LMFDB - Embedded newform 387.2.y.c.154.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [387,2,Mod(10,387)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(387, base_ring=CyclotomicField(42))

chi = DirichletCharacter(H, H._module([0, 10]))

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

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

chi := DirichletCharacter("387.10");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 387 = 3^{2} \cdot 43 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	387.y (of order $21$, degree $12$, 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:	$3.09021055822$
Analytic rank:	$0$
Dimension:	$36$
Relative dimension:	$3$ over $\Q(\zeta_{21})$
Twist minimal:	no (minimal twist has level 43)
Sato-Tate group:	$\mathrm{SU}(2)[C_{21}]$

Embedding invariants

Embedding label			154.2
Character	$\chi$	$=$	387.154
Dual form			387.2.y.c.289.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.118393 - 0.0570152i) q^{2} +(-1.23621 - 1.55016i) q^{4} +(1.30537 - 1.21121i) q^{5} +(-0.00749281 + 0.0129779i) q^{7} +(0.116458 + 0.510236i) q^{8} +O(q^{10})$	\(q+(-0.118393 - 0.0570152i) q^{2} +(-1.23621 - 1.55016i) q^{4} +(1.30537 - 1.21121i) q^{5} +(-0.00749281 + 0.0129779i) q^{7} +(0.116458 + 0.510236i) q^{8} +(-0.223604 + 0.0689728i) q^{10} +(1.29669 - 1.62599i) q^{11} +(-1.55224 - 0.478804i) q^{13} +(0.00162704 - 0.00110929i) q^{14} +(-0.867096 + 3.79899i) q^{16} +(-4.42356 - 4.10446i) q^{17} +(2.78497 - 7.09598i) q^{19} +(-3.49129 - 0.526227i) q^{20} +(-0.246225 + 0.118576i) q^{22} +(-5.24284 - 0.790231i) q^{23} +(-0.136680 + 1.82386i) q^{25} +(0.156476 + 0.145189i) q^{26} +(0.0293806 - 0.00442841i) q^{28} +(5.92981 - 4.04287i) q^{29} +(0.178251 + 2.37860i) q^{31} +(0.971874 - 1.21869i) q^{32} +(0.289703 + 0.738150i) q^{34} +(0.00593807 + 0.0260164i) q^{35} +(-2.52043 - 4.36551i) q^{37} +(-0.734300 + 0.681331i) q^{38} +(0.770022 + 0.524992i) q^{40} +(3.20110 + 1.54157i) q^{41} +(-1.84169 - 6.29350i) q^{43} -4.12354 q^{44} +(0.575662 + 0.392479i) q^{46} +(6.24911 + 7.83614i) q^{47} +(3.49989 + 6.06198i) q^{49} +(0.120170 - 0.208140i) q^{50} +(1.17668 + 2.99813i) q^{52} +(6.55236 - 2.02113i) q^{53} +(-0.276759 - 3.69309i) q^{55} +(-0.00749439 - 0.00231171i) q^{56} +(-0.932554 + 0.140560i) q^{58} +(-0.370875 + 1.62491i) q^{59} +(-0.452207 + 6.03428i) q^{61} +(0.114512 - 0.291773i) q^{62} +(6.83705 - 3.29255i) q^{64} +(-2.60619 + 1.25507i) q^{65} +(0.523545 - 1.33397i) q^{67} +(-0.894122 + 11.9312i) q^{68} +(0.000780301 - 0.00341872i) q^{70} +(-6.96679 + 1.05007i) q^{71} +(9.32817 + 2.87736i) q^{73} +(0.0495013 + 0.660549i) q^{74} +(-14.4427 + 4.45500i) q^{76} +(0.0113862 + 0.0290116i) q^{77} +(-6.00573 + 10.4022i) q^{79} +(3.46949 + 6.00933i) q^{80} +(-0.291096 - 0.365023i) q^{82} +(-7.49232 - 5.10817i) q^{83} -10.7457 q^{85} +(-0.140781 + 0.850113i) q^{86} +(0.980650 + 0.472256i) q^{88} +(13.1407 + 8.95920i) q^{89} +(0.0178445 - 0.0165573i) q^{91} +(5.25628 + 9.10415i) q^{92} +(-0.293074 - 1.28404i) q^{94} +(-4.95929 - 12.6361i) q^{95} +(8.44749 - 10.5928i) q^{97} +(-0.0687380 - 0.917245i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 36 q + 10 q^{2} - 18 q^{4} + 17 q^{5} + 6 q^{7} - 18 q^{8}+O(q^{10}) $ 36 * q + 10 * q^2 - 18 * q^4 + 17 * q^5 + 6 * q^7 - 18 * q^8	$ 36 q + 10 q^{2} - 18 q^{4} + 17 q^{5} + 6 q^{7} - 18 q^{8} - 7 q^{10} + 4 q^{11} - 18 q^{14} - 10 q^{16} + 10 q^{17} + 10 q^{19} + 3 q^{20} - 3 q^{22} - 4 q^{23} - 2 q^{25} + 15 q^{26} + 20 q^{28} - 9 q^{29} + 40 q^{31} - 48 q^{32} - 42 q^{34} - 11 q^{35} - 19 q^{37} + 21 q^{38} - 97 q^{40} + 28 q^{41} - 8 q^{43} - 14 q^{44} - 61 q^{46} + 30 q^{47} + 6 q^{49} + 3 q^{50} - 8 q^{52} + 24 q^{53} + 14 q^{55} - 39 q^{56} + 64 q^{58} + q^{59} - 14 q^{61} - 33 q^{62} + 48 q^{64} - 38 q^{65} + 66 q^{67} - 66 q^{68} + 47 q^{70} + 33 q^{71} + 29 q^{73} + 40 q^{74} - 39 q^{76} + 27 q^{77} - 17 q^{79} - 8 q^{80} - 54 q^{82} + 23 q^{83} - 56 q^{85} + 45 q^{86} - 17 q^{88} + 19 q^{89} - 13 q^{91} + 18 q^{92} + 44 q^{94} - q^{95} - 31 q^{97} + 5 q^{98}+O(q^{100}) $ 36 * q + 10 * q^2 - 18 * q^4 + 17 * q^5 + 6 * q^7 - 18 * q^8 - 7 * q^10 + 4 * q^11 - 18 * q^14 - 10 * q^16 + 10 * q^17 + 10 * q^19 + 3 * q^20 - 3 * q^22 - 4 * q^23 - 2 * q^25 + 15 * q^26 + 20 * q^28 - 9 * q^29 + 40 * q^31 - 48 * q^32 - 42 * q^34 - 11 * q^35 - 19 * q^37 + 21 * q^38 - 97 * q^40 + 28 * q^41 - 8 * q^43 - 14 * q^44 - 61 * q^46 + 30 * q^47 + 6 * q^49 + 3 * q^50 - 8 * q^52 + 24 * q^53 + 14 * q^55 - 39 * q^56 + 64 * q^58 + q^59 - 14 * q^61 - 33 * q^62 + 48 * q^64 - 38 * q^65 + 66 * q^67 - 66 * q^68 + 47 * q^70 + 33 * q^71 + 29 * q^73 + 40 * q^74 - 39 * q^76 + 27 * q^77 - 17 * q^79 - 8 * q^80 - 54 * q^82 + 23 * q^83 - 56 * q^85 + 45 * q^86 - 17 * q^88 + 19 * q^89 - 13 * q^91 + 18 * q^92 + 44 * q^94 - q^95 - 31 * q^97 + 5 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/387\mathbb{Z}\right)^\times$.

$n$	$46$	$173$
$\chi(n)$	$e\left(\frac{4}{21}\right)$	$1$

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 $

$2$	−0.118393	−	0.0570152i	−0.0837167	−	0.0403158i	0.391557	−	0.920154i	$-0.371937\pi$
$2$	−0.118393	−	0.0570152i	−0.0837167	−	0.0403158i	−0.475274	+	0.879838i	$0.657651\pi$
$3$		0			0
$3$		0			0
$4$	−1.23621	−	1.55016i	−0.618107	−	0.775081i
$5$	1.30537	−	1.21121i	0.583780	−	0.541669i	−0.332036	−	0.943267i	$-0.607736\pi$
$5$	1.30537	−	1.21121i	0.583780	−	0.541669i	0.915816	+	0.401598i	$0.131545\pi$
$6$		0			0
$7$	−0.00749281	+	0.0129779i	−0.00283201	+	0.00490519i	−0.867438	−	0.497545i	$-0.834235\pi$
$7$	−0.00749281	+	0.0129779i	−0.00283201	+	0.00490519i	0.864606	+	0.502451i	$0.167568\pi$
$8$	0.116458	+	0.510236i	0.0411741	+	0.180396i
$9$		0			0
$10$	−0.223604	+	0.0689728i	−0.0707099	+	0.0218111i
$11$	1.29669	−	1.62599i	0.390966	−	0.490256i	−0.546927	−	0.837180i	$-0.684203\pi$
$11$	1.29669	−	1.62599i	0.390966	−	0.490256i	0.937893	+	0.346924i	$0.112774\pi$
$12$		0			0
$13$	−1.55224	−	0.478804i	−0.430515	−	0.132796i	0.0719219	−	0.997410i	$-0.477087\pi$
$13$	−1.55224	−	0.478804i	−0.430515	−	0.132796i	−0.502437	+	0.864614i	$0.667563\pi$
$14$	0.00162704	−	0.00110929i	0.000434844	−	0.000296471i
$15$		0			0
$16$	−0.867096	+	3.79899i	−0.216774	+	0.949748i
$17$	−4.42356	−	4.10446i	−1.07287	−	0.995478i	−0.0728722	−	0.997341i	$-0.523217\pi$
$17$	−4.42356	−	4.10446i	−1.07287	−	0.995478i	−0.999998	+	0.00186302i	$0.999407\pi$
$18$		0			0
$19$	2.78497	−	7.09598i	0.638916	−	1.62793i	−0.132191	−	0.991224i	$-0.542201\pi$
$19$	2.78497	−	7.09598i	0.638916	−	1.62793i	0.771107	−	0.636706i	$-0.219704\pi$
$20$	−3.49129	−	0.526227i	−0.780676	−	0.117668i
$21$		0			0
$22$	−0.246225	+	0.118576i	−0.0524954	+	0.0252805i
$23$	−5.24284	−	0.790231i	−1.09321	−	0.164775i	−0.422403	−	0.906408i	$-0.638813\pi$
$23$	−5.24284	−	0.790231i	−1.09321	−	0.164775i	−0.670805	+	0.741634i	$0.734051\pi$
$24$		0			0
$25$	−0.136680	+	1.82386i	−0.0273359	+	0.364773i
$26$	0.156476	+	0.145189i	0.0306875	+	0.0284738i
$27$		0			0
$28$	0.0293806	−	0.00442841i	0.00555241	−	0.000836891i
$29$	5.92981	−	4.04287i	1.10114	−	0.750743i	0.130538	−	0.991443i	$-0.458329\pi$
$29$	5.92981	−	4.04287i	1.10114	−	0.750743i	0.970599	+	0.240700i	$0.0773771\pi$
$30$		0			0
$31$	0.178251	+	2.37860i	0.0320149	+	0.427209i	0.990065	+	0.140609i	$0.0449060\pi$
$31$	0.178251	+	2.37860i	0.0320149	+	0.427209i	−0.958050	+	0.286600i	$0.907475\pi$
$32$	0.971874	−	1.21869i	0.171805	−	0.215436i
$33$		0			0
$34$	0.289703	+	0.738150i	0.0496836	+	0.126592i
$35$	0.00593807	+	0.0260164i	0.00100372	+	0.00439757i
$36$		0			0
$37$	−2.52043	−	4.36551i	−0.414356	−	0.717685i	0.581005	−	0.813900i	$-0.302660\pi$
$37$	−2.52043	−	4.36551i	−0.414356	−	0.717685i	−0.995361	+	0.0962150i	$0.969326\pi$
$38$	−0.734300	+	0.681331i	−0.119119	+	0.110526i
$39$		0			0
$40$	0.770022	+	0.524992i	0.121751	+	0.0830086i
$41$	3.20110	+	1.54157i	0.499928	+	0.240753i	0.666815	−	0.745223i	$-0.267657\pi$
$41$	3.20110	+	1.54157i	0.499928	+	0.240753i	−0.166887	+	0.985976i	$0.553371\pi$
$42$		0			0
$43$	−1.84169	−	6.29350i	−0.280856	−	0.959750i
$43$	−1.84169	−	6.29350i	−0.280856	−	0.959750i
$44$	−4.12354			−0.621647
$45$		0			0
$46$	0.575662	+	0.392479i	0.0848767	+	0.0578679i
$47$	6.24911	+	7.83614i	0.911527	+	1.14302i	0.989278	+	0.146046i	$0.0466547\pi$
$47$	6.24911	+	7.83614i	0.911527	+	1.14302i	−0.0777509	+	0.996973i	$0.524774\pi$
$48$		0			0
$49$	3.49989	+	6.06198i	0.499984	+	0.865998i
$50$	0.120170	−	0.208140i	0.0169946	−	0.0294355i
$51$		0			0
$52$	1.17668	+	2.99813i	0.163176	+	0.415766i
$53$	6.55236	−	2.02113i	0.900035	−	0.277624i	0.189995	−	0.981785i	$-0.439153\pi$
$53$	6.55236	−	2.02113i	0.900035	−	0.277624i	0.710040	+	0.704161i	$0.248677\pi$
$54$		0			0
$55$	−0.276759	−	3.69309i	−0.0373181	−	0.497976i
$56$	−0.00749439	−	0.00231171i	−0.00100148	−	0.000308916i
$57$		0			0
$58$	−0.932554	+	0.140560i	−0.122450	+	0.0184564i
$59$	−0.370875	+	1.62491i	−0.0482838	+	0.211545i	−0.993315	−	0.115435i	$-0.963174\pi$
$59$	−0.370875	+	1.62491i	−0.0482838	+	0.211545i	0.945031	+	0.326980i	$0.106031\pi$
$60$		0			0
$61$	−0.452207	+	6.03428i	−0.0578992	+	0.772611i	0.890389	+	0.455200i	$0.150432\pi$
$61$	−0.452207	+	6.03428i	−0.0578992	+	0.772611i	−0.948288	+	0.317411i	$0.897187\pi$
$62$	0.114512	−	0.291773i	0.0145431	−	0.0370552i
$63$		0			0
$64$	6.83705	−	3.29255i	0.854631	−	0.411569i
$65$	−2.60619	+	1.25507i	−0.323258	+	0.155673i
$66$		0			0
$67$	0.523545	−	1.33397i	0.0639612	−	0.162970i	−0.895320	−	0.445424i	$-0.853053\pi$
$67$	0.523545	−	1.33397i	0.0639612	−	0.162970i	0.959281	+	0.282453i	$0.0911483\pi$
$68$	−0.894122	+	11.9312i	−0.108428	+	1.44687i
$69$		0			0
$70$	0.000780301	−	0.00341872i	9.32638e−5	−	0.000408615i
$71$	−6.96679	+	1.05007i	−0.826805	+	0.124621i	−0.548795	−	0.835957i	$-0.684913\pi$
$71$	−6.96679	+	1.05007i	−0.826805	+	0.124621i	−0.278011	+	0.960578i	$0.589675\pi$
$72$		0			0
$73$	9.32817	+	2.87736i	1.09178	+	0.336770i	0.787814	−	0.615913i	$-0.211213\pi$
$73$	9.32817	+	2.87736i	1.09178	+	0.336770i	0.303966	+	0.952683i	$0.401689\pi$
$74$	0.0495013	+	0.660549i	0.00575441	+	0.0767873i
$75$		0			0
$76$	−14.4427	+	4.45500i	−1.65670	+	0.511023i
$77$	0.0113862	+	0.0290116i	0.00129758	+	0.00330617i
$78$		0			0
$79$	−6.00573	+	10.4022i	−0.675697	+	1.17034i	0.300567	+	0.953761i	$0.402824\pi$
$79$	−6.00573	+	10.4022i	−0.675697	+	1.17034i	−0.976265	+	0.216581i	$0.930509\pi$
$80$	3.46949	+	6.00933i	0.387901	+	0.671864i
$81$		0			0
$82$	−0.291096	−	0.365023i	−0.0321462	−	0.0403100i
$83$	−7.49232	−	5.10817i	−0.822389	−	0.560695i	0.0774107	−	0.996999i	$-0.475335\pi$
$83$	−7.49232	−	5.10817i	−0.822389	−	0.560695i	−0.899799	+	0.436304i	$0.856287\pi$
$84$		0			0
$85$	−10.7457			−1.16554
$86$	−0.140781	+	0.850113i	−0.0151808	+	0.0916700i
$87$		0			0
$88$	0.980650	+	0.472256i	0.104538	+	0.0503427i
$89$	13.1407	+	8.95920i	1.39291	+	0.949673i	0.999541	+	0.0302945i	$0.00964451\pi$
$89$	13.1407	+	8.95920i	1.39291	+	0.949673i	0.393374	+	0.919379i	$0.371308\pi$
$90$		0			0
$91$	0.0178445	−	0.0165573i	0.00187061	−	0.00173568i
$92$	5.25628	+	9.10415i	0.548005	+	0.949173i
$93$		0			0
$94$	−0.293074	−	1.28404i	−0.0302283	−	0.132439i
$95$	−4.95929	−	12.6361i	−0.508813	−	1.29643i
$96$		0			0
$97$	8.44749	−	10.5928i	0.857712	−	1.07554i	−0.138652	−	0.990341i	$-0.544277\pi$
$97$	8.44749	−	10.5928i	0.857712	−	1.07554i	0.996364	−	0.0851960i	$-0.0271516\pi$
$98$	−0.0687380	−	0.917245i	−0.00694358	−	0.0926557i
$99$		0			0
$100$	2.99625	−	2.04281i	0.299625	−	0.204281i
$101$	3.08833	−	0.465490i	0.307300	−	0.0463180i	0.00641794	−	0.999979i	$-0.497957\pi$
$101$	3.08833	−	0.465490i	0.307300	−	0.0463180i	0.300882	+	0.953661i	$0.402719\pi$
$102$		0			0
$103$	0.386491	+	0.358612i	0.0380821	+	0.0353351i	0.698984	−	0.715137i	$-0.253636\pi$
$103$	0.386491	+	0.358612i	0.0380821	+	0.0353351i	−0.660902	+	0.750472i	$0.729826\pi$
$104$	0.0635316	−	0.847770i	0.00622978	−	0.0831307i
$105$		0			0
$106$	−0.890990	−	0.134295i	−0.0865406	−	0.0130439i
$107$	1.02320	−	0.492747i	0.0989164	−	0.0476356i	−0.383771	−	0.923428i	$-0.625375\pi$
$107$	1.02320	−	0.492747i	0.0989164	−	0.0476356i	0.482688	+	0.875793i	$0.339661\pi$
$108$		0			0
$109$	12.0642	+	1.81839i	1.15554	+	0.174170i	0.698725	−	0.715391i	$-0.253751\pi$
$109$	12.0642	+	1.81839i	1.15554	+	0.174170i	0.456817	+	0.889561i	$0.348989\pi$
$110$	−0.177796	+	0.453016i	−0.0169521	+	0.0431934i
$111$		0			0
$112$	−0.0428061	−	0.0397182i	−0.00404479	−	0.00375302i
$113$	−0.981156	+	4.29873i	−0.0922994	+	0.404390i	−0.999880	−	0.0154876i	$-0.995070\pi$
$113$	−0.981156	+	4.29873i	−0.0922994	+	0.404390i	0.907581	+	0.419878i	$0.137927\pi$
$114$		0			0
$115$	−7.80099	+	5.31863i	−0.727446	+	0.495964i
$116$	−13.5976	−	4.19431i	−1.26251	−	0.389432i
$117$		0			0
$118$	0.136554	−	0.171233i	0.0125708	−	0.0157633i
$119$	0.0864122	−	0.0266546i	0.00792140	−	0.00244343i
$120$		0			0
$121$	1.48527	+	6.50740i	0.135025	+	0.591581i
$122$	0.397584	−	0.688636i	0.0359956	−	0.0623462i
$123$		0			0
$124$	3.46686	−	3.21677i	0.311333	−	0.288875i
$125$	7.58202	+	9.50755i	0.678156	+	0.850381i
$126$		0			0
$127$	8.11611	+	3.90851i	0.720188	+	0.346824i	0.757817	−	0.652468i	$-0.226266\pi$
$127$	8.11611	+	3.90851i	0.720188	+	0.346824i	−0.0376287	+	0.999292i	$0.511980\pi$
$128$	−4.11472			−0.363693
$129$		0			0
$130$	0.380113			0.0333381
$131$	−4.11246	−	1.98046i	−0.359307	−	0.173033i	0.245517	−	0.969392i	$-0.421042\pi$
$131$	−4.11246	−	1.98046i	−0.359307	−	0.173033i	−0.604824	+	0.796359i	$0.706757\pi$
$132$		0			0
$133$	0.0712239	+	0.0893119i	0.00617589	+	0.00774433i
$134$	−0.138041	+	0.128083i	−0.0119249	+	0.0110647i
$135$		0			0
$136$	1.57908	−	2.73505i	0.135405	−	0.234529i
$137$	−3.46135	−	15.1652i	−0.295723	−	1.29565i	−0.876428	−	0.481534i	$-0.840080\pi$
$137$	−3.46135	−	15.1652i	−0.295723	−	1.29565i	0.580704	−	0.814115i	$-0.302777\pi$
$138$		0			0
$139$	−6.55460	+	2.02183i	−0.555954	+	0.171489i	−0.559985	−	0.828503i	$-0.689193\pi$
$139$	−6.55460	+	2.02183i	−0.555954	+	0.171489i	0.00403085	+	0.999992i	$0.498717\pi$
$140$	0.0329889	−	0.0413667i	0.00278807	−	0.00349613i
$141$		0			0
$142$	0.884690	+	0.272891i	0.0742416	+	0.0229005i
$143$	−2.79131	+	1.90308i	−0.233421	+	0.159144i
$144$		0			0
$145$	2.84384	−	12.4597i	0.236168	−	1.03472i
$146$	−0.940339	−	0.872507i	−0.0778230	−	0.0722092i
$147$		0			0
$148$	−3.65146	+	9.30377i	−0.300148	+	0.764765i
$149$	20.4091	+	3.07618i	1.67198	+	0.252010i	0.915591	−	0.402112i	$-0.131724\pi$
$149$	20.4091	+	3.07618i	1.67198	+	0.252010i	0.756389	+	0.654122i	$0.226962\pi$
$150$		0			0
$151$	3.49495	−	1.68308i	0.284415	−	0.136967i	−0.286238	−	0.958159i	$-0.592405\pi$
$151$	3.49495	−	1.68308i	0.284415	−	0.136967i	0.570652	+	0.821192i	$0.306690\pi$
$152$	3.94496	+	0.594606i	0.319978	+	0.0482289i
$153$		0			0
$154$	0.000306050	−	0.00408396i	2.46622e−5	−	0.000329095i
$155$	3.11366	+	2.88906i	0.250095	+	0.232055i
$156$		0			0
$157$	−1.36351	+	0.205515i	−0.108820	+	0.0164019i	−0.203226	−	0.979132i	$-0.565143\pi$
$157$	−1.36351	+	0.205515i	−0.108820	+	0.0164019i	0.0944067	+	0.995534i	$0.469905\pi$
$158$	1.30412	−	0.889136i	0.103750	−	0.0707358i
$159$		0			0
$160$	−0.207432	−	2.76799i	−0.0163989	−	0.218829i
$161$	0.0495391	−	0.0621201i	0.00390423	−	0.00489575i
$162$		0			0
$163$	−1.19480	−	3.04431i	−0.0935843	−	0.238449i	0.876415	−	0.481557i	$-0.159928\pi$
$163$	−1.19480	−	3.04431i	−0.0935843	−	0.238449i	−0.969999	+	0.243108i	$0.921833\pi$
$164$	−1.56756	−	6.86794i	−0.122406	−	0.536296i
$165$		0			0
$166$	0.595796	+	1.03195i	0.0462427	+	0.0800948i
$167$	2.54387	−	2.36037i	0.196851	−	0.182651i	−0.575588	−	0.817740i	$-0.695227\pi$
$167$	2.54387	−	2.36037i	0.196851	−	0.182651i	0.772439	+	0.635089i	$0.219036\pi$
$168$		0			0
$169$	−8.56090	−	5.83672i	−0.658531	−	0.448979i
$170$	1.27222	+	0.612671i	0.0975751	+	0.0469897i
$171$		0			0
$172$	−7.47922	+	10.6350i	−0.570285	+	0.810914i
$173$	−16.9268			−1.28692			−0.643459	−	0.765480i	$-0.722501\pi$
$173$	−16.9268			−1.28692			−0.643459	+	0.765480i	$0.722501\pi$
$174$		0			0
$175$	−0.0226458	−	0.0154397i	−0.00171187	−	0.00116713i
$176$	5.05279	+	6.33600i	0.380868	+	0.477594i
$177$		0			0
$178$	−1.04496	−	1.80993i	−0.0783233	−	0.135660i
$179$	4.71887	−	8.17331i	0.352705	−	0.610902i	−0.634018	−	0.773318i	$-0.718595\pi$
$179$	4.71887	−	8.17331i	0.352705	−	0.610902i	0.986722	+	0.162416i	$0.0519287\pi$
$180$		0			0
$181$	−2.69238	−	6.86008i	−0.200123	−	0.509906i	0.795218	−	0.606324i	$-0.207357\pi$
$181$	−2.69238	−	6.86008i	−0.200123	−	0.509906i	−0.995341	+	0.0964185i	$0.969261\pi$
$182$	−0.00305669		0.000942864i	−0.000226577		6.98897e-5i
$183$		0			0
$184$	−0.207366	−	2.76711i	−0.0152873	−	0.203994i
$185$	−8.57763	−	2.64585i	−0.630640	−	0.194527i
$186$		0			0
$187$	−12.4098	+	1.87048i	−0.907495	+	0.136783i
$188$	4.42205	−	19.3743i	0.322511	−	1.41301i
$189$		0			0
$190$	−0.133301	+	1.77878i	−0.00967069	+	0.129046i
$191$	−7.05849	+	17.9847i	−0.510735	+	1.30133i	0.410336	+	0.911935i	$0.365412\pi$
$191$	−7.05849	+	17.9847i	−0.510735	+	1.30133i	−0.921070	+	0.389396i	$0.872684\pi$
$192$		0			0
$193$	−1.90871	+	0.919185i	−0.137392	+	0.0661644i	−0.501317	−	0.865264i	$-0.667151\pi$
$193$	−1.90871	+	0.919185i	−0.137392	+	0.0661644i	0.363925	+	0.931428i	$0.381437\pi$
$194$	−1.60408	+	0.772482i	−0.115166	+	0.0554610i
$195$		0			0
$196$	5.07045	−	12.9193i	0.362175	−	0.922807i
$197$	1.38864	−	18.5301i	0.0989366	−	1.32022i	−0.697975	−	0.716122i	$-0.745915\pi$
$197$	1.38864	−	18.5301i	0.0989366	−	1.32022i	0.796912	−	0.604096i	$-0.206466\pi$
$198$		0			0
$199$	1.75537	−	7.69076i	0.124435	−	0.545184i	−0.873827	−	0.486238i	$-0.838369\pi$
$199$	1.75537	−	7.69076i	0.124435	−	0.545184i	0.998261	−	0.0589460i	$-0.0187740\pi$
$200$	−0.946518	+	0.142665i	−0.0669289	+	0.0100879i
$201$		0			0
$202$	−0.392177	−	0.120971i	−0.0275935	−	0.00851146i
$203$	0.00803721	+	0.107249i	0.000564101	+	0.00752741i
$204$		0			0
$205$	6.04579	−	1.86488i	0.422257	−	0.130249i
$206$	−0.0253117	−	0.0644931i	−0.00176355	−	0.00449344i
$207$		0			0
$208$	3.16491	−	5.48179i	0.219447	−	0.380094i
$209$	−7.92680	−	13.7296i	−0.548308	−	0.949697i
$210$		0			0
$211$	5.02386	+	6.29972i	0.345857	+	0.433691i	0.924087	−	0.382183i	$-0.124828\pi$
$211$	5.02386	+	6.29972i	0.345857	+	0.433691i	−0.578230	+	0.815874i	$0.696256\pi$
$212$	−11.2332	−	7.65866i	−0.771499	−	0.525999i
$213$		0			0
$214$	−0.149234			−0.0102014
$215$	−10.0268	−	5.98469i	−0.683825	−	0.408152i
$216$		0			0
$217$	−0.0322049	−	0.0155090i	−0.00218621	−	0.00105282i
$218$	−1.32465	−	0.903128i	−0.0897163	−	0.0611675i
$219$		0			0
$220$	−5.38275	+	4.99446i	−0.362905	+	0.336727i
$221$	4.90121	+	8.48914i	0.329691	+	0.571041i
$222$		0			0
$223$	−4.52520	−	19.8262i	−0.303030	−	1.32766i	−0.865527	−	0.500862i	$-0.833016\pi$
$223$	−4.52520	−	19.8262i	−0.303030	−	1.32766i	0.562497	−	0.826799i	$-0.309841\pi$
$224$	0.00853402	+	0.0217443i	0.000570203	+	0.00145285i
$225$		0			0
$226$	0.361255	−	0.452999i	0.0240303	−	0.0301331i
$227$	−0.383627	−	5.11915i	−0.0254622	−	0.339770i	−0.995357	−	0.0962474i	$-0.969316\pi$
$227$	−0.383627	−	5.11915i	−0.0254622	−	0.339770i	0.969895	−	0.243523i	$-0.0783030\pi$
$228$		0			0
$229$	−2.36542	+	1.61272i	−0.156312	+	0.106571i	−0.638950	−	0.769248i	$-0.720631\pi$
$229$	−2.36542	+	1.61272i	−0.156312	+	0.106571i	0.482638	+	0.875820i	$0.339679\pi$
$230$	1.22683	−	0.184914i	0.0808946	−	0.0121929i
$231$		0			0
$232$	2.75339	+	2.55477i	0.180769	+	0.167729i
$233$	−0.927985	+	12.3831i	−0.0607943	+	0.811244i	0.880584	+	0.473890i	$0.157151\pi$
$233$	−0.927985	+	12.3831i	−0.0607943	+	0.811244i	−0.941378	+	0.337353i	$0.890468\pi$
$234$		0			0
$235$	17.6486	+	2.66010i	1.15127	+	0.173526i
$236$	2.97735	−	1.43382i	0.193809	−	0.0933336i
$237$		0			0
$238$	−0.0117503	−	0.00177108i	−0.000761662	−	0.000114802i
$239$	8.50273	−	21.6646i	0.549996	−	1.40137i	−0.337838	−	0.941204i	$-0.609696\pi$
$239$	8.50273	−	21.6646i	0.549996	−	1.40137i	0.887834	−	0.460163i	$-0.152209\pi$
$240$		0			0
$241$	−2.57706	−	2.39116i	−0.166003	−	0.154028i	0.592797	−	0.805352i	$-0.298024\pi$
$241$	−2.57706	−	2.39116i	−0.166003	−	0.154028i	−0.758800	+	0.651324i	$0.774214\pi$
$242$	0.195174	−	0.855115i	0.0125463	−	0.0549688i
$243$		0			0
$244$	9.91315	−	6.75867i	0.634624	−	0.432679i
$245$	11.9110	+	3.67405i	0.760965	+	0.234726i
$246$		0			0
$247$	−7.72053	+	9.68124i	−0.491246	+	0.616002i
$248$	−1.19289	+	0.367957i	−0.0757484	+	0.0233653i
$249$		0			0
$250$	−0.355585	−	1.55792i	−0.0224892	−	0.0985315i
$251$	−6.92415	+	11.9930i	−0.437048	+	0.756990i	−0.997460	−	0.0712240i	$-0.977309\pi$
$251$	−6.92415	+	11.9930i	−0.437048	+	0.756990i	0.560412	+	0.828214i	$0.310643\pi$
$252$		0			0
$253$	−8.08323	+	7.50014i	−0.508189	+	0.471530i
$254$	−0.738048	−	0.925482i	−0.0463092	−	0.0580699i
$255$		0			0
$256$	−13.1869	−	6.35050i	−0.824184	−	0.396906i
$257$	−24.5832			−1.53346			−0.766728	−	0.641972i	$-0.778117\pi$
$257$	−24.5832			−1.53346			−0.766728	+	0.641972i	$0.778117\pi$
$258$		0			0
$259$	0.0755403			0.00469384
$260$	5.16737	+	2.48847i	0.320467	+	0.154329i
$261$		0			0
$262$	0.373971	+	0.468945i	0.0231040	+	0.0289715i
$263$	−5.19039	+	4.81598i	−0.320053	+	0.296966i	−0.823794	−	0.566889i	$-0.808147\pi$
$263$	−5.19039	+	4.81598i	−0.320053	+	0.296966i	0.503741	+	0.863855i	$0.331956\pi$
$264$		0			0
$265$	6.10525	−	10.5746i	0.375042	−	0.649593i
$266$	−0.00334029	−	0.0146348i	−0.000204806	−	0.000897315i
$267$		0			0
$268$	−2.71508	+	0.837492i	−0.165850	+	0.0511580i
$269$	5.70535	−	7.15429i	0.347862	−	0.436205i	−0.576863	−	0.816841i	$-0.695724\pi$
$269$	5.70535	−	7.15429i	0.347862	−	0.436205i	0.924725	+	0.380636i	$0.124295\pi$
$270$		0			0
$271$	3.16958	+	0.977687i	0.192539	+	0.0593903i	0.389525	−	0.921016i	$-0.372639\pi$
$271$	3.16958	+	0.977687i	0.192539	+	0.0593903i	−0.196986	+	0.980406i	$0.563115\pi$
$272$	19.4285	−	13.2461i	1.17802	−	0.803163i
$273$		0			0
$274$	−0.454844	+	1.99280i	−0.0274782	+	0.120390i
$275$	2.78836	+	2.58722i	0.168145	+	0.156015i
$276$		0			0
$277$	−0.698305	+	1.77925i	−0.0419571	+	0.106905i	−0.950316	−	0.311286i	$-0.899240\pi$
$277$	−0.698305	+	1.77925i	−0.0419571	+	0.106905i	0.908359	+	0.418191i	$0.137336\pi$
$278$	0.891296	+	0.134341i	0.0534564	+	0.00805725i
$279$		0			0
$280$	−0.0125829	+	0.00605962i	−0.000751974	+	0.000362132i
$281$	19.5257	+	2.94302i	1.16480	+	0.175566i	0.702850	−	0.711338i	$-0.251910\pi$
$281$	19.5257	+	2.94302i	1.16480	+	0.175566i	0.461954	+	0.886904i	$0.347148\pi$
$282$		0			0
$283$	−1.31220	+	17.5101i	−0.0780020	+	1.04086i	0.811626	+	0.584178i	$0.198583\pi$
$283$	−1.31220	+	17.5101i	−0.0780020	+	1.04086i	−0.889628	+	0.456687i	$0.849036\pi$
$284$	10.2402	+	9.50154i	0.607645	+	0.563812i
$285$		0			0
$286$	0.438976	−	0.0661650i	0.0259572	−	0.00391242i
$287$	−0.0439916	+	0.0299930i	−0.00259674	+	0.00177043i
$288$		0			0
$289$	1.45085	+	19.3602i	0.0853439	+	1.13883i
$290$	−1.04708	+	1.31300i	−0.0614868	+	0.0771020i
$291$		0			0
$292$	−7.07124	−	18.0172i	−0.413813	−	1.05438i
$293$	1.28000	+	5.60806i	0.0747786	+	0.327626i	0.998456	−	0.0555441i	$-0.0176893\pi$
$293$	1.28000	+	5.60806i	0.0747786	+	0.327626i	−0.923678	+	0.383170i	$0.874832\pi$
$294$		0			0
$295$	1.48397	+	2.57032i	0.0864003	+	0.149650i
$296$	1.93391	−	1.79441i	0.112406	−	0.104298i
$297$		0			0
$298$	−2.24091	−	1.52783i	−0.129813	−	0.0885047i
$299$	7.75980	+	3.73692i	0.448761	+	0.216112i
$300$		0			0
$301$	0.0954760	+	0.0232546i	0.00550315	+	0.00134037i
$302$	−0.509739			−0.0293322
$303$		0			0
$304$	24.5428	+	16.7330i	1.40762	+	0.959702i
$305$	6.71848	+	8.42470i	0.384699	+	0.482397i
$306$		0			0
$307$	7.61789	+	13.1946i	0.434776	+	0.753054i	0.997277	−	0.0737425i	$-0.0234943\pi$
$307$	7.61789	+	13.1946i	0.434776	+	0.753054i	−0.562502	+	0.826796i	$0.690161\pi$
$308$	0.0308969	−	0.0535149i	0.00176051	−	0.00304930i
$309$		0			0
$310$	−0.203916	−	0.519571i	−0.0115817	−	0.0295096i
$311$	−31.3624	+	9.67402i	−1.77840	+	0.548563i	−0.997135	−	0.0756385i	$-0.975900\pi$
$311$	−31.3624	+	9.67402i	−1.77840	+	0.548563i	−0.781263	+	0.624202i	$0.785424\pi$
$312$		0			0
$313$	1.45692	+	19.4413i	0.0823502	+	1.09889i	0.873357	+	0.487080i	$0.161938\pi$
$313$	1.45692	+	19.4413i	0.0823502	+	1.09889i	−0.791007	+	0.611807i	$0.790443\pi$
$314$	0.173147	+	0.0534089i	0.00977127	+	0.00301404i
$315$		0			0
$316$	23.5495	−	3.54952i	1.32476	−	0.199676i
$317$	−3.76022	+	16.4746i	−0.211195	+	0.925306i	0.752561	+	0.658522i	$0.228818\pi$
$317$	−3.76022	+	16.4746i	−0.211195	+	0.925306i	−0.963756	+	0.266784i	$0.914039\pi$
$318$		0			0
$319$	1.11541	−	14.8842i	0.0624512	−	0.833354i
$320$	4.93693	−	12.5791i	0.275983	−	0.703193i
$321$		0			0
$322$	−0.00940689	+	0.00453012i	−0.000524225	+	0.000252454i
$323$	−41.4447	+	19.9587i	−2.30604	+	1.11053i
$324$		0			0
$325$	1.08543	−	2.76564i	0.0602090	−	0.153410i
$326$	−0.0321152	+	0.428548i	−0.00177870	+	0.0237351i
$327$		0			0
$328$	−0.413770	+	1.81284i	−0.0228466	+	0.100098i
$329$	−0.148520	+	0.0223858i	−0.00818818	+	0.00123417i
$330$		0			0
$331$	−27.4650	−	8.47184i	−1.50962	−	0.465655i	−0.574053	−	0.818818i	$-0.694630\pi$
$331$	−27.4650	−	8.47184i	−1.50962	−	0.465655i	−0.935562	+	0.353163i	$0.885106\pi$
$332$	1.34360	+	17.9291i	0.0737397	+	0.983987i
$333$		0			0
$334$	−0.435754	+	0.134412i	−0.0238434	+	0.00735471i
$335$	−0.932295	−	2.37545i	−0.0509367	−	0.129785i
$336$		0			0
$337$	−8.51965	+	14.7565i	−0.464095	+	0.803836i	−0.999160	−	0.0409748i	$-0.986954\pi$
$337$	−8.51965	+	14.7565i	−0.464095	+	0.803836i	0.535065	+	0.844811i	$0.320287\pi$
$338$	0.680771	+	1.17913i	0.0370290	+	0.0641362i
$339$		0			0
$340$	13.2840	+	16.6577i	0.720428	+	0.903388i
$341$	4.09872	+	2.79446i	0.221958	+	0.151329i
$342$		0			0
$343$	−0.209795			−0.0113279
$344$	2.99669	−	1.67263i	0.161571	−	0.0901820i
$345$		0			0
$346$	2.00401	+	0.965083i	0.107736	+	0.0518832i
$347$	22.9814	+	15.6684i	1.23371	+	0.841126i	0.991628	−	0.129131i	$-0.0412187\pi$
$347$	22.9814	+	15.6684i	1.23371	+	0.841126i	0.242078	+	0.970257i	$0.422171\pi$
$348$		0			0
$349$	9.18897	−	8.52612i	0.491874	−	0.456393i	−0.394814	−	0.918761i	$-0.629191\pi$
$349$	9.18897	−	8.52612i	0.491874	−	0.456393i	0.886688	+	0.462369i	$0.153000\pi$
$350$	0.00180082	+	0.00311911i	9.62578e−5	+	0.000166723i
$351$		0			0
$352$	−0.721369	−	3.16052i	−0.0384491	−	0.168456i
$353$	0.273094	+	0.695831i	0.0145353	+	0.0370353i	0.937957	−	0.346751i	$-0.112715\pi$
$353$	0.273094	+	0.695831i	0.0145353	+	0.0370353i	−0.923422	+	0.383786i	$0.874620\pi$
$354$		0			0
$355$	−7.82239	+	9.80897i	−0.415169	+	0.520606i
$356$	−2.35653	−	31.4458i	−0.124896	−	1.66662i
$357$		0			0
$358$	−1.02468	+	0.698618i	−0.0541563	+	0.0369231i
$359$	0.374896	−	0.0565064i	0.0197862	−	0.00298230i	−0.139142	−	0.990272i	$-0.544434\pi$
$359$	0.374896	−	0.0565064i	0.0197862	−	0.00298230i	0.158928	+	0.987290i	$0.449196\pi$
$360$		0			0
$361$	−28.6690	−	26.6009i	−1.50889	−	1.40005i
$362$	−0.0723687	+	0.965693i	−0.00380362	+	0.0507557i
$363$		0			0
$364$	−0.0477262	−	0.00719356i	−0.00250153	−	0.000377045i
$365$	15.6618	−	7.54233i	0.819777	−	0.394784i
$366$		0			0
$367$	−17.0718	−	2.57316i	−0.891142	−	0.134318i	−0.312517	−	0.949912i	$-0.601172\pi$
$367$	−17.0718	−	2.57316i	−0.891142	−	0.134318i	−0.578624	+	0.815594i	$0.696410\pi$
$368$	7.54813	−	19.2323i	0.393473	−	1.00255i
$369$		0			0
$370$	0.864680	+	0.802306i	0.0449526	+	0.0417099i
$371$	−0.0228654	+	0.100180i	−0.00118711	+	0.00520108i
$372$		0			0
$373$	23.7980	−	16.2252i	1.23221	−	0.840108i	0.240760	−	0.970585i	$-0.422603\pi$
$373$	23.7980	−	16.2252i	1.23221	−	0.840108i	0.991451	+	0.130477i	$0.0416509\pi$
$374$	1.57588	+	0.486095i	0.0814869	+	0.0251354i
$375$		0			0
$376$	−3.27052	+	4.10110i	−0.168664	+	0.211498i
$377$	−11.1402	+	3.43631i	−0.573752	+	0.176979i
$378$		0			0
$379$	−4.28454	−	18.7718i	−0.220082	−	0.964242i	−0.957416	−	0.288713i	$-0.906773\pi$
$379$	−4.28454	−	18.7718i	−0.220082	−	0.964242i	0.737334	−	0.675529i	$-0.236085\pi$
$380$	−13.4572	+	23.3086i	−0.690341	+	1.19571i
$381$		0			0
$382$	1.86108	−	1.72683i	0.0952212	−	0.0883524i
$383$	8.54764	+	10.7184i	0.436764	+	0.547685i	0.950687	−	0.310151i	$-0.100380\pi$
$383$	8.54764	+	10.7184i	0.436764	+	0.547685i	−0.513923	+	0.857836i	$0.671808\pi$
$384$		0			0
$385$	0.0500023	+	0.0240798i	0.00254835	+	0.00122722i
$386$	0.278386			0.0141695
$387$		0			0
$388$	−26.8635			−1.36379
$389$	26.3431	+	12.6862i	1.33565	+	0.643215i	0.959070	−	0.283170i	$-0.0913859\pi$
$389$	26.3431	+	12.6862i	1.33565	+	0.643215i	0.376579	+	0.926384i	$0.377100\pi$
$390$		0			0
$391$	19.9485	+	25.0147i	1.00884	+	1.26505i
$392$	−2.68545	+	2.49173i	−0.135636	+	0.125852i
$393$		0			0
$394$	−1.22090	+	2.11467i	−0.0615083	+	0.106536i
$395$	4.75955	+	20.8530i	0.239479	+	1.04923i
$396$		0			0
$397$	17.8679	−	5.51152i	0.896764	−	0.276615i	0.188091	−	0.982152i	$-0.439770\pi$
$397$	17.8679	−	5.51152i	0.896764	−	0.276615i	0.708674	+	0.705536i	$0.249294\pi$
$398$	−0.646314	+	0.810452i	−0.0323968	+	0.0406243i
$399$		0			0
$400$	−6.81033	−	2.10071i	−0.340517	−	0.105035i
$401$	4.37678	−	2.98404i	0.218566	−	0.149016i	−0.449088	−	0.893488i	$-0.648251\pi$
$401$	4.37678	−	2.98404i	0.218566	−	0.149016i	0.667654	+	0.744472i	$0.267299\pi$
$402$		0			0
$403$	0.862192	−	3.77751i	0.0429488	−	0.188171i
$404$	−4.53941	−	4.21196i	−0.225844	−	0.209553i
$405$		0			0
$406$	0.00516327	−	0.0131558i	0.000256249	−	0.000652912i
$407$	−10.3665	−	1.56250i	−0.513848	−	0.0774501i
$408$		0			0
$409$	−5.49230	+	2.64495i	−0.271577	+	0.130784i	−0.564716	−	0.825285i	$-0.691014\pi$
$409$	−5.49230	+	2.64495i	−0.271577	+	0.130784i	0.293139	+	0.956070i	$0.405300\pi$
$410$	−0.822108	−	0.123913i	−0.0406010	−	0.00611962i
$411$		0			0
$412$	0.0781204	−	1.04244i	0.00384872	−	0.0513576i
$413$	−0.0183091	−	0.0169883i	−0.000900930	−	0.000835941i
$414$		0			0
$415$	−15.9673	+	2.40669i	−0.783805	+	0.118140i
$416$	−2.09210	+	1.42637i	−0.102574	+	0.0699335i
$417$		0			0
$418$	0.155683	+	2.07744i	0.00761469	+	0.101611i
$419$	−3.35789	+	4.21066i	−0.164044	+	0.205704i	−0.857059	−	0.515219i	$-0.827711\pi$
$419$	−3.35789	+	4.21066i	−0.164044	+	0.205704i	0.693015	+	0.720923i	$0.256282\pi$
$420$		0			0
$421$	13.0829	+	33.3348i	0.637623	+	1.62464i	0.773415	+	0.633900i	$0.218547\pi$
$421$	13.0829	+	33.3348i	0.637623	+	1.62464i	−0.135791	+	0.990737i	$0.543358\pi$
$422$	−0.235611	−	1.03228i	−0.0114694	−	0.0502506i
$423$		0			0
$424$	1.79433	+	3.10787i	0.0871403	+	0.150931i
$425$	8.09059	−	7.50697i	0.392451	−	0.364142i
$426$		0			0
$427$	−0.0749242	−	0.0510824i	−0.00362583	−	0.00247205i
$428$	−2.02873	−	0.976985i	−0.0980624	−	0.0472243i
$429$		0			0
$430$	0.845892	+	1.28023i	0.0407925	+	0.0617381i
$431$	−2.38810			−0.115031			−0.0575153	−	0.998345i	$-0.518318\pi$
$431$	−2.38810			−0.115031			−0.0575153	+	0.998345i	$0.518318\pi$
$432$		0			0
$433$	−6.98440	−	4.76188i	−0.335649	−	0.228841i	0.383753	−	0.923436i	$-0.374631\pi$
$433$	−6.98440	−	4.76188i	−0.335649	−	0.228841i	−0.719402	+	0.694594i	$0.755584\pi$
$434$	0.00292859	+	0.00367233i	0.000140577	+	0.000176278i
$435$		0			0
$436$	−12.0951	−	20.9494i	−0.579252	−	1.00329i
$437$	−20.2086	+	35.0023i	−0.966709	+	1.67439i
$438$		0			0
$439$	1.42478	+	3.63029i	0.0680013	+	0.173264i	0.960834	−	0.277123i	$-0.0893810\pi$
$439$	1.42478	+	3.63029i	0.0680013	+	0.173264i	−0.892833	+	0.450388i	$0.851286\pi$
$440$	1.85211	−	0.571301i	0.0882960	−	0.0272357i
$441$		0			0
$442$	−0.0962599	−	1.28450i	−0.00457862	−	0.0610974i
$443$	−24.1906	−	7.46180i	−1.14933	−	0.354521i	−0.339166	−	0.940726i	$-0.610145\pi$
$443$	−24.1906	−	7.46180i	−1.14933	−	0.354521i	−0.810162	+	0.586205i	$0.800621\pi$
$444$		0			0
$445$	28.0050	−	4.22107i	1.32756	−	0.200098i
$446$	−0.594642	+	2.60529i	−0.0281571	+	0.123364i
$447$		0			0
$448$	−0.00849824	+	0.113401i	−0.000401504	+	0.00535770i
$449$	13.0603	−	33.2771i	0.616353	−	1.57044i	−0.191778	−	0.981438i	$-0.561425\pi$
$449$	13.0603	−	33.2771i	0.616353	−	1.57044i	0.808131	−	0.589003i	$-0.200480\pi$
$450$		0			0
$451$	6.65741	−	3.20604i	0.313485	−	0.150967i
$452$	7.87664	−	3.79319i	0.370486	−	0.178417i
$453$		0			0
$454$	−0.246450	+	0.627946i	−0.0115665	+	0.0294709i
$455$	0.00323941	−	0.0432269i	0.000151866	−	0.00202651i
$456$		0			0
$457$	−4.21771	+	18.4790i	−0.197296	+	0.864411i	0.775241	+	0.631665i	$0.217628\pi$
$457$	−4.21771	+	18.4790i	−0.197296	+	0.864411i	−0.972538	+	0.232746i	$0.925229\pi$
$458$	0.372000	−	0.0560699i	0.0173824	−	0.00261998i
$459$		0			0
$460$	17.8884	+	5.51785i	0.834052	+	0.257271i
$461$	−1.05220	−	14.0407i	−0.0490060	−	0.653940i	−0.966578	−	0.256371i	$-0.917473\pi$
$461$	−1.05220	−	14.0407i	−0.0490060	−	0.653940i	0.917572	−	0.397569i	$-0.130146\pi$
$462$		0			0
$463$	17.8943	−	5.51965i	0.831618	−	0.256520i	0.150422	−	0.988622i	$-0.451937\pi$
$463$	17.8943	−	5.51965i	0.831618	−	0.256520i	0.681195	+	0.732102i	$0.261460\pi$
$464$	10.2171	+	26.0329i	0.474319	+	1.20855i
$465$		0			0
$466$	0.815892	−	1.41317i	0.0377955	−	0.0654636i
$467$	−1.07575	−	1.86325i	−0.0497796	−	0.0862208i	0.840062	−	0.542491i	$-0.182519\pi$
$467$	−1.07575	−	1.86325i	−0.0497796	−	0.0862208i	−0.889842	+	0.456270i	$0.849185\pi$
$468$		0			0
$469$	0.0133893	+	0.0167897i	0.000618262	+	0.000775276i
$470$	−1.93781	−	1.32118i	−0.0893845	−	0.0609413i
$471$		0			0
$472$	−0.872278			−0.0401499
$473$	−12.6213	−	5.16612i	−0.580328	−	0.237538i
$474$		0			0
$475$	12.5615	+	6.04928i	0.576359	+	0.277560i
$476$	−0.148143	−	0.101002i	−0.00679012	−	0.00462943i
$477$		0			0
$478$	−2.24188	+	2.08016i	−0.102541	+	0.0951442i
$479$	14.0491	+	24.3337i	0.641919	+	1.11184i	0.985004	+	0.172532i	$0.0551949\pi$
$479$	14.0491	+	24.3337i	0.641919	+	1.11184i	−0.343085	+	0.939304i	$0.611472\pi$
$480$		0			0
$481$	1.82209	+	7.98312i	0.0830804	+	0.363999i
$482$	0.168774	+	0.430029i	0.00768744	+	0.0195873i
$483$		0			0
$484$	8.25141	−	10.3469i	0.375064	−	0.470315i
$485$	−1.80299	−	24.0592i	−0.0818696	−	1.09247i
$486$		0			0
$487$	−15.6116	+	10.6438i	−0.707431	+	0.482318i	−0.862805	−	0.505538i	$-0.831294\pi$
$487$	−15.6116	+	10.6438i	−0.707431	+	0.482318i	0.155374	+	0.987856i	$0.450342\pi$
$488$	−3.13157	+	0.472008i	−0.141759	+	0.0213668i
$489$		0			0
$490$	−1.20070	−	1.11409i	−0.0542422	−	0.0503294i
$491$	2.02122	−	26.9713i	0.0912165	−	1.21720i	−0.744342	−	0.667798i	$-0.767237\pi$
$491$	2.02122	−	26.9713i	0.0912165	−	1.21720i	0.835559	−	0.549401i	$-0.185144\pi$
$492$		0			0
$493$	−42.8247	−	6.45478i	−1.92873	−	0.290709i
$494$	1.46604	−	0.706006i	0.0659601	−	0.0317647i
$495$		0			0
$496$	−9.19084	−	1.38530i	−0.412681	−	0.0622016i
$497$	0.0385730	−	0.0982824i	0.00173024	−	0.00440857i
$498$		0			0
$499$	−5.20488	−	4.82942i	−0.233002	−	0.216195i	0.555027	−	0.831832i	$-0.312708\pi$
$499$	−5.20488	−	4.82942i	−0.233002	−	0.216195i	−0.788029	+	0.615638i	$0.788898\pi$
$500$	5.36525	−	23.5067i	0.239941	−	1.05125i
$501$		0			0
$502$	1.50355	−	1.02511i	0.0671069	−	0.0457527i
$503$	18.5296	+	5.71564i	0.826196	+	0.254848i	0.678887	−	0.734243i	$-0.262463\pi$
$503$	18.5296	+	5.71564i	0.826196	+	0.254848i	0.147309	+	0.989091i	$0.452939\pi$
$504$		0			0
$505$	3.46761	−	4.34824i	0.154307	−	0.193494i
$506$	1.38462	−	0.427099i	0.0615540	−	0.0189869i
$507$		0			0
$508$	−3.97441	−	17.4130i	−0.176336	−	0.772579i
$509$	−12.0737	+	20.9122i	−0.535156	+	0.926917i	0.464000	+	0.885835i	$0.346414\pi$
$509$	−12.0737	+	20.9122i	−0.535156	+	0.926917i	−0.999156	+	0.0410815i	$0.986920\pi$
$510$		0			0
$511$	−0.107236	+	0.0995008i	−0.00474386	+	0.00440166i
$512$	6.33014	+	7.93774i	0.279755	+	0.350802i
$513$		0			0
$514$	2.91048	+	1.40161i	0.128376	+	0.0618226i
$515$	0.938868			0.0413715
$516$		0			0
$517$	20.8447			0.916747
$518$	−0.00894346	−	0.00430694i	−0.000392953	−	0.000189236i
$519$		0			0
$520$	−0.943894	−	1.18361i	−0.0413925	−	0.0519045i
$521$	1.66226	−	1.54235i	0.0728250	−	0.0675718i	−0.642921	−	0.765933i	$-0.722277\pi$
$521$	1.66226	−	1.54235i	0.0728250	−	0.0675718i	0.715746	+	0.698361i	$0.246087\pi$
$522$		0			0
$523$	−15.7289	+	27.2432i	−0.687775	+	1.19126i	0.284780	+	0.958593i	$0.408079\pi$
$523$	−15.7289	+	27.2432i	−0.687775	+	1.19126i	−0.972556	+	0.232669i	$0.925254\pi$
$524$	2.01385	+	8.82324i	0.0879753	+	0.385445i
$525$		0			0
$526$	0.889090	−	0.274248i	0.0387662	−	0.0119578i
$527$	8.97436	−	11.2535i	0.390929	−	0.490210i
$528$		0			0
$529$	4.88473	+	1.50674i	0.212380	+	0.0655104i
$530$	−1.32573	+	0.903869i	−0.0575862	+	0.0392616i
$531$		0			0
$532$	0.0504001	−	0.220817i	0.00218512	−	0.00957364i
$533$	−4.23078	−	3.92559i	−0.183255	−	0.170036i
$534$		0			0
$535$	0.738837	−	1.88253i	0.0319427	−	0.0813887i
$536$	0.741610	+	0.111780i	0.0320327	+	0.00482815i
$537$		0			0
$538$	−1.08338	+	0.521727i	−0.0467077	+	0.0224933i
$539$	14.3950	+	2.16970i	0.620037	+	0.0934555i
$540$		0			0
$541$	−0.0680679	+	0.908302i	−0.00292647	+	0.0390510i	−0.998476	−	0.0551903i	$-0.982423\pi$
$541$	−0.0680679	+	0.908302i	−0.00292647	+	0.0390510i	0.995549	+	0.0942413i	$0.0300425\pi$
$542$	−0.319514	−	0.296466i	−0.0137243	−	0.0127343i
$543$		0			0
$544$	−9.30122	+	1.40193i	−0.398786	+	0.0601074i
$545$	17.9507	−	12.2386i	0.768925	−	0.524244i
$546$		0			0
$547$	−2.81219	−	37.5260i	−0.120240	−	1.60450i	−0.652415	−	0.757862i	$-0.726244\pi$
$547$	−2.81219	−	37.5260i	−0.120240	−	1.60450i	0.532175	−	0.846635i	$-0.321375\pi$
$548$	−19.2295	+	24.1131i	−0.821444	+	1.03006i
$549$		0			0
$550$	−0.182612	−	0.465288i	−0.00778661	−	0.0198400i
$551$	−12.1738	−	53.3371i	−0.518623	−	2.27224i
$552$		0			0
$553$	−0.0899995	−	0.155884i	−0.00382717	−	0.00662885i
$554$	0.184119	−	0.170838i	0.00782247	−	0.00725819i
$555$		0			0
$556$	11.2370	+	7.66129i	0.476557	+	0.324911i
$557$	−37.3275	−	17.9760i	−1.58162	−	0.761667i	−0.582912	−	0.812535i	$-0.698087\pi$
$557$	−37.3275	−	17.9760i	−1.58162	−	0.761667i	−0.998705	+	0.0508683i	$0.983801\pi$
$558$		0			0
$559$	−0.154594	+	10.6509i	−0.00653861	+	0.450483i
$560$	−0.103985			−0.00439416
$561$		0			0
$562$	−2.14391	−	1.46169i	−0.0904355	−	0.0616579i
$563$	−14.7605	−	18.5091i	−0.622083	−	0.780067i	0.366553	−	0.930397i	$-0.380538\pi$
$563$	−14.7605	−	18.5091i	−0.622083	−	0.780067i	−0.988636	+	0.150330i	$0.951966\pi$
$564$		0			0
$565$	3.92588	+	6.79982i	0.165163	+	0.286071i
$566$	1.15369	−	1.99826i	0.0484934	−	0.0839930i
$567$		0			0
$568$	−1.34712	−	3.43241i	−0.0565240	−	0.144021i
$569$	−4.53414	+	1.39860i	−0.190081	+	0.0586322i	−0.388334	−	0.921519i	$-0.626949\pi$
$569$	−4.53414	+	1.39860i	−0.190081	+	0.0586322i	0.198253	+	0.980151i	$0.436473\pi$
$570$		0			0
$571$	−2.70647	−	36.1153i	−0.113262	−	1.51138i	−0.707284	−	0.706930i	$-0.750080\pi$
$571$	−2.70647	−	36.1153i	−0.113262	−	1.51138i	0.594021	−	0.804449i	$-0.297539\pi$
$572$	6.40073	+	1.97436i	0.267628	+	0.0825523i
$573$		0			0
$574$	0.00691837	−	0.00104278i	0.000288767	−	4.35246e-5i
$575$	2.15786	−	9.45422i	0.0899891	−	0.394268i
$576$		0			0
$577$	1.54710	−	20.6446i	0.0644065	−	0.859445i	−0.867660	−	0.497158i	$-0.834377\pi$
$577$	1.54710	−	20.6446i	0.0644065	−	0.859445i	0.932067	−	0.362287i	$-0.118004\pi$
$578$	0.932054	−	2.37484i	0.0387683	−	0.0987801i
$579$		0			0
$580$	−22.8301	+	10.9944i	−0.947970	+	0.456518i
$581$	0.122432	−	0.0589601i	0.00507933	−	0.00244608i
$582$		0			0
$583$	5.21000	−	13.2749i	0.215776	−	0.549789i
$584$	−0.381792	+	5.09466i	−0.0157987	+	0.210818i
$585$		0			0
$586$	0.168201	−	0.736936i	0.00694831	−	0.0304425i
$587$	−22.4886	+	3.38961i	−0.928203	+	0.139904i	−0.595708	−	0.803201i	$-0.703128\pi$
$587$	−22.4886	+	3.38961i	−0.928203	+	0.139904i	−0.332495	+	0.943105i	$0.607890\pi$
$588$		0			0
$589$	17.3749	+	5.35945i	0.715921	+	0.220832i
$590$	−0.0291453	−	0.388917i	−0.00119989	−	0.0160115i
$591$		0			0
$592$	18.7700	−	5.78977i	0.771442	−	0.237958i
$593$	3.19236	+	8.13401i	0.131095	+	0.334024i	0.981316	−	0.192401i	$-0.0616274\pi$
$593$	3.19236	+	8.13401i	0.131095	+	0.334024i	−0.850222	+	0.526425i	$0.823532\pi$
$594$		0			0
$595$	0.0805158	−	0.139457i	0.00330083	−	0.00571720i
$596$	−20.4614	−	35.4403i	−0.838133	−	1.45169i
$597$		0			0
$598$	−0.705646	−	0.884852i	−0.0288560	−	0.0361843i
$599$	−17.4200	−	11.8767i	−0.711760	−	0.485270i	0.152507	−	0.988302i	$-0.451265\pi$
$599$	−17.4200	−	11.8767i	−0.711760	−	0.485270i	−0.864268	+	0.503032i	$0.832218\pi$
$600$		0			0
$601$	−9.25003			−0.377316			−0.188658	−	0.982043i	$-0.560414\pi$
$601$	−9.25003			−0.377316			−0.188658	+	0.982043i	$0.560414\pi$
$602$	−0.00997785	−	0.00819677i	−0.000406667	−	0.000334075i
$603$		0			0
$604$	−6.92954	−	3.33709i	−0.281959	−	0.135784i
$605$	9.82064	+	6.69560i	0.399266	+	0.272215i
$606$		0			0
$607$	26.3944	−	24.4904i	1.07132	−	0.994035i	0.0713212	−	0.997453i	$-0.477278\pi$
$607$	26.3944	−	24.4904i	1.07132	−	0.994035i	0.999994	+	0.00341803i	$0.00108800\pi$
$608$	−5.94118	−	10.2904i	−0.240947	−	0.417332i
$609$		0			0
$610$	−0.315086	−	1.38048i	−0.0127575	−	0.0558941i
$611$	−5.94817	−	15.1557i	−0.240637	−	0.613134i
$612$		0			0
$613$	−4.70938	+	5.90537i	−0.190210	+	0.238516i	−0.867787	−	0.496936i	$-0.834458\pi$
$613$	−4.70938	+	5.90537i	−0.190210	+	0.238516i	0.677577	+	0.735452i	$0.263030\pi$
$614$	−0.149616	−	1.99648i	−0.00603800	−	0.0805715i
$615$		0			0
$616$	−0.0134767	+	0.00918827i	−0.000542992	+	0.000370206i
$617$	13.9051	−	2.09586i	0.559798	−	0.0843760i	0.136952	−	0.990578i	$-0.456269\pi$
$617$	13.9051	−	2.09586i	0.559798	−	0.0843760i	0.422846	+	0.906202i	$0.361031\pi$
$618$		0			0
$619$	4.50835	+	4.18313i	0.181206	+	0.168134i	0.765560	−	0.643364i	$-0.222462\pi$
$619$	4.50835	+	4.18313i	0.181206	+	0.168134i	−0.584355	+	0.811498i	$0.698652\pi$
$620$	0.629356	−	8.39817i	0.0252755	−	0.337279i
$621$		0			0
$622$	4.26466	+	0.642794i	0.170997	+	0.0257737i
$623$	−0.214733	+	0.103410i	−0.00860308	+	0.00414303i
$624$		0			0
$625$	12.3702	+	1.86451i	0.494809	+	0.0745804i
$626$	0.935959	−	2.38479i	0.0374085	−	0.0953152i
$627$		0			0
$628$	2.00417	+	1.85960i	0.0799750	+	0.0742059i
$629$	−6.76880	+	29.6561i	−0.269890	+	1.18246i
$630$		0			0
$631$	−25.7287	+	17.5415i	−1.02424	+	0.698317i	−0.954182	−	0.299226i	$-0.903272\pi$
$631$	−25.7287	+	17.5415i	−1.02424	+	0.698317i	−0.0700608	+	0.997543i	$0.522319\pi$
$632$	−6.00700	−	1.85291i	−0.238946	−	0.0737050i
$633$		0			0
$634$	1.38449	−	1.73609i	0.0549850	−	0.0689490i
$635$	15.3286	−	4.72823i	0.608295	−	0.187634i
$636$		0			0
$637$	−2.53018	−	11.0854i	−0.100249	−	0.439221i
$638$	−0.980682	+	1.69859i	−0.0388256	+	0.0672478i
$639$		0			0
$640$	−5.37124	+	4.98378i	−0.212317	+	0.197001i
$641$	16.5022	+	20.6931i	0.651798	+	0.817329i	0.992423	−	0.122871i	$-0.0392100\pi$
$641$	16.5022	+	20.6931i	0.651798	+	0.817329i	−0.340625	+	0.940199i	$0.610639\pi$
$642$		0			0
$643$	−15.1982	−	7.31905i	−0.599357	−	0.288635i	0.109501	−	0.993987i	$-0.465075\pi$
$643$	−15.1982	−	7.31905i	−0.599357	−	0.288635i	−0.708858	+	0.705352i	$0.750789\pi$
$644$	−0.157537			−0.00620784
$645$		0			0
$646$	6.04472			0.237826
$647$	7.97769	+	3.84185i	0.313635	+	0.151039i	0.584079	−	0.811697i	$-0.301456\pi$
$647$	7.97769	+	3.84185i	0.313635	+	0.151039i	−0.270443	+	0.962736i	$0.587170\pi$
$648$		0			0
$649$	2.16118	+	2.71004i	0.0848339	+	0.106378i
$650$	−0.286191	+	0.265547i	−0.0112253	+	0.0104156i
$651$		0			0
$652$	−3.24214	+	5.61556i	−0.126972	+	0.219922i
$653$	0.952035	+	4.17114i	0.0372560	+	0.163229i	0.990134	−	0.140125i	$-0.0447505\pi$
$653$	0.952035	+	4.17114i	0.0372560	+	0.163229i	−0.952878	+	0.303354i	$0.901893\pi$
$654$		0			0
$655$	−7.76703	+	2.39581i	−0.303483	+	0.0936121i
$656$	−8.63208	+	10.8243i	−0.337026	+	0.422617i
$657$		0			0
$658$	0.0188601	+	0.00581758i	0.000735244	+	0.000226793i
$659$	18.1765	−	12.3925i	0.708056	−	0.482744i	−0.154960	−	0.987921i	$-0.549525\pi$
$659$	18.1765	−	12.3925i	0.708056	−	0.482744i	0.863016	+	0.505176i	$0.168573\pi$
$660$		0			0
$661$	3.37614	−	14.7918i	0.131317	−	0.575336i	−0.865863	−	0.500281i	$-0.833230\pi$
$661$	3.37614	−	14.7918i	0.131317	−	0.575336i	0.997179	−	0.0750541i	$-0.0239130\pi$
$662$	2.76865	+	2.56893i	0.107607	+	0.0998444i
$663$		0			0
$664$	1.73383	−	4.41773i	0.0672858	−	0.171441i
$665$	0.201149	+	0.0303183i	0.00780022	+	0.00117569i
$666$		0			0
$667$	−34.2838	+	16.5102i	−1.32748	+	0.639279i
$668$	−6.80372	−	1.02550i	−0.263244	−	0.0396776i
$669$		0			0
$670$	−0.0250592	+	0.334392i	−0.000968122	+	0.0129187i
$671$	9.22534	+	8.55986i	0.356140	+	0.330450i
$672$		0			0
$673$	−18.2365	+	2.74871i	−0.702965	+	0.105955i	−0.490791	−	0.871277i	$-0.663292\pi$
$673$	−18.2365	+	2.74871i	−0.702965	+	0.105955i	−0.212174	+	0.977232i	$0.568054\pi$
$674$	1.85001	−	1.26132i	0.0712598	−	0.0485841i
$675$		0			0
$676$	1.53523	+	20.4862i	0.0590473	+	0.787931i
$677$	−14.3763	+	18.0274i	−0.552528	+	0.692848i	−0.977157	−	0.212520i	$-0.931833\pi$
$677$	−14.3763	+	18.0274i	−0.552528	+	0.692848i	0.424629	+	0.905367i	$0.360405\pi$
$678$		0			0
$679$	0.0741773	+	0.189001i	0.00284666	+	0.00725318i
$680$	−1.25143	−	5.48286i	−0.0479901	−	0.210258i
$681$		0			0
$682$	−0.325934	−	0.564535i	−0.0124807	−	0.0216172i
$683$	34.9487	−	32.4277i	1.33728	−	1.24081i	0.389833	−	0.920886i	$-0.372533\pi$
$683$	34.9487	−	32.4277i	1.33728	−	1.24081i	0.947443	−	0.319925i	$-0.103658\pi$
$684$		0			0
$685$	−22.8865	−	15.6038i	−0.874450	−	0.596190i
$686$	0.0248383	+	0.0119615i	0.000948332	+	0.000456693i
$687$		0			0
$688$	25.5059	−	1.53952i	0.972403	−	0.0586936i
$689$	−11.1386			−0.424346
$690$		0			0
$691$	13.3788	+	9.12151i	0.508953	+	0.346998i	0.790413	−	0.612575i	$-0.209866\pi$
$691$	13.3788	+	9.12151i	0.508953	+	0.346998i	−0.281459	+	0.959573i	$0.590819\pi$
$692$	20.9251	+	26.2392i	0.795453	+	0.997466i
$693$		0			0
$694$	−1.82750	−	3.16533i	−0.0693710	−	0.120154i
$695$	−6.10734	+	10.5782i	−0.231665	+	0.401255i
$696$		0			0
$697$	−7.83295	−	19.9580i	−0.296694	−	0.755964i
$698$	−1.57403	+	0.485524i	−0.0595779	+	0.0183773i
$699$		0			0
$700$	0.00406109	+	0.0541915i	0.000153495	+	0.00204825i
$701$	28.2831	+	8.72419i	1.06824	+	0.329508i	0.778530	−	0.627607i	$-0.215965\pi$
$701$	28.2831	+	8.72419i	1.06824	+	0.329508i	0.289708	+	0.957115i	$0.406442\pi$
$702$		0			0
$703$	−37.9969	+	5.72711i	−1.43308	+	0.216002i
$704$	3.51185	−	15.3864i	0.132358	−	0.579897i
$705$		0			0
$706$	0.00734050	−	0.0979522i	0.000276263	−	0.00368648i
$707$	−0.0170991	+	0.0435679i	−0.000643079	+	0.00163854i
$708$		0			0
$709$	16.3466	−	7.87211i	0.613910	−	0.295643i	−0.100971	−	0.994889i	$-0.532195\pi$
$709$	16.3466	−	7.87211i	0.613910	−	0.295643i	0.714881	+	0.699246i	$0.246481\pi$
$710$	1.48538	−	0.715320i	0.0557452	−	0.0268455i
$711$		0			0
$712$	−3.04096	+	7.74824i	−0.113965	+	0.290377i
$713$	0.945099	−	12.6115i	0.0353942	−	0.472303i
$714$		0			0
$715$	−1.33867	+	5.86508i	−0.0500633	+	0.219342i
$716$	−18.5035	+	2.78895i	−0.691508	+	0.104228i
$717$		0			0
$718$	−0.0476068	−	0.0146848i	−0.00177667	−	0.000548031i
$719$	−1.34139	−	17.8996i	−0.0500254	−	0.667542i	−0.964700	−	0.263351i	$-0.915172\pi$
$719$	−1.34139	−	17.8996i	−0.0500254	−	0.667542i	0.914675	−	0.404191i	$-0.132447\pi$
$720$		0			0
$721$	−0.00754994	+	0.00232885i	−0.000281174	+	8.67308e-5i
$722$	1.87756	+	4.78393i	0.0698754	+	0.178040i
$723$		0			0
$724$	−7.30588	+	12.6541i	−0.271521	+	0.470288i
$725$	6.56317	+	11.3677i	0.243750	+	0.422187i
$726$		0			0
$727$	7.71422	+	9.67332i	0.286105	+	0.358764i	0.904027	−	0.427475i	$-0.140597\pi$
$727$	7.71422	+	9.67332i	0.286105	+	0.358764i	−0.617923	+	0.786239i	$0.712025\pi$
$728$	0.0105263	+	0.00717668i	0.000390129	+	0.000265986i
$729$		0			0
$730$	−2.28428			−0.0845450
$731$	−17.6846	+	35.3988i	−0.654088	+	1.30927i
$732$		0			0
$733$	17.8504	+	8.59631i	0.659320	+	0.317512i	0.733457	−	0.679736i	$-0.237906\pi$
$733$	17.8504	+	8.59631i	0.659320	+	0.317512i	−0.0741364	+	0.997248i	$0.523620\pi$
$734$	1.87448	+	1.27800i	0.0691883	+	0.0471718i
$735$		0			0
$736$	−6.05843	+	5.62140i	−0.223317	+	0.207208i
$737$	−1.49015	−	2.58102i	−0.0548905	−	0.0950732i
$738$		0			0
$739$	6.50578	+	28.5037i	0.239319	+	1.04852i	0.941629	+	0.336653i	$0.109295\pi$
$739$	6.50578	+	28.5037i	0.239319	+	1.04852i	−0.702310	+	0.711871i	$0.747848\pi$
$740$	6.50229	+	16.5676i	0.239029	+	0.609036i
$741$		0			0
$742$	0.00841889	−	0.0105570i	0.000309067	−	0.000387558i
$743$	1.38658	+	18.5026i	0.0508686	+	0.678795i	0.963104	+	0.269129i	$0.0867357\pi$
$743$	1.38658	+	18.5026i	0.0508686	+	0.678795i	−0.912236	+	0.409666i	$0.865645\pi$
$744$		0			0
$745$	30.3674	−	20.7041i	1.11257	−	0.758541i
$746$	−3.74260	+	0.564106i	−0.137026	+	0.0206534i
$747$		0			0
$748$	18.2407	+	16.9249i	0.666946	+	0.618836i
$749$	−0.00127180	+	0.0169711i	−4.64707e−5	+	0.000620109i
$750$		0			0
$751$	41.0993	+	6.19473i	1.49974	+	0.226049i	0.847023	−	0.531557i	$-0.178393\pi$
$751$	41.0993	+	6.19473i	1.49974	+	0.226049i	0.652713	+	0.757606i	$0.273631\pi$
$752$	−35.1880	+	16.9457i	−1.28318	+	0.617945i
$753$		0			0
$754$	1.51485	+	0.228327i	0.0551676	+	0.00831518i
$755$	2.52365	−	6.43015i	0.0918449	−	0.234017i
$756$		0			0
$757$	18.4171	+	17.0886i	0.669381	+	0.621095i	0.939831	−	0.341639i	$-0.110982\pi$
$757$	18.4171	+	17.0886i	0.669381	+	0.621095i	−0.270450	+	0.962734i	$0.587172\pi$
$758$	−0.563016	+	2.46674i	−0.0204497	+	0.0895959i
$759$		0			0
$760$	5.86983	−	4.00198i	0.212921	−	0.145167i
$761$	−2.55267	−	0.787394i	−0.0925342	−	0.0285430i	0.248142	−	0.968724i	$-0.420180\pi$
$761$	−2.55267	−	0.787394i	−0.0925342	−	0.0285430i	−0.340677	+	0.940181i	$0.610656\pi$
$762$		0			0
$763$	−0.113994	+	0.142944i	−0.00412685	+	0.00517490i
$764$	36.6051	−	11.2912i	1.32433	−	0.408500i
$765$		0			0
$766$	−0.400871	−	1.75633i	−0.0144841	−	0.0634588i
$767$	1.35370	−	2.34468i	0.0488793	−	0.0846614i
$768$		0			0
$769$	27.1593	−	25.2001i	0.979389	−	0.908741i	−0.0164501	−	0.999865i	$-0.505236\pi$
$769$	27.1593	−	25.2001i	0.979389	−	0.908741i	0.995840	+	0.0911240i	$0.0290460\pi$
$770$	−0.00454701	−	0.00570178i	−0.000163863	−	0.000205478i
$771$		0			0
$772$	3.78446	+	1.82250i	0.136206	+	0.0655931i
$773$	−46.2293			−1.66275			−0.831376	−	0.555711i	$-0.812446\pi$
$773$	−46.2293			−1.66275			−0.831376	+	0.555711i	$0.812446\pi$
$774$		0			0
$775$	−4.36260			−0.156709
$776$	6.38861	+	3.07659i	0.229338	+	0.110443i
$777$		0			0
$778$	−2.39554	−	3.00392i	−0.0858844	−	0.107696i
$779$	19.8539	−	18.4218i	0.711341	−	0.660028i
$780$		0			0
$781$	−7.32633	+	12.6896i	−0.262157	+	0.454069i
$782$	−0.935556	−	4.09894i	−0.0334554	−	0.146578i
$783$		0			0
$784$	−26.0642	+	8.03973i	−0.930863	+	0.287133i
$785$	−1.53096	+	1.91976i	−0.0546423	+	0.0685193i
$786$		0			0
$787$	12.3410	+	3.80671i	0.439911	+	0.135695i	0.506796	−	0.862066i	$-0.330830\pi$
$787$	12.3410	+	3.80671i	0.439911	+	0.135695i	−0.0668849	+	0.997761i	$0.521306\pi$
$788$	−30.4414	+	20.7546i	−1.08443	+	0.739351i
$789$		0			0
$790$	0.625437	−	2.74022i	0.0222520	−	0.0974925i
$791$	−0.0484369	−	0.0449429i	−0.00172222	−	0.00159799i
$792$		0			0
$793$	3.59117	−	9.15016i	0.127526	−	0.324932i
$794$	−2.42968	−	0.366215i	−0.0862261	−	0.0129965i
$795$		0			0
$796$	−14.0919	+	6.78632i	−0.499476	+	0.240535i
$797$	34.6051	+	5.21589i	1.22578	+	0.184756i	0.729850	−	0.683608i	$-0.239590\pi$
$797$	34.6051	+	5.21589i	1.22578	+	0.184756i	0.495928	+	0.868364i	$0.334828\pi$
$798$		0			0
$799$	4.51983	−	60.3129i	0.159900	−	2.13372i
$800$	2.08989	+	1.93914i	0.0738889	+	0.0685588i
$801$		0			0
$802$	−0.688316	+	0.103747i	−0.0243053	+	0.00366343i
$803$	16.7743	−	11.4365i	0.591952	−	0.403586i
$804$		0			0
$805$	−0.0105734	−	0.141092i	−0.000372663	−	0.00497284i
$806$	−0.317453	+	0.398073i	−0.0111818	+	0.0140215i
$807$		0			0
$808$	0.597170	+	1.52156i	0.0210084	+	0.0535284i
$809$	−4.51483	−	19.7807i	−0.158733	−	0.695454i	−0.990174	−	0.139841i	$-0.955341\pi$
$809$	−4.51483	−	19.7807i	−0.158733	−	0.695454i	0.831441	−	0.555613i	$-0.187516\pi$
$810$		0			0
$811$	−3.52831	−	6.11121i	−0.123896	−	0.214593i	0.797405	−	0.603444i	$-0.206205\pi$
$811$	−3.52831	−	6.11121i	−0.123896	−	0.214593i	−0.921301	+	0.388851i	$0.872872\pi$
$812$	0.156318	−	0.145042i	0.00548568	−	0.00508997i
$813$		0			0
$814$	1.13824	+	0.776037i	0.0398952	+	0.0272001i
$815$	−5.24696	−	2.52680i	−0.183793	−	0.0885100i
$816$		0			0
$817$	−49.7876	−	4.45857i	−1.74185	−	0.155986i
$818$	0.801053			0.0280082
$819$		0			0
$820$	−10.3648	−	7.06657i	−0.361953	−	0.246775i
$821$	18.1800	+	22.7970i	0.634486	+	0.795621i	0.990301	−	0.138936i	$-0.0443681\pi$
$821$	18.1800	+	22.7970i	0.634486	+	0.795621i	−0.355815	+	0.934556i	$0.615797\pi$
$822$		0			0
$823$	24.5454	+	42.5140i	0.855600	+	1.48194i	0.876087	+	0.482153i	$0.160145\pi$
$823$	24.5454	+	42.5140i	0.855600	+	1.48194i	−0.0204864	+	0.999790i	$0.506521\pi$
$824$	−0.137966	+	0.238965i	−0.00480629	+	0.00832473i
$825$		0			0
$826$	0.00119908	+	0.00305520i	4.17212e−5	+	0.000106304i
$827$	−4.63646	+	1.43016i	−0.161225	+	0.0497314i	−0.374317	−	0.927301i	$-0.622123\pi$
$827$	−4.63646	+	1.43016i	−0.161225	+	0.0497314i	0.213092	+	0.977032i	$0.431647\pi$
$828$		0			0
$829$	2.29136	+	30.5761i	0.0795823	+	1.06195i	0.883876	+	0.467721i	$0.154925\pi$
$829$	2.29136	+	30.5761i	0.0795823	+	1.06195i	−0.804294	+	0.594231i	$0.797456\pi$
$830$	2.02764	+	0.625444i	0.0703804	+	0.0217095i
$831$		0			0
$832$	−12.1892	+	1.83723i	−0.422586	+	0.0636946i
$833$	9.39922	−	41.1807i	0.325664	−	1.42683i
$834$		0			0
$835$	0.461802	−	6.16232i	0.0159813	−	0.213256i
$836$	−11.4839	+	29.2606i	−0.397180	+	1.01200i
$837$		0			0
$838$	0.637624	−	0.307063i	0.0220263	−	0.0106073i
$839$	−28.7846	+	13.8619i	−0.993755	+	0.478567i	−0.858815	−	0.512286i	$-0.828799\pi$
$839$	−28.7846	+	13.8619i	−0.993755	+	0.478567i	−0.134941	+	0.990854i	$0.543084\pi$
$840$		0			0
$841$	8.22290	−	20.9516i	0.283548	−	0.722469i
$842$	0.351657	−	4.69254i	0.0121189	−	0.161716i
$843$		0			0
$844$	3.55503	−	15.5756i	0.122369	−	0.536134i
$845$	−18.2446	+	2.74994i	−0.627635	+	0.0946007i
$846$		0			0
$847$	−0.0955813	−	0.0294829i	−0.00328421	−	0.00101305i
$848$	1.99676	+	26.6449i	0.0685689	+	0.914989i
$849$		0			0
$850$	−1.38588	+	0.427488i	−0.0475354	+	0.0146627i
$851$	9.76444	+	24.8794i	0.334721	+	0.852854i
$852$		0			0
$853$	−12.0620	+	20.8920i	−0.412996	+	0.715330i	−0.995216	−	0.0977017i	$-0.968851\pi$
$853$	−12.0620	+	20.8920i	−0.412996	+	0.715330i	0.582220	+	0.813031i	$0.302184\pi$
$854$	0.00595804	+	0.0103196i	0.000203880	+	0.000353130i
$855$		0			0
$856$	0.370577	+	0.464688i	0.0126660	+	0.0158827i
$857$	−37.7821	−	25.7594i	−1.29061	−	0.879924i	−0.293506	−	0.955957i	$-0.594822\pi$
$857$	−37.7821	−	25.7594i	−1.29061	−	0.879924i	−0.997105	+	0.0760330i	$0.975775\pi$
$858$		0			0
$859$	−31.4601			−1.07341			−0.536703	−	0.843771i	$-0.680330\pi$
$859$	−31.4601			−1.07341			−0.536703	+	0.843771i	$0.680330\pi$
$860$	3.11808	+	22.9416i	0.106325	+	0.782301i
$861$		0			0
$862$	0.282734	+	0.136158i	0.00962997	+	0.00463755i
$863$	7.50021	+	5.11356i	0.255310	+	0.174068i	0.684211	−	0.729284i	$-0.260147\pi$
$863$	7.50021	+	5.11356i	0.255310	+	0.174068i	−0.428901	+	0.903352i	$0.641099\pi$
$864$		0			0
$865$	−22.0957	+	20.5018i	−0.751277	+	0.697083i
$866$	0.555406	+	0.961991i	0.0188735	+	0.0326898i
$867$		0			0
$868$	0.0157705	+	0.0690952i	0.000535287	+	0.00234525i
$869$	9.12641	+	23.2537i	0.309592	+	0.788828i
$870$		0			0
$871$	−1.45138	+	1.81997i	−0.0491781	+	0.0616674i
$872$	0.477167	+	6.36735i	0.0161589	+	0.215626i
$873$		0			0
$874$	4.38823	−	2.99184i	0.148434	−	0.101201i
$875$	−0.180199	+	0.0271606i	−0.00609183	+	0.000918196i
$876$		0			0
$877$	32.2254	+	29.9008i	1.08817	+	1.00968i	0.999908	+	0.0135802i	$0.00432285\pi$
$877$	32.2254	+	29.9008i	1.08817	+	1.00968i	0.0882654	+	0.996097i	$0.471868\pi$
$878$	0.0382969	−	0.511036i	0.00129246	−	0.0172466i
$879$		0			0
$880$	14.2700	+	2.15085i	0.481041	+	0.0725053i
$881$	18.7576	−	9.03321i	0.631961	−	0.304336i	−0.0903444	−	0.995911i	$-0.528797\pi$
$881$	18.7576	−	9.03321i	0.631961	−	0.304336i	0.722305	+	0.691574i	$0.243082\pi$
$882$		0			0
$883$	50.0003	+	7.53634i	1.68264	+	0.253618i	0.919636	−	0.392771i	$-0.128483\pi$
$883$	50.0003	+	7.53634i	1.68264	+	0.253618i	0.763008	+	0.646389i	$0.223721\pi$
$884$	7.10061	−	18.0921i	0.238819	−	0.608502i
$885$		0			0
$886$	2.43856	+	2.26266i	0.0819252	+	0.0760154i
$887$	−12.3944	+	54.3035i	−0.416164	+	1.82333i	0.137389	+	0.990517i	$0.456129\pi$
$887$	−12.3944	+	54.3035i	−0.416164	+	1.82333i	−0.553552	+	0.832814i	$0.686728\pi$
$888$		0			0
$889$	−0.111537	+	0.0760445i	−0.00374082	+	0.00255045i
$890$	−3.55627	−	1.09696i	−0.119206	−	0.0367703i
$891$		0			0
$892$	−25.1397	+	31.5242i	−0.841741	+	1.05551i
$893$	73.0087	−	22.5202i	2.44314	−	0.753610i
$894$		0			0
$895$	−3.73971	−	16.3847i	−0.125005	−	0.547682i
$896$	0.0308308	−	0.0534005i	0.00102998	−	0.00178398i
$897$		0			0
$898$	−3.44355	+	3.19514i	−0.114913	+	0.106623i
$899$	10.6734	+	13.3840i	0.355977	+	0.446381i
$900$		0			0
$901$	−37.2804	−	17.9533i	−1.24199	−	0.598111i
$902$	−0.970986			−0.0323303
$903$		0			0
$904$	−2.30763			−0.0767505
$905$	−11.8235	−	5.69392i	−0.393028	−	0.189272i
$906$		0			0
$907$	−26.2597	−	32.9286i	−0.871939	−	1.09338i	−0.994890	−	0.100964i	$-0.967807\pi$
$907$	−26.2597	−	32.9286i	−0.871939	−	1.09338i	0.122951	−	0.992413i	$-0.460764\pi$
$908$	−7.46127	+	6.92305i	−0.247611	+	0.229749i
$909$		0			0
$910$	−0.00284811	+	0.00493308i	−9.44140e−5	+	0.000163530i
$911$	−3.51500	−	15.4002i	−0.116457	−	0.510232i	−0.999186	−	0.0403485i	$-0.987153\pi$
$911$	−3.51500	−	15.4002i	−0.116457	−	0.510232i	0.882729	−	0.469883i	$-0.155704\pi$
$912$		0			0
$913$	−18.0211	+	5.55876i	−0.596410	+	0.183968i
$914$	1.55293	−	1.94732i	0.0513664	−	0.0644115i
$915$		0			0
$916$	5.42415	+	1.67313i	0.179219	+	0.0552817i
$917$	0.0565160	−	0.0385320i	0.00186632	−	0.00127244i
$918$		0			0
$919$	−6.32627	+	27.7172i	−0.208684	+	0.914306i	0.756759	+	0.653694i	$0.226782\pi$
$919$	−6.32627	+	27.7172i	−0.208684	+	0.914306i	−0.965444	+	0.260612i	$0.916076\pi$
$920$	−3.62224	−	3.36095i	−0.119422	−	0.110807i
$921$		0			0
$922$	−0.675958	+	1.72231i	−0.0222615	+	0.0567214i
$923$	11.3169	+	1.70575i	0.372501	+	0.0561455i
$924$		0			0
$925$	8.30658	−	4.00024i	0.273119	−	0.131527i
$926$	−2.43327	−	0.366756i	−0.0799621	−	0.0120523i
$927$		0			0
$928$	0.836010	−	11.1558i	0.0274434	−	0.366206i
$929$	−32.4893	−	30.1457i	−1.06594	−	0.989047i	−0.0659776	−	0.997821i	$-0.521017\pi$
$929$	−32.4893	−	30.1457i	−1.06594	−	0.989047i	−0.999962	+	0.00877413i	$0.997207\pi$
$930$		0			0
$931$	52.7628	−	7.95271i	1.72923	−	0.260640i
$932$	20.3430	−	13.8696i	0.666357	−	0.454315i
$933$		0			0
$934$	0.0211277	+	0.281930i	0.000691320	+	0.00922502i
$935$	−13.9339	+	17.4725i	−0.455686	+	0.571413i
$936$		0			0
$937$	11.1997	+	28.5364i	0.365879	+	0.932245i	0.988704	+	0.149883i	$0.0478897\pi$
$937$	11.1997	+	28.5364i	0.365879	+	0.932245i	−0.622825	+	0.782361i	$0.714015\pi$
$938$	−0.000627940	−	0.00275118i	−2.05030e−5	−	8.98293e-5i
$939$		0			0
$940$	−17.6939	−	30.6467i	−0.577110	−	0.999584i
$941$	−26.1851	+	24.2962i	−0.853609	+	0.792033i	−0.979802	−	0.199973i	$-0.935915\pi$
$941$	−26.1851	+	24.2962i	−0.853609	+	0.792033i	0.126193	+	0.992006i	$0.459724\pi$
$942$		0			0
$943$	−15.5647	−	10.6118i	−0.506856	−	0.345568i
$944$	−5.85144	−	2.81790i	−0.190448	−	0.0917150i
$945$		0			0
$946$	1.19973	+	1.33124i	0.0390066	+	0.0432823i
$947$	40.7779			1.32510			0.662552	−	0.749016i	$-0.269473\pi$
$947$	40.7779			1.32510			0.662552	+	0.749016i	$0.269473\pi$
$948$		0			0
$949$	−13.1019	−	8.93272i	−0.425306	−	0.289969i
$950$	−1.14229	−	1.43239i	−0.0370608	−	0.0464728i
$951$		0			0
$952$	0.0236635	+	0.0409865i	0.000766940	+	0.00132838i
$953$	−12.4281	+	21.5261i	−0.402586	+	0.697300i	−0.994037	−	0.109041i	$-0.965222\pi$
$953$	−12.4281	+	21.5261i	−0.402586	+	0.697300i	0.591451	+	0.806341i	$0.298555\pi$
$954$		0			0
$955$	12.5693	+	32.0261i	0.406734	+	1.03634i
$956$	−44.0949	+	13.6015i	−1.42613	+	0.439903i
$957$		0			0
$958$	−0.275925	−	3.68196i	−0.00891472	−	0.118959i
$959$	0.222748	+	0.0687086i	0.00719290	+	0.00221872i
$960$		0			0
$961$	25.0278	−	3.77233i	0.807348	−	0.121688i
$962$	0.239435	−	1.04903i	0.00771970	−	0.0338222i
$963$		0			0
$964$	−0.520894	+	6.95085i	−0.0167769	+	0.223872i
$965$	−1.37825	+	3.51172i	−0.0443674	+	0.113046i
$966$		0			0
$967$	11.2144	−	5.40056i	0.360630	−	0.173670i	−0.244791	−	0.969576i	$-0.578719\pi$
$967$	11.2144	−	5.40056i	0.360630	−	0.173670i	0.605421	+	0.795906i	$0.293005\pi$
$968$	−3.14733	+	1.51568i	−0.101159	+	0.0487157i
$969$		0			0
$970$	−1.15828	+	2.95125i	−0.0371901	+	0.0947588i
$971$	−2.26263	+	30.1927i	−0.0726113	+	0.968931i	0.835307	+	0.549784i	$0.185290\pi$
$971$	−2.26263	+	30.1927i	−0.0726113	+	0.968931i	−0.907918	+	0.419147i	$0.862329\pi$
$972$		0			0
$973$	0.0228733	−	0.100214i	0.000733283	−	0.00321272i
$974$	2.45517	−	0.370058i	0.0786688	−	0.0118574i
$975$		0			0
$976$	−22.5321	−	6.95023i	−0.721235	−	0.222472i
$977$	−2.68390	−	35.8142i	−0.0858656	−	1.14580i	−0.859145	−	0.511732i	$-0.829004\pi$
$977$	−2.68390	−	35.8142i	−0.0858656	−	1.14580i	0.773280	−	0.634065i	$-0.218615\pi$
$978$		0			0
$979$	31.6070	−	9.74947i	1.01016	−	0.311595i
$980$	−9.02914	−	23.0059i	−0.288425	−	0.734895i
$981$		0			0
$982$	−1.77707	+	3.07798i	−0.0567087	+	0.0982224i
$983$	24.1540	+	41.8359i	0.770392	+	1.33436i	0.937348	+	0.348394i	$0.113273\pi$
$983$	24.1540	+	41.8359i	0.770392	+	1.33436i	−0.166956	+	0.985964i	$0.553394\pi$
$984$		0			0
$985$	−20.6312	−	25.8707i	−0.657364	−	0.824308i
$986$	4.70213	+	3.20586i	0.149746	+	0.102095i
$987$		0			0
$988$	24.5517			0.781094
$989$	4.68239	+	34.4512i	0.148891	+	1.09548i
$990$		0			0
$991$	10.0373	+	4.83373i	0.318847	+	0.153548i	0.586461	−	0.809978i	$-0.300521\pi$
$991$	10.0373	+	4.83373i	0.318847	+	0.153548i	−0.267614	+	0.963526i	$0.586235\pi$
$992$	3.07202	+	2.09446i	0.0975366	+	0.0664993i
$993$		0			0
$994$	−0.0101704	+	0.00943672i	−0.000322585	+	0.000299315i
$995$	−7.02371	−	12.1654i	−0.222667	−	0.385670i
$996$		0			0
$997$	8.80699	+	38.5859i	0.278920	+	1.22203i	0.899161	+	0.437618i	$0.144178\pi$
$997$	8.80699	+	38.5859i	0.278920	+	1.22203i	−0.620241	+	0.784411i	$0.712965\pi$
$998$	0.340872	+	0.868528i	0.0107901	+	0.0274928i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	387.2.y.c.154.2		36
3.2	odd	2		43.2.g.a.25.2	✓	36
12.11	even	2		688.2.bg.c.369.1		36
43.31	even	21	inner	387.2.y.c.289.2		36
129.17	odd	42		1849.2.a.n.1.10		18
129.26	even	42		1849.2.a.o.1.9		18
129.74	odd	42		43.2.g.a.31.2	yes	36
516.203	even	42		688.2.bg.c.289.1		36

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
43.2.g.a.25.2	✓	36	3.2	odd	2
43.2.g.a.31.2	yes	36	129.74	odd	42
387.2.y.c.154.2		36	1.1	even	1	trivial
387.2.y.c.289.2		36	43.31	even	21	inner
688.2.bg.c.289.1		36	516.203	even	42
688.2.bg.c.369.1		36	12.11	even	2
1849.2.a.n.1.10		18	129.17	odd	42
1849.2.a.o.1.9		18	129.26	even	42

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:	\( N \)	\(=\)	\( 387 = 3^{2} \cdot 43 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	387.y (of order \(21\), degree \(12\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.118393 - 0.0570152i) q^{2} +(-1.23621 - 1.55016i) q^{4} +(1.30537 - 1.21121i) q^{5} +(-0.00749281 + 0.0129779i) q^{7} +(0.116458 + 0.510236i) q^{8} +O(q^{10})\)	\(q+(-0.118393 - 0.0570152i) q^{2} +(-1.23621 - 1.55016i) q^{4} +(1.30537 - 1.21121i) q^{5} +(-0.00749281 + 0.0129779i) q^{7} +(0.116458 + 0.510236i) q^{8} +(-0.223604 + 0.0689728i) q^{10} +(1.29669 - 1.62599i) q^{11} +(-1.55224 - 0.478804i) q^{13} +(0.00162704 - 0.00110929i) q^{14} +(-0.867096 + 3.79899i) q^{16} +(-4.42356 - 4.10446i) q^{17} +(2.78497 - 7.09598i) q^{19} +(-3.49129 - 0.526227i) q^{20} +(-0.246225 + 0.118576i) q^{22} +(-5.24284 - 0.790231i) q^{23} +(-0.136680 + 1.82386i) q^{25} +(0.156476 + 0.145189i) q^{26} +(0.0293806 - 0.00442841i) q^{28} +(5.92981 - 4.04287i) q^{29} +(0.178251 + 2.37860i) q^{31} +(0.971874 - 1.21869i) q^{32} +(0.289703 + 0.738150i) q^{34} +(0.00593807 + 0.0260164i) q^{35} +(-2.52043 - 4.36551i) q^{37} +(-0.734300 + 0.681331i) q^{38} +(0.770022 + 0.524992i) q^{40} +(3.20110 + 1.54157i) q^{41} +(-1.84169 - 6.29350i) q^{43} -4.12354 q^{44} +(0.575662 + 0.392479i) q^{46} +(6.24911 + 7.83614i) q^{47} +(3.49989 + 6.06198i) q^{49} +(0.120170 - 0.208140i) q^{50} +(1.17668 + 2.99813i) q^{52} +(6.55236 - 2.02113i) q^{53} +(-0.276759 - 3.69309i) q^{55} +(-0.00749439 - 0.00231171i) q^{56} +(-0.932554 + 0.140560i) q^{58} +(-0.370875 + 1.62491i) q^{59} +(-0.452207 + 6.03428i) q^{61} +(0.114512 - 0.291773i) q^{62} +(6.83705 - 3.29255i) q^{64} +(-2.60619 + 1.25507i) q^{65} +(0.523545 - 1.33397i) q^{67} +(-0.894122 + 11.9312i) q^{68} +(0.000780301 - 0.00341872i) q^{70} +(-6.96679 + 1.05007i) q^{71} +(9.32817 + 2.87736i) q^{73} +(0.0495013 + 0.660549i) q^{74} +(-14.4427 + 4.45500i) q^{76} +(0.0113862 + 0.0290116i) q^{77} +(-6.00573 + 10.4022i) q^{79} +(3.46949 + 6.00933i) q^{80} +(-0.291096 - 0.365023i) q^{82} +(-7.49232 - 5.10817i) q^{83} -10.7457 q^{85} +(-0.140781 + 0.850113i) q^{86} +(0.980650 + 0.472256i) q^{88} +(13.1407 + 8.95920i) q^{89} +(0.0178445 - 0.0165573i) q^{91} +(5.25628 + 9.10415i) q^{92} +(-0.293074 - 1.28404i) q^{94} +(-4.95929 - 12.6361i) q^{95} +(8.44749 - 10.5928i) q^{97} +(-0.0687380 - 0.917245i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 36 q + 10 q^{2} - 18 q^{4} + 17 q^{5} + 6 q^{7} - 18 q^{8}+O(q^{10}) \) 36 * q + 10 * q^2 - 18 * q^4 + 17 * q^5 + 6 * q^7 - 18 * q^8	\( 36 q + 10 q^{2} - 18 q^{4} + 17 q^{5} + 6 q^{7} - 18 q^{8} - 7 q^{10} + 4 q^{11} - 18 q^{14} - 10 q^{16} + 10 q^{17} + 10 q^{19} + 3 q^{20} - 3 q^{22} - 4 q^{23} - 2 q^{25} + 15 q^{26} + 20 q^{28} - 9 q^{29} + 40 q^{31} - 48 q^{32} - 42 q^{34} - 11 q^{35} - 19 q^{37} + 21 q^{38} - 97 q^{40} + 28 q^{41} - 8 q^{43} - 14 q^{44} - 61 q^{46} + 30 q^{47} + 6 q^{49} + 3 q^{50} - 8 q^{52} + 24 q^{53} + 14 q^{55} - 39 q^{56} + 64 q^{58} + q^{59} - 14 q^{61} - 33 q^{62} + 48 q^{64} - 38 q^{65} + 66 q^{67} - 66 q^{68} + 47 q^{70} + 33 q^{71} + 29 q^{73} + 40 q^{74} - 39 q^{76} + 27 q^{77} - 17 q^{79} - 8 q^{80} - 54 q^{82} + 23 q^{83} - 56 q^{85} + 45 q^{86} - 17 q^{88} + 19 q^{89} - 13 q^{91} + 18 q^{92} + 44 q^{94} - q^{95} - 31 q^{97} + 5 q^{98}+O(q^{100}) \) 36 * q + 10 * q^2 - 18 * q^4 + 17 * q^5 + 6 * q^7 - 18 * q^8 - 7 * q^10 + 4 * q^11 - 18 * q^14 - 10 * q^16 + 10 * q^17 + 10 * q^19 + 3 * q^20 - 3 * q^22 - 4 * q^23 - 2 * q^25 + 15 * q^26 + 20 * q^28 - 9 * q^29 + 40 * q^31 - 48 * q^32 - 42 * q^34 - 11 * q^35 - 19 * q^37 + 21 * q^38 - 97 * q^40 + 28 * q^41 - 8 * q^43 - 14 * q^44 - 61 * q^46 + 30 * q^47 + 6 * q^49 + 3 * q^50 - 8 * q^52 + 24 * q^53 + 14 * q^55 - 39 * q^56 + 64 * q^58 + q^59 - 14 * q^61 - 33 * q^62 + 48 * q^64 - 38 * q^65 + 66 * q^67 - 66 * q^68 + 47 * q^70 + 33 * q^71 + 29 * q^73 + 40 * q^74 - 39 * q^76 + 27 * q^77 - 17 * q^79 - 8 * q^80 - 54 * q^82 + 23 * q^83 - 56 * q^85 + 45 * q^86 - 17 * q^88 + 19 * q^89 - 13 * q^91 + 18 * q^92 + 44 * q^94 - q^95 - 31 * q^97 + 5 * q^98

Introduction

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