$	12.6582	+	21.9247i	0.403120	+	0.698224i
$987$		0			0
$988$	29.0069	−	50.2414i	0.922831	−	1.59839i
$989$	0.292204	−	0.506111i	0.00929153	−	0.0160934i
$990$		0			0
$991$	−20.1047	−	34.8224i	−0.638648	−	1.10617i	−0.985730	−	0.168335i	$-0.946161\pi$
$991$	−20.1047	−	34.8224i	−0.638648	−	1.10617i	0.347082	−	0.937835i	$-0.387172\pi$
$992$	10.4666	+	18.1286i	0.332314	+	0.575584i
$993$		0			0
$994$		0			0
$995$	−2.90033	−	5.02352i	−0.0919466	−	0.159256i
$996$		0			0
$997$	−28.7202			−0.909577			−0.454789	−	0.890599i	$-0.650285\pi$
$997$	−28.7202			−0.909577			−0.454789	+	0.890599i	$0.650285\pi$
$998$	−17.0205	−	29.4804i	−0.538776	−	0.933187i
$999$		0			0

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
63.2.f.a.22.1	✓	6	63.5	even	6
63.2.f.a.43.1	yes	6	21.5	even	6
189.2.f.b.64.3		6	63.40	odd	6
189.2.f.b.127.3		6	7.5	odd	6
441.2.f.c.148.1		6	63.23	odd	6
441.2.f.c.295.1		6	21.2	odd	6
441.2.g.b.67.1		6	63.32	odd	6
441.2.g.b.79.1		6	3.2	odd	2
441.2.g.c.67.1		6	63.59	even	6
441.2.g.c.79.1		6	21.20	even	2
441.2.h.d.214.3		6	21.17	even	6
441.2.h.d.373.3		6	63.41	even	6
441.2.h.e.214.3		6	21.11	odd	6
441.2.h.e.373.3		6	9.5	odd	6
567.2.a.c.1.1		3	63.61	odd	6
567.2.a.h.1.3		3	63.47	even	6
1008.2.r.h.337.3		6	252.131	odd	6
1008.2.r.h.673.3		6	84.47	odd	6
1323.2.f.d.442.3		6	63.58	even	3
1323.2.f.d.883.3		6	7.2	even	3
1323.2.g.d.361.3		6	63.31	odd	6
1323.2.g.d.667.3		6	7.6	odd	2
1323.2.g.e.361.3		6	63.4	even	3	inner
1323.2.g.e.667.3		6	1.1	even	1	trivial
1323.2.h.b.226.1		6	9.4	even	3
1323.2.h.b.802.1		6	7.4	even	3
1323.2.h.c.226.1		6	63.13	odd	6
1323.2.h.c.802.1		6	7.3	odd	6
3024.2.r.k.1009.1		6	252.103	even	6
3024.2.r.k.2017.1		6	28.19	even	6
3969.2.a.l.1.1		3	63.16	even	3
3969.2.a.q.1.3		3	63.2	odd	6
9072.2.a.bs.1.3		3	252.187	even	6
9072.2.a.ca.1.1		3	252.47	odd	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:	\( N \)	\(=\)	\( 1323 = 3^{3} \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1323.g (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(1.26604 + 2.19285i) q^{2} +(-2.20574 + 3.82045i) q^{4} -0.879385 q^{5} -6.10607 q^{8} +O(q^{10})\)	\(q+(1.26604 + 2.19285i) q^{2} +(-2.20574 + 3.82045i) q^{4} -0.879385 q^{5} -6.10607 q^{8} +(-1.11334 - 1.92836i) q^{10} -3.87939 q^{11} +(-2.72668 - 4.72275i) q^{13} +(-3.31908 - 5.74881i) q^{16} +(-0.826352 - 1.43128i) q^{17} +(1.20574 - 2.08840i) q^{19} +(1.93969 - 3.35965i) q^{20} +(-4.91147 - 8.50692i) q^{22} -3.16250 q^{23} -4.22668 q^{25} +(6.90420 - 11.9584i) q^{26} +(-3.02481 + 5.23913i) q^{29} +(-2.27719 + 3.94421i) q^{31} +(2.29813 - 3.98048i) q^{32} +(2.09240 - 3.62414i) q^{34} +(2.27719 - 3.94421i) q^{37} +6.10607 q^{38} +5.36959 q^{40} +(0.592396 + 1.02606i) q^{41} +(-0.0923963 + 0.160035i) q^{43} +(8.55690 - 14.8210i) q^{44} +(-4.00387 - 6.93491i) q^{46} +(0.511144 + 0.885328i) q^{47} +(-5.35117 - 9.26849i) q^{50} +24.0574 q^{52} +(3.64543 + 6.31407i) q^{53} +3.41147 q^{55} -15.3182 q^{58} +(-3.33022 + 5.76811i) q^{59} +(-1.29813 - 2.24843i) q^{61} -11.5321 q^{62} -1.63816 q^{64} +(2.39780 + 4.15312i) q^{65} +(1.47906 - 2.56180i) q^{67} +7.29086 q^{68} +3.68004 q^{71} +(-6.39053 - 11.0687i) q^{73} +11.5321 q^{74} +(5.31908 + 9.21291i) q^{76} +(2.97906 + 5.15988i) q^{79} +(2.91875 + 5.05542i) q^{80} +(-1.50000 + 2.59808i) q^{82} +(0.109470 - 0.189608i) q^{83} +(0.726682 + 1.25865i) q^{85} -0.467911 q^{86} +23.6878 q^{88} +(-5.51367 + 9.54996i) q^{89} +(6.97565 - 12.0822i) q^{92} +(-1.29426 + 2.24173i) q^{94} +(-1.06031 + 1.83651i) q^{95} +(6.25150 - 10.8279i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q + 3 q^{2} - 3 q^{4} + 6 q^{5} - 12 q^{8}+O(q^{10}) \) 6 * q + 3 * q^2 - 3 * q^4 + 6 * q^5 - 12 * q^8	\( 6 q + 3 q^{2} - 3 q^{4} + 6 q^{5} - 12 q^{8} - 12 q^{11} - 3 q^{13} - 3 q^{16} - 6 q^{17} - 3 q^{19} + 6 q^{20} - 9 q^{22} - 24 q^{23} - 12 q^{25} + 3 q^{26} + 9 q^{29} - 3 q^{31} + 9 q^{34} + 3 q^{37} + 12 q^{38} + 18 q^{40} + 3 q^{43} + 15 q^{44} - 3 q^{47} - 6 q^{50} + 42 q^{52} + 6 q^{53} - 18 q^{58} + 3 q^{59} + 6 q^{61} - 60 q^{62} + 24 q^{64} + 15 q^{65} + 12 q^{67} + 12 q^{68} - 18 q^{71} - 21 q^{73} + 60 q^{74} + 15 q^{76} + 21 q^{79} + 15 q^{80} - 9 q^{82} + 18 q^{83} - 9 q^{85} - 12 q^{86} + 54 q^{88} - 12 q^{89} + 3 q^{92} - 18 q^{94} - 12 q^{95} - 3 q^{97}+O(q^{100}) \) 6 * q + 3 * q^2 - 3 * q^4 + 6 * q^5 - 12 * q^8 - 12 * q^11 - 3 * q^13 - 3 * q^16 - 6 * q^17 - 3 * q^19 + 6 * q^20 - 9 * q^22 - 24 * q^23 - 12 * q^25 + 3 * q^26 + 9 * q^29 - 3 * q^31 + 9 * q^34 + 3 * q^37 + 12 * q^38 + 18 * q^40 + 3 * q^43 + 15 * q^44 - 3 * q^47 - 6 * q^50 + 42 * q^52 + 6 * q^53 - 18 * q^58 + 3 * q^59 + 6 * q^61 - 60 * q^62 + 24 * q^64 + 15 * q^65 + 12 * q^67 + 12 * q^68 - 18 * q^71 - 21 * q^73 + 60 * q^74 + 15 * q^76 + 21 * q^79 + 15 * q^80 - 9 * q^82 + 18 * q^83 - 9 * q^85 - 12 * q^86 + 54 * q^88 - 12 * q^89 + 3 * q^92 - 18 * q^94 - 12 * q^95 - 3 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more