LMFDB - Embedded newform 648.2.f.c.323.10

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [648,2,Mod(323,648)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(648, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("648.323");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 648 = 2^{3} \cdot 3^{4} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	648.f (of order $2$, degree $1$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$5.17430605098$
Analytic rank:	$0$
Dimension:	$24$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			323.10
Character	$\chi$	$=$	648.323
Dual form			648.2.f.c.323.9

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.537150 + 1.30823i) q^{2} +(-1.42294 - 1.40543i) q^{4} -0.949666 q^{5} +4.71000i q^{7} +(2.60297 - 1.10660i) q^{8} +O(q^{10})$	\(q+(-0.537150 + 1.30823i) q^{2} +(-1.42294 - 1.40543i) q^{4} -0.949666 q^{5} +4.71000i q^{7} +(2.60297 - 1.10660i) q^{8} +(0.510114 - 1.24238i) q^{10} -4.29556i q^{11} +4.06857i q^{13} +(-6.16177 - 2.52998i) q^{14} +(0.0495098 + 3.99969i) q^{16} +1.19178i q^{17} -3.17693 q^{19} +(1.35132 + 1.33469i) q^{20} +(5.61959 + 2.30736i) q^{22} +0.750651 q^{23} -4.09813 q^{25} +(-5.32263 - 2.18544i) q^{26} +(6.61959 - 6.70204i) q^{28} -7.74362 q^{29} -0.573791i q^{31} +(-5.25912 - 2.08367i) q^{32} +(-1.55912 - 0.640165i) q^{34} -4.47293i q^{35} -4.87320i q^{37} +(1.70649 - 4.15616i) q^{38} +(-2.47195 + 1.05090i) q^{40} +9.75877i q^{41} -5.31540 q^{43} +(-6.03713 + 6.11233i) q^{44} +(-0.403212 + 0.982025i) q^{46} -9.82024 q^{47} -15.1841 q^{49} +(2.20131 - 5.36131i) q^{50} +(5.71811 - 5.78933i) q^{52} +0.877682 q^{53} +4.07935i q^{55} +(5.21210 + 12.2600i) q^{56} +(4.15949 - 10.1304i) q^{58} -1.75441i q^{59} +9.92114i q^{61} +(0.750651 + 0.308212i) q^{62} +(5.55086 - 5.76090i) q^{64} -3.86379i q^{65} +10.9667 q^{67} +(1.67497 - 1.69583i) q^{68} +(5.85162 + 2.40263i) q^{70} -9.91048 q^{71} +8.74944 q^{73} +(6.37527 + 2.61764i) q^{74} +(4.52057 + 4.46496i) q^{76} +20.2321 q^{77} -5.74545i q^{79} +(-0.0470178 - 3.79837i) q^{80} +(-12.7667 - 5.24193i) q^{82} -12.5035i q^{83} -1.13179i q^{85} +(2.85517 - 6.95377i) q^{86} +(-4.75349 - 11.1812i) q^{88} +10.1440i q^{89} -19.1630 q^{91} +(-1.06813 - 1.05499i) q^{92} +(5.27494 - 12.8471i) q^{94} +3.01702 q^{95} +7.83023 q^{97} +(8.15614 - 19.8643i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q+O(q^{10}) $ 24 * q	$ 24 q + 12 q^{16} - 12 q^{22} + 24 q^{25} + 12 q^{28} - 24 q^{34} - 24 q^{40} - 12 q^{46} - 24 q^{49} - 12 q^{58} + 24 q^{64} + 48 q^{67} - 36 q^{70} - 60 q^{76} - 36 q^{82} - 60 q^{88} + 48 q^{94}+O(q^{100}) $ 24 * q + 12 * q^16 - 12 * q^22 + 24 * q^25 + 12 * q^28 - 24 * q^34 - 24 * q^40 - 12 * q^46 - 24 * q^49 - 12 * q^58 + 24 * q^64 + 48 * q^67 - 36 * q^70 - 60 * q^76 - 36 * q^82 - 60 * q^88 + 48 * q^94

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/648\mathbb{Z}\right)^\times$.

$n$	$325$	$487$	$569$
$\chi(n)$	$-1$	$-1$	$-1$

Coefficient data

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

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

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

$2$	−0.537150	+	1.30823i	−0.379823	+	0.925059i
$2$	−0.537150	+	1.30823i	−0.379823	+	0.925059i
$3$		0			0
$3$		0			0
$4$	−1.42294	−	1.40543i	−0.711469	−	0.702717i
$5$	−0.949666			−0.424704			−0.212352	−	0.977193i	$-0.568112\pi$
$5$	−0.949666			−0.424704			−0.212352	+	0.977193i	$0.568112\pi$
$6$		0			0
$7$			4.71000i			1.78021i	0.455754	+	0.890106i	$0.349370\pi$
$7$			4.71000i			1.78021i	−0.455754	+	0.890106i	$0.650630\pi$
$8$	2.60297	−	1.10660i	0.920287	−	0.391243i
$9$		0			0
$10$	0.510114	−	1.24238i	0.161312	−	0.392876i
$11$		−	4.29556i		−	1.29516i	−0.761997	−	0.647581i	$-0.775781\pi$
$11$		−	4.29556i		−	1.29516i	0.761997	−	0.647581i	$-0.224219\pi$
$12$		0			0
$13$			4.06857i			1.12842i	0.825632	+	0.564210i	$0.190819\pi$
$13$			4.06857i			1.12842i	−0.825632	+	0.564210i	$0.809181\pi$
$14$	−6.16177	−	2.52998i	−1.64680	−	0.676165i
$15$		0			0
$16$	0.0495098	+	3.99969i	0.0123774	+	0.999923i
$17$			1.19178i			0.289049i	0.989501	+	0.144524i	$0.0461652\pi$
$17$			1.19178i			0.289049i	−0.989501	+	0.144524i	$0.953835\pi$
$18$		0			0
$19$	−3.17693			−0.728837			−0.364418	−	0.931235i	$-0.618732\pi$
$19$	−3.17693			−0.728837			−0.364418	+	0.931235i	$0.618732\pi$
$20$	1.35132	+	1.33469i	0.302164	+	0.298446i
$21$		0			0
$22$	5.61959	+	2.30736i	1.19810	+	0.491932i
$23$	0.750651			0.156522			0.0782608	−	0.996933i	$-0.475063\pi$
$23$	0.750651			0.156522			0.0782608	+	0.996933i	$0.475063\pi$
$24$		0			0
$25$	−4.09813			−0.819627
$26$	−5.32263	−	2.18544i	−1.04385	−	0.428599i
$27$		0			0
$28$	6.61959	−	6.70204i	1.25099	−	1.26657i
$29$	−7.74362			−1.43795			−0.718977	−	0.695034i	$-0.755389\pi$
$29$	−7.74362			−1.43795			−0.718977	+	0.695034i	$0.755389\pi$
$30$		0			0
$31$		−	0.573791i		−	0.103056i	−0.998672	−	0.0515279i	$-0.983591\pi$
$31$		−	0.573791i		−	0.103056i	0.998672	−	0.0515279i	$-0.0164091\pi$
$32$	−5.25912	−	2.08367i	−0.929690	−	0.368344i
$33$		0			0
$34$	−1.55912	−	0.640165i	−0.267387	−	0.109787i
$35$		−	4.47293i		−	0.756062i
$36$		0			0
$37$		−	4.87320i		−	0.801148i	−0.916264	−	0.400574i	$-0.868811\pi$
$37$		−	4.87320i		−	0.801148i	0.916264	−	0.400574i	$-0.131189\pi$
$38$	1.70649	−	4.15616i	0.276829	−	0.674217i
$39$		0			0
$40$	−2.47195	+	1.05090i	−0.390849	+	0.166163i
$41$			9.75877i			1.52406i	0.647539	+	0.762032i	$0.275798\pi$
$41$			9.75877i			1.52406i	−0.647539	+	0.762032i	$0.724202\pi$
$42$		0			0
$43$	−5.31540			−0.810591			−0.405295	−	0.914186i	$-0.632831\pi$
$43$	−5.31540			−0.810591			−0.405295	+	0.914186i	$0.632831\pi$
$44$	−6.03713	+	6.11233i	−0.910132	+	0.921468i
$45$		0			0
$46$	−0.403212	+	0.982025i	−0.0594504	+	0.144792i
$47$	−9.82024			−1.43243			−0.716214	−	0.697880i	$-0.754127\pi$
$47$	−9.82024			−1.43243			−0.716214	+	0.697880i	$0.754127\pi$
$48$		0			0
$49$	−15.1841			−2.16915
$50$	2.20131	−	5.36131i	0.311313	−	0.758203i
$51$		0			0
$52$	5.71811	−	5.78933i	0.792959	−	0.802836i
$53$	0.877682			0.120559			0.0602794	−	0.998182i	$-0.480801\pi$
$53$	0.877682			0.120559			0.0602794	+	0.998182i	$0.480801\pi$
$54$		0			0
$55$			4.07935i			0.550060i
$56$	5.21210	+	12.2600i	0.696496	+	1.63831i
$57$		0			0
$58$	4.15949	−	10.1304i	0.546168	−	1.33019i
$59$		−	1.75441i		−	0.228405i	−0.993458	−	0.114202i	$-0.963569\pi$
$59$		−	1.75441i		−	0.228405i	0.993458	−	0.114202i	$-0.0364312\pi$
$60$		0			0
$61$			9.92114i			1.27027i	0.772400	+	0.635136i	$0.219056\pi$
$61$			9.92114i			1.27027i	−0.772400	+	0.635136i	$0.780944\pi$
$62$	0.750651	+	0.308212i	0.0953328	+	0.0391429i
$63$		0			0
$64$	5.55086	−	5.76090i	0.693857	−	0.720113i
$65$		−	3.86379i		−	0.479244i
$66$		0			0
$67$	10.9667			1.33980			0.669898	−	0.742453i	$-0.266338\pi$
$67$	10.9667			1.33980			0.669898	+	0.742453i	$0.266338\pi$
$68$	1.67497	−	1.69583i	0.203120	−	0.205649i
$69$		0			0
$70$	5.85162	+	2.40263i	0.699403	+	0.287170i
$71$	−9.91048			−1.17616			−0.588079	−	0.808804i	$-0.700116\pi$
$71$	−9.91048			−1.17616			−0.588079	+	0.808804i	$0.700116\pi$
$72$		0			0
$73$	8.74944			1.02404			0.512022	−	0.858972i	$-0.328897\pi$
$73$	8.74944			1.02404			0.512022	+	0.858972i	$0.328897\pi$
$74$	6.37527	+	2.61764i	0.741110	+	0.304294i
$75$		0			0
$76$	4.52057	+	4.46496i	0.518545	+	0.512166i
$77$	20.2321			2.30566
$78$		0			0
$79$		−	5.74545i		−	0.646414i	−0.946328	−	0.323207i	$-0.895239\pi$
$79$		−	5.74545i		−	0.646414i	0.946328	−	0.323207i	$-0.104761\pi$
$80$	−0.0470178	−	3.79837i	−0.00525675	−	0.424671i
$81$		0			0
$82$	−12.7667	−	5.24193i	−1.40985	−	0.578874i
$83$		−	12.5035i		−	1.37243i	−0.727397	−	0.686217i	$-0.759270\pi$
$83$		−	12.5035i		−	1.37243i	0.727397	−	0.686217i	$-0.240730\pi$
$84$		0			0
$85$		−	1.13179i		−	0.122760i
$86$	2.85517	−	6.95377i	0.307881	−	0.749845i
$87$		0			0
$88$	−4.75349	−	11.1812i	−0.506723	−	1.19192i
$89$			10.1440i			1.07527i	0.843179	+	0.537633i	$0.180681\pi$
$89$			10.1440i			1.07527i	−0.843179	+	0.537633i	$0.819319\pi$
$90$		0			0
$91$	−19.1630			−2.00882
$92$	−1.06813	−	1.05499i	−0.111360	−	0.109990i
$93$		0			0
$94$	5.27494	−	12.8471i	0.544069	−	1.32508i
$95$	3.01702			0.309540
$96$		0			0
$97$	7.83023			0.795039			0.397520	−	0.917594i	$-0.369871\pi$
$97$	7.83023			0.795039			0.397520	+	0.917594i	$0.369871\pi$
$98$	8.15614	−	19.8643i	0.823894	−	2.00660i
$99$		0			0
$100$	5.83139	+	5.75966i	0.583139	+	0.575966i
$101$	17.8531			1.77645			0.888226	−	0.459407i	$-0.151938\pi$
$101$	17.8531			1.77645			0.888226	+	0.459407i	$0.151938\pi$
$102$		0			0
$103$			2.45412i			0.241812i	0.992664	+	0.120906i	$0.0385800\pi$
$103$			2.45412i			0.241812i	−0.992664	+	0.120906i	$0.961420\pi$
$104$	4.50230	+	10.5904i	0.441487	+	1.03847i
$105$		0			0
$106$	−0.471447	+	1.14821i	−0.0457910	+	0.111524i
$107$		−	0.283208i		−	0.0273788i	−0.999906	−	0.0136894i	$-0.995642\pi$
$107$		−	0.283208i		−	0.0273788i	0.999906	−	0.0136894i	$-0.00435760\pi$
$108$		0			0
$109$			9.74716i			0.933609i	0.884361	+	0.466805i	$0.154595\pi$
$109$			9.74716i			0.933609i	−0.884361	+	0.466805i	$0.845405\pi$
$110$	−5.33674	−	2.19123i	−0.508838	−	0.208925i
$111$		0			0
$112$	−18.8385	+	0.233191i	−1.78008	+	0.0220345i
$113$			4.72734i			0.444711i	0.974966	+	0.222356i	$0.0713746\pi$
$113$			4.72734i			0.444711i	−0.974966	+	0.222356i	$0.928625\pi$
$114$		0			0
$115$	−0.712868			−0.0664753
$116$	11.0187	+	10.8831i	1.02306	+	1.01047i
$117$		0			0
$118$	2.29517	+	0.942381i	0.211288	+	0.0867532i
$119$	−5.61328			−0.514568
$120$		0			0
$121$	−7.45187			−0.677443
$122$	−12.9791	−	5.32915i	−1.17508	−	0.482478i
$123$		0			0
$124$	−0.806425	+	0.816469i	−0.0724191	+	0.0733211i
$125$	8.64019			0.772802
$126$		0			0
$127$			13.8042i			1.22492i	0.790500	+	0.612462i	$0.209821\pi$
$127$			13.8042i			1.22492i	−0.790500	+	0.612462i	$0.790179\pi$
$128$	4.55495	+	10.3563i	0.402604	+	0.915374i
$129$		0			0
$130$	5.05473	+	2.07543i	0.443329	+	0.182028i
$131$			4.73463i			0.413666i	0.978376	+	0.206833i	$0.0663157\pi$
$131$			4.73463i			0.413666i	−0.978376	+	0.206833i	$0.933684\pi$
$132$		0			0
$133$		−	14.9633i		−	1.29748i
$134$	−5.89077	+	14.3470i	−0.508885	+	1.23939i
$135$		0			0
$136$	1.31883	+	3.10216i	0.113088	+	0.266008i
$137$			15.5543i			1.32890i	0.747334	+	0.664448i	$0.231333\pi$
$137$			15.5543i			1.32890i	−0.747334	+	0.664448i	$0.768667\pi$
$138$		0			0
$139$	7.88979			0.669204			0.334602	−	0.942360i	$-0.391398\pi$
$139$	7.88979			0.669204			0.334602	+	0.942360i	$0.391398\pi$
$140$	−6.28640	+	6.36470i	−0.531298	+	0.537915i
$141$		0			0
$142$	5.32342	−	12.9652i	0.446731	−	1.08802i
$143$	17.4768			1.46148
$144$		0			0
$145$	7.35385			0.610704
$146$	−4.69976	+	11.4463i	−0.388955	+	0.947301i
$147$		0			0
$148$	−6.84896	+	6.93426i	−0.562981	+	0.569993i
$149$	−16.0069			−1.31133			−0.655667	−	0.755050i	$-0.727613\pi$
$149$	−16.0069			−1.31133			−0.655667	+	0.755050i	$0.727613\pi$
$150$		0			0
$151$		−	1.82348i		−	0.148392i	−0.997244	−	0.0741962i	$-0.976361\pi$
$151$		−	1.82348i		−	0.148392i	0.997244	−	0.0741962i	$-0.0236391\pi$
$152$	−8.26943	+	3.51560i	−0.670739	+	0.285153i
$153$		0			0
$154$	−10.8677	+	26.4683i	−0.875743	+	2.13287i
$155$			0.544909i			0.0437682i
$156$		0			0
$157$			20.4887i			1.63518i	0.575802	+	0.817589i	$0.304690\pi$
$157$			20.4887i			1.63518i	−0.575802	+	0.817589i	$0.695310\pi$
$158$	7.51638	+	3.08617i	0.597971	+	0.245523i
$159$		0			0
$160$	4.99441	+	1.97879i	0.394843	+	0.156437i
$161$			3.53556i			0.278641i
$162$		0			0
$163$	−7.59374			−0.594787			−0.297394	−	0.954755i	$-0.596117\pi$
$163$	−7.59374			−0.594787			−0.297394	+	0.954755i	$0.596117\pi$
$164$	13.7153	−	13.8861i	1.07099	−	1.08433i
$165$		0			0
$166$	16.3574	+	6.71624i	1.26958	+	0.521282i
$167$	−5.61328			−0.434368			−0.217184	−	0.976131i	$-0.569687\pi$
$167$	−5.61328			−0.434368			−0.217184	+	0.976131i	$0.569687\pi$
$168$		0			0
$169$	−3.55328			−0.273329
$170$	1.48065	+	0.607943i	0.113560	+	0.0466271i
$171$		0			0
$172$	7.56349	+	7.47044i	0.576711	+	0.569616i
$173$	−12.6324			−0.960427			−0.480214	−	0.877152i	$-0.659441\pi$
$173$	−12.6324			−0.960427			−0.480214	+	0.877152i	$0.659441\pi$
$174$		0			0
$175$		−	19.3022i		−	1.45911i
$176$	17.1809	−	0.212672i	1.29506	−	0.0160308i
$177$		0			0
$178$	−13.2708	−	5.44888i	−0.994685	−	0.408411i
$179$		−	20.5282i		−	1.53435i	−0.641439	−	0.767174i	$-0.721662\pi$
$179$		−	20.5282i		−	1.53435i	0.641439	−	0.767174i	$-0.278338\pi$
$180$		0			0
$181$		−	9.96062i		−	0.740367i	−0.928959	−	0.370184i	$-0.879295\pi$
$181$		−	9.96062i		−	0.740367i	0.928959	−	0.370184i	$-0.120705\pi$
$182$	10.2934	−	25.0696i	0.762997	−	1.85828i
$183$		0			0
$184$	1.95392	−	0.830673i	0.144045	−	0.0612380i
$185$			4.62791i			0.340251i
$186$		0			0
$187$	5.11936			0.374365
$188$	13.9736	+	13.8017i	1.01913	+	1.00659i
$189$		0			0
$190$	−1.62059	+	3.94696i	−0.117570	+	0.286343i
$191$	22.9998			1.66421			0.832105	−	0.554618i	$-0.187135\pi$
$191$	22.9998			1.66421			0.832105	+	0.554618i	$0.187135\pi$
$192$		0			0
$193$	−1.00000			−0.0719816			−0.0359908	−	0.999352i	$-0.511459\pi$
$193$	−1.00000			−0.0719816			−0.0359908	+	0.999352i	$0.511459\pi$
$194$	−4.20601	+	10.2437i	−0.301974	+	0.735458i
$195$		0			0
$196$	21.6060	+	21.3402i	1.54329	+	1.52430i
$197$	0.519639			0.0370228			0.0185114	−	0.999829i	$-0.494107\pi$
$197$	0.519639			0.0370228			0.0185114	+	0.999829i	$0.494107\pi$
$198$		0			0
$199$		−	0.630646i		−	0.0447053i	−0.999750	−	0.0223527i	$-0.992884\pi$
$199$		−	0.630646i		−	0.0447053i	0.999750	−	0.0223527i	$-0.00711567\pi$
$200$	−10.6673	+	4.53501i	−0.754292	+	0.320674i
$201$		0			0
$202$	−9.58981	+	23.3560i	−0.674737	+	1.64332i
$203$		−	36.4724i		−	2.55986i
$204$		0			0
$205$		−	9.26758i		−	0.647276i
$206$	−3.21056	−	1.31823i	−0.223690	−	0.0918457i
$207$		0			0
$208$	−16.2730	+	0.201434i	−1.12833	+	0.0139669i
$209$			13.6467i			0.943961i
$210$		0			0
$211$	9.91793			0.682778			0.341389	−	0.939922i	$-0.389103\pi$
$211$	9.91793			0.682778			0.341389	+	0.939922i	$0.389103\pi$
$212$	−1.24889	−	1.23352i	−0.0857739	−	0.0847188i
$213$		0			0
$214$	0.370502	+	0.152125i	0.0253270	+	0.0103991i
$215$	5.04785			0.344261
$216$		0			0
$217$	2.70255			0.183461
$218$	−12.7515	−	5.23569i	−0.863644	−	0.354606i
$219$		0			0
$220$	5.73326	−	5.80467i	0.386536	−	0.391351i
$221$	−4.84884			−0.326168
$222$		0			0
$223$			7.10727i			0.475938i	0.971273	+	0.237969i	$0.0764816\pi$
$223$			7.10727i			0.475938i	−0.971273	+	0.237969i	$0.923518\pi$
$224$	9.81407	−	24.7704i	0.655730	−	1.65504i
$225$		0			0
$226$	−6.18446	−	2.53929i	−0.411384	−	0.168911i
$227$			12.4621i			0.827138i	0.910473	+	0.413569i	$0.135718\pi$
$227$			12.4621i			0.827138i	−0.910473	+	0.413569i	$0.864282\pi$
$228$		0			0
$229$		−	9.76872i		−	0.645535i	−0.946478	−	0.322768i	$-0.895387\pi$
$229$		−	9.76872i		−	0.645535i	0.946478	−	0.322768i	$-0.104613\pi$
$230$	0.382917	−	0.932596i	0.0252488	−	0.0614935i
$231$		0			0
$232$	−20.1564	+	8.56912i	−1.32333	+	0.562590i
$233$			4.66388i			0.305541i	0.988262	+	0.152771i	$0.0488196\pi$
$233$			4.66388i			0.305541i	−0.988262	+	0.152771i	$0.951180\pi$
$234$		0			0
$235$	9.32595			0.608358
$236$	−2.46571	+	2.49642i	−0.160504	+	0.162503i
$237$		0			0
$238$	3.01517	−	7.34346i	0.195445	−	0.476006i
$239$	−3.42532			−0.221565			−0.110783	−	0.993845i	$-0.535336\pi$
$239$	−3.42532			−0.221565			−0.110783	+	0.993845i	$0.535336\pi$
$240$		0			0
$241$	1.25572			0.0808880			0.0404440	−	0.999182i	$-0.487123\pi$
$241$	1.25572			0.0808880			0.0404440	+	0.999182i	$0.487123\pi$
$242$	4.00278	−	9.74877i	0.257308	−	0.626675i
$243$		0			0
$244$	13.9435	−	14.1172i	0.892642	−	0.903760i
$245$	14.4198			0.921248
$246$		0			0
$247$		−	12.9256i		−	0.822434i
$248$	−0.634959	−	1.49356i	−0.0403199	−	0.0948410i
$249$		0			0
$250$	−4.64108	+	11.3034i	−0.293528	+	0.714888i
$251$			20.2340i			1.27716i	0.769556	+	0.638579i	$0.220477\pi$
$251$			20.2340i			1.27716i	−0.769556	+	0.638579i	$0.779523\pi$
$252$		0			0
$253$		−	3.22447i		−	0.202721i
$254$	−18.0591	−	7.41492i	−1.13313	−	0.465254i
$255$		0			0
$256$	−15.9951	+	0.396048i	−0.999694	+	0.0247530i
$257$		−	1.17614i		−	0.0733655i	−0.999327	−	0.0366828i	$-0.988321\pi$
$257$		−	1.17614i		−	0.0733655i	0.999327	−	0.0366828i	$-0.0116791\pi$
$258$		0			0
$259$	22.9527			1.42621
$260$	−5.43030	+	5.49793i	−0.336773	+	0.340967i
$261$		0			0
$262$	−6.19399	−	2.54321i	−0.382666	−	0.157120i
$263$	7.02434			0.433139			0.216570	−	0.976267i	$-0.430513\pi$
$263$	7.02434			0.433139			0.216570	+	0.976267i	$0.430513\pi$
$264$		0			0
$265$	−0.833505			−0.0512018
$266$	19.5755	+	8.03755i	1.20025	+	0.492814i
$267$		0			0
$268$	−15.6049	−	15.4130i	−0.953224	−	0.941497i
$269$	−11.4172			−0.696119			−0.348060	−	0.937472i	$-0.613159\pi$
$269$	−11.4172			−0.696119			−0.348060	+	0.937472i	$0.613159\pi$
$270$		0			0
$271$		−	10.9905i		−	0.667625i	−0.942639	−	0.333813i	$-0.891665\pi$
$271$		−	10.9905i		−	0.667625i	0.942639	−	0.333813i	$-0.108335\pi$
$272$	−4.76675	+	0.0590047i	−0.289027	+	0.00357769i
$273$		0			0
$274$	−20.3487	−	8.35501i	−1.22931	−	0.504745i
$275$			17.6038i			1.06155i
$276$		0			0
$277$			3.60170i			0.216405i	0.994129	+	0.108203i	$0.0345096\pi$
$277$			3.60170i			0.216405i	−0.994129	+	0.108203i	$0.965490\pi$
$278$	−4.23801	+	10.3217i	−0.254179	+	0.619053i
$279$		0			0
$280$	−4.94976	−	11.6429i	−0.295804	−	0.695795i
$281$		−	12.2741i		−	0.732209i	−0.930574	−	0.366104i	$-0.880691\pi$
$281$		−	12.2741i		−	0.732209i	0.930574	−	0.366104i	$-0.119309\pi$
$282$		0			0
$283$	−2.54474			−0.151269			−0.0756344	−	0.997136i	$-0.524098\pi$
$283$	−2.54474			−0.151269			−0.0756344	+	0.997136i	$0.524098\pi$
$284$	14.1020	+	13.9285i	0.836800	+	0.826506i
$285$		0			0
$286$	−9.38768	+	22.8637i	−0.555105	+	1.35196i
$287$	−45.9638			−2.71316
$288$		0			0
$289$	15.5797			0.916451
$290$	−3.95013	+	9.62054i	−0.231959	+	0.564938i
$291$		0			0
$292$	−12.4499	−	12.2968i	−0.728576	−	0.719613i
$293$	−1.85934			−0.108624			−0.0543120	−	0.998524i	$-0.517297\pi$
$293$	−1.85934			−0.108624			−0.0543120	+	0.998524i	$0.517297\pi$
$294$		0			0
$295$			1.66610i			0.0970042i
$296$	−5.39270	−	12.6848i	−0.313444	−	0.737287i
$297$		0			0
$298$	8.59810	−	20.9407i	0.498075	−	1.21306i
$299$			3.05408i			0.176622i
$300$		0			0
$301$		−	25.0355i		−	1.44302i
$302$	2.38553	+	0.979482i	0.137272	+	0.0563628i
$303$		0			0
$304$	−0.157289	−	12.7067i	−0.00902114	−	0.728781i
$305$		−	9.42177i		−	0.539489i
$306$		0			0
$307$	29.0809			1.65973			0.829867	−	0.557961i	$-0.188416\pi$
$307$	29.0809			1.65973			0.829867	+	0.557961i	$0.188416\pi$
$308$	−28.7890	−	28.4349i	−1.64041	−	1.62023i
$309$		0			0
$310$	−0.712868	−	0.292698i	−0.0404882	−	0.0166241i
$311$	−18.7260			−1.06185			−0.530927	−	0.847417i	$-0.678156\pi$
$311$	−18.7260			−1.06185			−0.530927	+	0.847417i	$0.678156\pi$
$312$		0			0
$313$	16.6393			0.940511			0.470256	−	0.882530i	$-0.344162\pi$
$313$	16.6393			0.940511			0.470256	+	0.882530i	$0.344162\pi$
$314$	−26.8040	−	11.0055i	−1.51264	−	0.621078i
$315$		0			0
$316$	−8.07486	+	8.17543i	−0.454246	+	0.459904i
$317$	13.1121			0.736449			0.368224	−	0.929737i	$-0.379966\pi$
$317$	13.1121			0.736449			0.368224	+	0.929737i	$0.379966\pi$
$318$		0			0
$319$			33.2632i			1.86238i
$320$	−5.27146	+	5.47093i	−0.294684	+	0.305834i
$321$		0			0
$322$	−4.62534	−	1.89913i	−0.257760	−	0.105834i
$323$		−	3.78619i		−	0.210669i
$324$		0			0
$325$		−	16.6736i		−	0.924883i
$326$	4.07898	−	9.93437i	0.225914	−	0.550214i
$327$		0			0
$328$	10.7991	+	25.4018i	0.596280	+	1.40258i
$329$		−	46.2533i		−	2.55003i
$330$		0			0
$331$	−32.7952			−1.80258			−0.901292	−	0.433211i	$-0.857380\pi$
$331$	−32.7952			−1.80258			−0.901292	+	0.433211i	$0.857380\pi$
$332$	−17.5728	+	17.7917i	−0.964433	+	0.976445i
$333$		0			0
$334$	3.01517	−	7.34346i	0.164983	−	0.401816i
$335$	−10.4147			−0.569016
$336$		0			0
$337$	28.2701			1.53997			0.769986	−	0.638060i	$-0.220263\pi$
$337$	28.2701			1.53997			0.769986	+	0.638060i	$0.220263\pi$
$338$	1.90865	−	4.64852i	0.103817	−	0.252846i
$339$		0			0
$340$	−1.59066	+	1.61047i	−0.0862656	+	0.0873400i
$341$	−2.46475			−0.133474
$342$		0			0
$343$		−	38.5470i		−	2.08134i
$344$	−13.8358	+	5.88204i	−0.745976	+	0.317138i
$345$		0			0
$346$	6.78552	−	16.5262i	0.364792	−	0.888452i
$347$		−	6.84376i		−	0.367392i	−0.982983	−	0.183696i	$-0.941194\pi$
$347$		−	6.84376i		−	0.367392i	0.982983	−	0.183696i	$-0.0588062\pi$
$348$		0			0
$349$			14.4443i			0.773183i	0.922251	+	0.386592i	$0.126348\pi$
$349$			14.4443i			0.773183i	−0.922251	+	0.386592i	$0.873652\pi$
$350$	25.2517	+	10.3682i	1.34976	+	0.554203i
$351$		0			0
$352$	−8.95052	+	22.5909i	−0.477065	+	1.20410i
$353$			15.8826i			0.845343i	0.906283	+	0.422671i	$0.138908\pi$
$353$			15.8826i			0.845343i	−0.906283	+	0.422671i	$0.861092\pi$
$354$		0			0
$355$	9.41165			0.499518
$356$	14.2568	−	14.4344i	0.755608	−	0.765019i
$357$		0			0
$358$	26.8556	+	11.0267i	1.41936	+	0.582780i
$359$	3.84545			0.202955			0.101477	−	0.994838i	$-0.467643\pi$
$359$	3.84545			0.202955			0.101477	+	0.994838i	$0.467643\pi$
$360$		0			0
$361$	−8.90714			−0.468797
$362$	13.0308	+	5.35035i	0.684884	+	0.281208i
$363$		0			0
$364$	27.2677	+	26.9323i	1.42922	+	1.41164i
$365$	−8.30904			−0.434915
$366$		0			0
$367$		−	27.5746i		−	1.43938i	−0.694294	−	0.719692i	$-0.744283\pi$
$367$		−	27.5746i		−	1.43938i	0.694294	−	0.719692i	$-0.255717\pi$
$368$	0.0371646	+	3.00237i	0.00193734	+	0.156510i
$369$		0			0
$370$	−6.05438	−	2.48588i	−0.314752	−	0.129235i
$371$			4.13388i			0.214620i
$372$		0			0
$373$		−	8.09190i		−	0.418982i	−0.977811	−	0.209491i	$-0.932819\pi$
$373$		−	8.09190i		−	0.418982i	0.977811	−	0.209491i	$-0.0671808\pi$
$374$	−2.74987	+	6.69731i	−0.142192	+	0.346310i
$375$		0			0
$376$	−25.5617	+	10.8671i	−1.31825	+	0.560428i
$377$		−	31.5055i		−	1.62261i
$378$		0			0
$379$	−17.9143			−0.920195			−0.460098	−	0.887868i	$-0.652186\pi$
$379$	−17.9143			−0.920195			−0.460098	+	0.887868i	$0.652186\pi$
$380$	−4.29303	−	4.24022i	−0.220228	−	0.217519i
$381$		0			0
$382$	−12.3544	+	30.0891i	−0.632105	+	1.53949i
$383$	−5.77515			−0.295096			−0.147548	−	0.989055i	$-0.547138\pi$
$383$	−5.77515			−0.295096			−0.147548	+	0.989055i	$0.547138\pi$
$384$		0			0
$385$	−19.2137			−0.979223
$386$	0.537150	−	1.30823i	0.0273402	−	0.0665872i
$387$		0			0
$388$	−11.1419	−	11.0049i	−0.565646	−	0.558688i
$389$	−22.0326			−1.11709			−0.558547	−	0.829473i	$-0.688641\pi$
$389$	−22.0326			−1.11709			−0.558547	+	0.829473i	$0.688641\pi$
$390$		0			0
$391$			0.894610i			0.0452424i
$392$	−39.5236	+	16.8028i	−1.99625	+	0.848668i
$393$		0			0
$394$	−0.279124	+	0.679808i	−0.0140621	+	0.0342483i
$395$			5.45626i			0.274534i
$396$		0			0
$397$		−	26.3815i		−	1.32405i	−0.749481	−	0.662026i	$-0.769697\pi$
$397$		−	26.3815i		−	1.32405i	0.749481	−	0.662026i	$-0.230303\pi$
$398$	0.825031	+	0.338752i	0.0413551	+	0.0169801i
$399$		0			0
$400$	−0.202898	−	16.3913i	−0.0101449	−	0.819564i
$401$		−	1.29121i		−	0.0644801i	−0.999480	−	0.0322401i	$-0.989736\pi$
$401$		−	1.29121i		−	0.0644801i	0.999480	−	0.0322401i	$-0.0102641\pi$
$402$		0			0
$403$	2.33451			0.116290
$404$	−25.4039	−	25.0914i	−1.26389	−	1.24834i
$405$		0			0
$406$	47.7144	+	19.5912i	2.36803	+	0.972294i
$407$	−20.9331			−1.03762
$408$		0			0
$409$	−1.54485			−0.0763880			−0.0381940	−	0.999270i	$-0.512160\pi$
$409$	−1.54485			−0.0763880			−0.0381940	+	0.999270i	$0.512160\pi$
$410$	12.1241	+	4.97808i	0.598768	+	0.245850i
$411$		0			0
$412$	3.44911	−	3.49207i	0.169925	−	0.172042i
$413$	8.26326			0.406608
$414$		0			0
$415$			11.8741i			0.582878i
$416$	8.47755	−	21.3971i	0.415646	−	1.04908i
$417$		0			0
$418$	−17.8530	−	7.33033i	−0.873220	−	0.358538i
$419$			14.9313i			0.729444i	0.931116	+	0.364722i	$0.118836\pi$
$419$			14.9313i			0.729444i	−0.931116	+	0.364722i	$0.881164\pi$
$420$		0			0
$421$			14.8896i			0.725673i	0.931853	+	0.362836i	$0.118192\pi$
$421$			14.8896i			0.725673i	−0.931853	+	0.362836i	$0.881808\pi$
$422$	−5.32742	+	12.9749i	−0.259335	+	0.631611i
$423$		0			0
$424$	2.28458	−	0.971246i	0.110949	−	0.0471679i
$425$		−	4.88407i		−	0.236912i
$426$		0			0
$427$	−46.7286			−2.26135
$428$	−0.398031	+	0.402988i	−0.0192395	+	0.0194792i
$429$		0			0
$430$	−2.71146	+	6.60376i	−0.130758	+	0.318462i
$431$	30.8436			1.48568			0.742842	−	0.669467i	$-0.233477\pi$
$431$	30.8436			1.48568			0.742842	+	0.669467i	$0.233477\pi$
$432$		0			0
$433$	−29.1892			−1.40275			−0.701373	−	0.712795i	$-0.747429\pi$
$433$	−29.1892			−1.40275			−0.701373	+	0.712795i	$0.747429\pi$
$434$	−1.45168	+	3.53556i	−0.0696827	+	0.169713i
$435$		0			0
$436$	13.6990	−	13.8696i	0.656063	−	0.664234i
$437$	−2.38476			−0.114079
$438$		0			0
$439$			1.24969i			0.0596443i	0.999555	+	0.0298221i	$0.00949409\pi$
$439$			1.24969i			0.0596443i	−0.999555	+	0.0298221i	$0.990506\pi$
$440$	4.51423	+	10.6184i	0.215207	+	0.506213i
$441$		0			0
$442$	2.60456	−	6.34340i	0.123886	−	0.301725i
$443$			27.4266i			1.30308i	0.758616	+	0.651538i	$0.225876\pi$
$443$			27.4266i			1.30308i	−0.758616	+	0.651538i	$0.774124\pi$
$444$		0			0
$445$		−	9.63345i		−	0.456669i
$446$	−9.29795	−	3.81767i	−0.440271	−	0.180772i
$447$		0			0
$448$	27.1338	+	26.1445i	1.28195	+	1.23521i
$449$			16.2552i			0.767132i	0.923513	+	0.383566i	$0.125304\pi$
$449$			16.2552i			0.767132i	−0.923513	+	0.383566i	$0.874696\pi$
$450$		0			0
$451$	41.9194			1.97391
$452$	6.64397	−	6.72672i	0.312506	−	0.316398i
$453$		0			0
$454$	−16.3033	−	6.69402i	−0.765152	−	0.314166i
$455$	18.1984			0.853155
$456$		0			0
$457$	18.8861			0.883456			0.441728	−	0.897149i	$-0.354366\pi$
$457$	18.8861			0.883456			0.441728	+	0.897149i	$0.354366\pi$
$458$	12.7798	+	5.24727i	0.597159	+	0.245189i
$459$		0			0
$460$	1.01437	+	1.00189i	0.0472951	+	0.0467133i
$461$	19.3048			0.899114			0.449557	−	0.893252i	$-0.351582\pi$
$461$	19.3048			0.899114			0.449557	+	0.893252i	$0.351582\pi$
$462$		0			0
$463$		−	2.34200i		−	0.108842i	−0.998518	−	0.0544209i	$-0.982669\pi$
$463$		−	2.34200i		−	0.108842i	0.998518	−	0.0544209i	$-0.0173313\pi$
$464$	−0.383385	−	30.9721i	−0.0177982	−	1.43784i
$465$		0			0
$466$	−6.10144	−	2.50521i	−0.282644	−	0.116051i
$467$		−	12.2034i		−	0.564708i	−0.959310	−	0.282354i	$-0.908885\pi$
$467$		−	12.2034i		−	0.564708i	0.959310	−	0.282354i	$-0.0911153\pi$
$468$		0			0
$469$			51.6531i			2.38512i
$470$	−5.00944	+	12.2005i	−0.231068	+	0.562767i
$471$		0			0
$472$	−1.94143	−	4.56666i	−0.0893618	−	0.210198i
$473$			22.8326i			1.04985i
$474$		0			0
$475$	13.0195			0.597374
$476$	7.98735	+	7.88909i	0.366100	+	0.361596i
$477$		0			0
$478$	1.83991	−	4.48111i	0.0841555	−	0.204961i
$479$	35.4473			1.61963			0.809815	−	0.586685i	$-0.199567\pi$
$479$	35.4473			1.61963			0.809815	+	0.586685i	$0.199567\pi$
$480$		0			0
$481$	19.8270			0.904031
$482$	−0.674510	+	1.64277i	−0.0307231	+	0.0748262i
$483$		0			0
$484$	10.6036	+	10.4731i	0.481980	+	0.476051i
$485$	−7.43610			−0.337656
$486$		0			0
$487$			18.7853i			0.851242i	0.904902	+	0.425621i	$0.139944\pi$
$487$			18.7853i			0.851242i	−0.904902	+	0.425621i	$0.860056\pi$
$488$	10.9788	+	25.8244i	0.496986	+	1.16902i
$489$		0			0
$490$	−7.74561	+	18.8644i	−0.349911	+	0.852209i
$491$		−	1.22936i		−	0.0554803i	−0.999615	−	0.0277402i	$-0.991169\pi$
$491$		−	1.22936i		−	0.0554803i	0.999615	−	0.0277402i	$-0.00883110\pi$
$492$		0			0
$493$		−	9.22868i		−	0.415639i
$494$	16.9096	+	6.94297i	0.760800	+	0.312379i
$495$		0			0
$496$	2.29499	−	0.0284082i	0.103048	−	0.00127557i
$497$		−	46.6783i		−	2.09381i
$498$		0			0
$499$	−3.47322			−0.155483			−0.0777413	−	0.996974i	$-0.524771\pi$
$499$	−3.47322			−0.155483			−0.0777413	+	0.996974i	$0.524771\pi$
$500$	−12.2945	−	12.1432i	−0.549825	−	0.543061i
$501$		0			0
$502$	−26.4707	−	10.8687i	−1.18145	−	0.485094i
$503$	31.5709			1.40768			0.703838	−	0.710360i	$-0.251468\pi$
$503$	31.5709			1.40768			0.703838	+	0.710360i	$0.251468\pi$
$504$		0			0
$505$	−16.9545			−0.754465
$506$	4.21835	+	1.73202i	0.187529	+	0.0769979i
$507$		0			0
$508$	19.4009	−	19.6425i	0.860775	−	0.871495i
$509$	−31.5773			−1.39964			−0.699820	−	0.714319i	$-0.746736\pi$
$509$	−31.5773			−1.39964			−0.699820	+	0.714319i	$0.746736\pi$
$510$		0			0
$511$			41.2098i			1.82302i
$512$	8.07365	−	21.1380i	0.356808	−	0.934178i
$513$		0			0
$514$	1.53866	+	0.631764i	0.0678675	+	0.0278659i
$515$		−	2.33060i		−	0.102698i
$516$		0			0
$517$			42.1835i			1.85523i
$518$	−12.3291	+	30.0275i	−0.541708	+	1.31933i
$519$		0			0
$520$	−4.27568	−	10.0573i	−0.187501	−	0.441042i
$521$		−	8.99232i		−	0.393961i	−0.980407	−	0.196980i	$-0.936886\pi$
$521$		−	8.99232i		−	0.393961i	0.980407	−	0.196980i	$-0.0631136\pi$
$522$		0			0
$523$	2.78978			0.121988			0.0609942	−	0.998138i	$-0.480573\pi$
$523$	2.78978			0.121988			0.0609942	+	0.998138i	$0.480573\pi$
$524$	6.65421	−	6.73708i	0.290690	−	0.294311i
$525$		0			0
$526$	−3.77313	+	9.18946i	−0.164516	+	0.400679i
$527$	0.683832			0.0297882
$528$		0			0
$529$	−22.4365			−0.975501
$530$	0.447717	−	1.09042i	0.0194476	−	0.0473647i
$531$		0			0
$532$	−21.0300	+	21.2919i	−0.911764	+	0.923120i
$533$	−39.7043			−1.71978
$534$		0			0
$535$			0.268953i			0.0116279i
$536$	28.5459	−	12.1358i	1.23300	−	0.524186i
$537$		0			0
$538$	6.13276	−	14.9363i	0.264402	−	0.643952i
$539$			65.2242i			2.80940i
$540$		0			0
$541$			38.5456i			1.65721i	0.559836	+	0.828603i	$0.310864\pi$
$541$			38.5456i			1.65721i	−0.559836	+	0.828603i	$0.689136\pi$
$542$	14.3781	+	5.90355i	0.617593	+	0.253579i
$543$		0			0
$544$	2.48327	−	6.26771i	0.106469	−	0.268726i
$545$		−	9.25655i		−	0.396507i
$546$		0			0
$547$	21.7781			0.931163			0.465581	−	0.885005i	$-0.345845\pi$
$547$	21.7781			0.931163			0.465581	+	0.885005i	$0.345845\pi$
$548$	21.8606	−	22.1329i	0.933838	−	0.945469i
$549$		0			0
$550$	−23.0298	−	9.45589i	−0.981996	−	0.403200i
$551$	24.6009			1.04803
$552$		0			0
$553$	27.0611			1.15075
$554$	−4.71186	−	1.93466i	−0.200188	−	0.0821957i
$555$		0			0
$556$	−11.2267	−	11.0886i	−0.476118	−	0.470261i
$557$	−22.9871			−0.973995			−0.486998	−	0.873403i	$-0.661908\pi$
$557$	−22.9871			−0.973995			−0.486998	+	0.873403i	$0.661908\pi$
$558$		0			0
$559$		−	21.6261i		−	0.914686i
$560$	17.8903	−	0.221454i	0.756004	−	0.00935812i
$561$		0			0
$562$	16.0573	+	6.59301i	0.677336	+	0.278109i
$563$			41.2641i			1.73907i	0.493867	+	0.869537i	$0.335583\pi$
$563$			41.2641i			1.73907i	−0.493867	+	0.869537i	$0.664417\pi$
$564$		0			0
$565$		−	4.48940i		−	0.188870i
$566$	1.36691	−	3.32910i	0.0574553	−	0.139933i
$567$		0			0
$568$	−25.7966	+	10.9670i	−1.08240	+	0.460164i
$569$		−	28.4760i		−	1.19378i	−0.802325	−	0.596888i	$-0.796404\pi$
$569$		−	28.4760i		−	1.19378i	0.802325	−	0.596888i	$-0.203596\pi$
$570$		0			0
$571$	−35.5206			−1.48649			−0.743245	−	0.669019i	$-0.766714\pi$
$571$	−35.5206			−1.48649			−0.743245	+	0.669019i	$0.766714\pi$
$572$	−24.8684	−	24.5625i	−1.03980	−	1.02701i
$573$		0			0
$574$	24.6895	−	60.1313i	1.03052	−	2.50983i
$575$	−3.07627			−0.128289
$576$		0			0
$577$	−30.5676			−1.27255			−0.636273	−	0.771464i	$-0.719525\pi$
$577$	−30.5676			−1.27255			−0.636273	+	0.771464i	$0.719525\pi$
$578$	−8.36862	+	20.3818i	−0.348089	+	0.847771i
$579$		0			0
$580$	−10.4641	−	10.3354i	−0.434497	−	0.429152i
$581$	58.8913			2.44322
$582$		0			0
$583$		−	3.77014i		−	0.156143i
$584$	22.7745	−	9.68216i	0.942415	−	0.400651i
$585$		0			0
$586$	0.998748	−	2.43245i	0.0412579	−	0.100484i
$587$		−	18.6609i		−	0.770217i	−0.922871	−	0.385109i	$-0.874164\pi$
$587$		−	18.6609i		−	0.770217i	0.922871	−	0.385109i	$-0.125836\pi$
$588$		0			0
$589$			1.82289i			0.0751109i
$590$	−2.17965	−	0.894947i	−0.0897346	−	0.0368444i
$591$		0			0
$592$	19.4913	−	0.241271i	0.801087	−	0.00991617i
$593$		−	0.676531i		−	0.0277818i	−0.999904	−	0.0138909i	$-0.995578\pi$
$593$		−	0.676531i		−	0.0277818i	0.999904	−	0.0138909i	$-0.00442175\pi$
$594$		0			0
$595$	5.33074			0.218539
$596$	22.7768	+	22.4966i	0.932975	+	0.921497i
$597$		0			0
$598$	−3.99544	−	1.64050i	−0.163386	−	0.0670850i
$599$	37.7371			1.54189			0.770947	−	0.636899i	$-0.219783\pi$
$599$	37.7371			1.54189			0.770947	+	0.636899i	$0.219783\pi$
$600$		0			0
$601$	−23.1123			−0.942771			−0.471386	−	0.881927i	$-0.656246\pi$
$601$	−23.1123			−0.942771			−0.471386	+	0.881927i	$0.656246\pi$
$602$	32.7523	+	13.4478i	1.33488	+	0.548093i
$603$		0			0
$604$	−2.56278	+	2.59470i	−0.104278	+	0.105577i
$605$	7.07679			0.287712
$606$		0			0
$607$		−	2.35798i		−	0.0957075i	−0.998854	−	0.0478537i	$-0.984762\pi$
$607$		−	2.35798i		−	0.0957075i	0.998854	−	0.0478537i	$-0.0152381\pi$
$608$	16.7078	+	6.61966i	0.677592	+	0.268463i
$609$		0			0
$610$	12.3259	+	5.06091i	0.499059	+	0.204910i
$611$		−	39.9543i		−	1.61638i
$612$		0			0
$613$			23.7808i			0.960497i	0.877132	+	0.480249i	$0.159454\pi$
$613$			23.7808i			0.960497i	−0.877132	+	0.480249i	$0.840546\pi$
$614$	−15.6208	+	38.0445i	−0.630405	+	1.53535i
$615$		0			0
$616$	52.6635	−	22.3889i	2.12187	−	0.902075i
$617$			3.66608i			0.147591i	0.997273	+	0.0737954i	$0.0235112\pi$
$617$			3.66608i			0.147591i	−0.997273	+	0.0737954i	$0.976489\pi$
$618$		0			0
$619$	−17.5872			−0.706889			−0.353444	−	0.935456i	$-0.614990\pi$
$619$	−17.5872			−0.706889			−0.353444	+	0.935456i	$0.614990\pi$
$620$	0.765834	−	0.775373i	0.0307566	−	0.0311397i
$621$		0			0
$622$	10.0587	−	24.4979i	0.403316	−	0.982278i
$623$	−47.7784			−1.91420
$624$		0			0
$625$	12.2854			0.491415
$626$	−8.93783	+	21.7681i	−0.357228	+	0.870029i
$627$		0			0
$628$	28.7955	−	29.1542i	1.14907	−	1.16338i
$629$	5.80777			0.231571
$630$		0			0
$631$			21.9248i			0.872811i	0.899750	+	0.436405i	$0.143749\pi$
$631$			21.9248i			0.872811i	−0.899750	+	0.436405i	$0.856251\pi$
$632$	−6.35794	−	14.9552i	−0.252905	−	0.594887i
$633$		0			0
$634$	−7.04317	+	17.1537i	−0.279720	+	0.681259i
$635$		−	13.1094i		−	0.520229i
$636$		0			0
$637$		−	61.7775i		−	2.44772i
$638$	−43.5160	−	17.8674i	−1.72281	−	0.707375i
$639$		0			0
$640$	−4.32568	−	9.83500i	−0.170988	−	0.388763i
$641$			20.8495i			0.823507i	0.911295	+	0.411754i	$0.135084\pi$
$641$			20.8495i			0.823507i	−0.911295	+	0.411754i	$0.864916\pi$
$642$		0			0
$643$	−25.7081			−1.01383			−0.506914	−	0.861997i	$-0.669214\pi$
$643$	−25.7081			−1.01383			−0.506914	+	0.861997i	$0.669214\pi$
$644$	4.96900	−	5.03089i	0.195806	−	0.198245i
$645$		0			0
$646$	4.95322	+	2.03376i	0.194882	+	0.0800171i
$647$	−26.0025			−1.02226			−0.511131	−	0.859503i	$-0.670773\pi$
$647$	−26.0025			−1.02226			−0.511131	+	0.859503i	$0.670773\pi$
$648$		0			0
$649$	−7.53617			−0.295821
$650$	21.8129	+	8.95621i	0.855571	+	0.351291i
$651$		0			0
$652$	10.8054	+	10.6725i	0.423173	+	0.417967i
$653$	−21.5340			−0.842691			−0.421346	−	0.906900i	$-0.638442\pi$
$653$	−21.5340			−0.842691			−0.421346	+	0.906900i	$0.638442\pi$
$654$		0			0
$655$		−	4.49631i		−	0.175686i
$656$	−39.0321	+	0.483155i	−1.52395	+	0.0188640i
$657$		0			0
$658$	60.5100	+	24.8450i	2.35893	+	0.968558i
$659$			13.3884i			0.521538i	0.965401	+	0.260769i	$0.0839760\pi$
$659$			13.3884i			0.521538i	−0.965401	+	0.260769i	$0.916024\pi$
$660$		0			0
$661$		−	16.7021i		−	0.649635i	−0.945777	−	0.324818i	$-0.894697\pi$
$661$		−	16.7021i		−	0.649635i	0.945777	−	0.324818i	$-0.105303\pi$
$662$	17.6159	−	42.9037i	0.684663	−	1.66750i
$663$		0			0
$664$	−13.8364	−	32.5461i	−0.536956	−	1.26303i
$665$			14.2102i			0.551046i
$666$		0			0
$667$	−5.81275			−0.225071
$668$	7.98735	+	7.88909i	0.309040	+	0.305238i
$669$		0			0
$670$	5.59426	−	13.6248i	0.216125	−	0.526374i
$671$	42.6169			1.64521
$672$		0			0
$673$	10.9578			0.422391			0.211196	−	0.977444i	$-0.432264\pi$
$673$	10.9578			0.422391			0.211196	+	0.977444i	$0.432264\pi$
$674$	−15.1853	+	36.9839i	−0.584917	+	1.42457i
$675$		0			0
$676$	5.05610	+	4.99391i	0.194466	+	0.192073i
$677$	−22.5484			−0.866604			−0.433302	−	0.901249i	$-0.642652\pi$
$677$	−22.5484			−0.866604			−0.433302	+	0.901249i	$0.642652\pi$
$678$		0			0
$679$			36.8804i			1.41534i
$680$	−1.25245	−	2.94602i	−0.0480291	−	0.112975i
$681$		0			0
$682$	1.32394	−	3.22447i	0.0506964	−	0.123471i
$683$			36.4666i			1.39536i	0.716412	+	0.697678i	$0.245783\pi$
$683$			36.4666i			1.39536i	−0.716412	+	0.697678i	$0.754217\pi$
$684$		0			0
$685$		−	14.7714i		−	0.564387i
$686$	50.4284	+	20.7055i	1.92537	+	0.790541i
$687$		0			0
$688$	−0.263164	−	21.2600i	−0.0100330	−	0.810529i
$689$			3.57091i			0.136041i
$690$		0			0
$691$	5.00515			0.190405			0.0952025	−	0.995458i	$-0.469650\pi$
$691$	5.00515			0.190405			0.0952025	+	0.995458i	$0.469650\pi$
$692$	17.9752	+	17.7541i	0.683315	+	0.674909i
$693$		0			0
$694$	8.95322	+	3.67613i	0.339860	+	0.139544i
$695$	−7.49267			−0.284213
$696$		0			0
$697$	−11.6303			−0.440529
$698$	−18.8964	−	7.75874i	−0.715240	−	0.293672i
$699$		0			0
$700$	−27.1280	+	27.4659i	−1.02534	+	1.03811i
$701$	11.4972			0.434243			0.217122	−	0.976145i	$-0.430333\pi$
$701$	11.4972			0.434243			0.217122	+	0.976145i	$0.430333\pi$
$702$		0			0
$703$			15.4818i			0.583907i
$704$	−24.7463	−	23.8441i	−0.932662	−	0.898657i
$705$		0			0
$706$	−20.7781	−	8.53132i	−0.781992	−	0.321080i
$707$			84.0881i			3.16246i
$708$		0			0
$709$			34.3370i			1.28955i	0.764371	+	0.644776i	$0.223049\pi$
$709$			34.3370i			1.28955i	−0.764371	+	0.644776i	$0.776951\pi$
$710$	−5.05547	+	12.3126i	−0.189728	+	0.462084i
$711$		0			0
$712$	11.2254	+	26.4046i	0.420691	+	0.989554i
$713$		−	0.430716i		−	0.0161305i
$714$		0			0
$715$	−16.5971			−0.620698
$716$	−28.8510	+	29.2103i	−1.07821	+	1.09164i
$717$		0			0
$718$	−2.06558	+	5.03073i	−0.0770869	+	0.187745i
$719$	40.5660			1.51286			0.756429	−	0.654076i	$-0.226942\pi$
$719$	40.5660			1.51286			0.756429	+	0.654076i	$0.226942\pi$
$720$		0			0
$721$	−11.5589			−0.430477
$722$	4.78447	−	11.6526i	0.178060	−	0.433665i
$723$		0			0
$724$	−13.9990	+	14.1734i	−0.520269	+	0.526749i
$725$	31.7344			1.17859
$726$		0			0
$727$		−	38.9815i		−	1.44575i	−0.690981	−	0.722873i	$-0.742821\pi$
$727$		−	38.9815i		−	1.44575i	0.690981	−	0.722873i	$-0.257179\pi$
$728$	−49.8805	+	21.2058i	−1.84870	+	0.785940i
$729$		0			0
$730$	4.46321	−	10.8701i	0.165191	−	0.402322i
$731$		−	6.33478i		−	0.234300i
$732$		0			0
$733$		−	36.3971i		−	1.34436i	−0.740388	−	0.672179i	$-0.765358\pi$
$733$		−	36.3971i		−	1.34436i	0.740388	−	0.672179i	$-0.234642\pi$
$734$	36.0740	+	14.8117i	1.33152	+	0.546711i
$735$		0			0
$736$	−3.94776	−	1.56411i	−0.145516	−	0.0576537i
$737$		−	47.1082i		−	1.73525i
$738$		0			0
$739$	−19.8657			−0.730770			−0.365385	−	0.930857i	$-0.619063\pi$
$739$	−19.8657			−0.730770			−0.365385	+	0.930857i	$0.619063\pi$
$740$	6.50422	−	6.58523i	0.239100	−	0.242078i
$741$		0			0
$742$	−5.40807	−	2.22052i	−0.198537	−	0.0815177i
$743$	−12.2738			−0.450282			−0.225141	−	0.974326i	$-0.572284\pi$
$743$	−12.2738			−0.450282			−0.225141	+	0.974326i	$0.572284\pi$
$744$		0			0
$745$	15.2012			0.556929
$746$	10.5861	+	4.34657i	0.387584	+	0.159139i
$747$		0			0
$748$	−7.28454	−	7.19493i	−0.266349	−	0.263073i
$749$	1.33391			0.0487400
$750$		0			0
$751$		−	4.95743i		−	0.180899i	−0.995901	−	0.0904496i	$-0.971170\pi$
$751$		−	4.95743i		−	0.180899i	0.995901	−	0.0904496i	$-0.0288304\pi$
$752$	−0.486198	−	39.2779i	−0.0177298	−	1.43232i
$753$		0			0
$754$	41.2165	+	16.9232i	1.50101	+	0.616306i
$755$			1.73169i			0.0630228i
$756$		0			0
$757$			0.135856i			0.00493778i	0.999997	+	0.00246889i	$0.000785872\pi$
$757$			0.135856i			0.00493778i	−0.999997	+	0.00246889i	$0.999214\pi$
$758$	9.62267	−	23.4360i	0.349511	−	0.851235i
$759$		0			0
$760$	7.85320	−	3.33865i	0.284865	−	0.121105i
$761$			2.14729i			0.0778390i	0.999242	+	0.0389195i	$0.0123916\pi$
$761$			2.14729i			0.0778390i	−0.999242	+	0.0389195i	$0.987608\pi$
$762$		0			0
$763$	−45.9091			−1.66202
$764$	−32.7274	−	32.3248i	−1.18403	−	1.16947i
$765$		0			0
$766$	3.10212	−	7.55523i	0.112084	−	0.272981i
$767$	7.13794			0.257736
$768$		0			0
$769$	−13.7117			−0.494457			−0.247228	−	0.968957i	$-0.579520\pi$
$769$	−13.7117			−0.494457			−0.247228	+	0.968957i	$0.579520\pi$
$770$	10.3207	−	25.1360i	0.371931	−	0.905839i
$771$		0			0
$772$	1.42294	+	1.40543i	0.0512127	+	0.0505827i
$773$	21.2269			0.763477			0.381738	−	0.924270i	$-0.375326\pi$
$773$	21.2269			0.763477			0.381738	+	0.924270i	$0.375326\pi$
$774$		0			0
$775$			2.35147i			0.0844673i
$776$	20.3818	−	8.66496i	0.731664	−	0.311054i
$777$		0			0
$778$	11.8348	−	28.8237i	0.424298	−	1.03338i
$779$		−	31.0029i		−	1.11079i
$780$		0			0
$781$			42.5711i			1.52331i
$782$	−1.17036	−	0.480540i	−0.0418519	−	0.0171841i
$783$		0			0
$784$	−0.751761	−	60.7317i	−0.0268486	−	2.16899i
$785$		−	19.4574i		−	0.694466i
$786$		0			0
$787$	21.2066			0.755933			0.377966	−	0.925819i	$-0.376623\pi$
$787$	21.2066			0.755933			0.377966	+	0.925819i	$0.376623\pi$
$788$	−0.739415	−	0.730319i	−0.0263406	−	0.0260165i
$789$		0			0
$790$	−7.13805	−	2.93083i	−0.253961	−	0.104274i
$791$	−22.2658			−0.791680
$792$		0			0
$793$	−40.3649			−1.43340
$794$	34.5132	+	14.1709i	1.22483	+	0.502905i
$795$		0			0
$796$	−0.886332	+	0.897371i	−0.0314152	+	0.0318065i
$797$	35.2871			1.24993			0.624967	−	0.780651i	$-0.285113\pi$
$797$	35.2871			1.24993			0.624967	+	0.780651i	$0.285113\pi$
$798$		0			0
$799$		−	11.7036i		−	0.414042i
$800$	21.5526	+	8.53915i	0.761999	+	0.301904i
$801$		0			0
$802$	1.68921	+	0.693576i	0.0596479	+	0.0244910i
$803$		−	37.5838i		−	1.32630i
$804$		0			0
$805$		−	3.35761i		−	0.118340i
$806$	−1.25398	+	3.05408i	−0.0441696	+	0.107575i
$807$		0			0
$808$	46.4710	−	19.7563i	1.63485	−	0.695025i
$809$		−	26.8216i		−	0.942996i	−0.881867	−	0.471498i	$-0.843714\pi$
$809$		−	26.8216i		−	0.942996i	0.881867	−	0.471498i	$-0.156286\pi$
$810$		0			0
$811$	7.68860			0.269983			0.134992	−	0.990847i	$-0.456899\pi$
$811$	7.68860			0.269983			0.134992	+	0.990847i	$0.456899\pi$
$812$	−51.2596	+	51.8980i	−1.79886	+	1.82126i
$813$		0			0
$814$	11.2442	−	27.3854i	0.394110	−	0.959857i
$815$	7.21151			0.252608
$816$		0			0
$817$	16.8866			0.590789
$818$	0.829818	−	2.02102i	0.0290139	−	0.0706634i
$819$		0			0
$820$	−13.0250	+	13.1872i	−0.454852	+	0.460517i
$821$	−24.7379			−0.863360			−0.431680	−	0.902027i	$-0.642079\pi$
$821$	−24.7379			−0.863360			−0.431680	+	0.902027i	$0.642079\pi$
$822$		0			0
$823$			31.5126i			1.09846i	0.835671	+	0.549230i	$0.185079\pi$
$823$			31.5126i			1.09846i	−0.835671	+	0.549230i	$0.814921\pi$
$824$	2.71574	+	6.38800i	0.0946074	+	0.222536i
$825$		0			0
$826$	−4.43861	+	10.8103i	−0.154439	+	0.376137i
$827$		−	15.9087i		−	0.553200i	−0.960985	−	0.276600i	$-0.910792\pi$
$827$		−	15.9087i		−	0.553200i	0.960985	−	0.276600i	$-0.0892077\pi$
$828$		0			0
$829$		−	40.2678i		−	1.39856i	−0.714848	−	0.699280i	$-0.753504\pi$
$829$		−	40.2678i		−	1.39856i	0.714848	−	0.699280i	$-0.246496\pi$
$830$	−15.5341	−	6.37819i	−0.539196	−	0.221390i
$831$		0			0
$832$	23.4386	+	22.5841i	0.812589	+	0.782961i
$833$		−	18.0961i		−	0.626992i
$834$		0			0
$835$	5.33074			0.184478
$836$	19.1795	−	19.4184i	0.663338	−	0.671600i
$837$		0			0
$838$	−19.5337	−	8.02038i	−0.674779	−	0.277059i
$839$	5.33781			0.184282			0.0921408	−	0.995746i	$-0.470629\pi$
$839$	5.33781			0.184282			0.0921408	+	0.995746i	$0.470629\pi$
$840$		0			0
$841$	30.9637			1.06771
$842$	−19.4790	−	7.99793i	−0.671290	−	0.275627i
$843$		0			0
$844$	−14.1126	−	13.9390i	−0.485776	−	0.479800i
$845$	3.37443			0.116084
$846$		0			0
$847$		−	35.0983i		−	1.20599i
$848$	0.0434538	+	3.51046i	0.00149221	+	0.120550i
$849$		0			0
$850$	6.38949	+	2.62348i	0.219158	+	0.0899846i
$851$		−	3.65807i		−	0.125397i
$852$		0			0
$853$			32.4923i			1.11252i	0.831009	+	0.556258i	$0.187763\pi$
$853$			32.4923i			1.11252i	−0.831009	+	0.556258i	$0.812237\pi$
$854$	25.1003	−	61.1318i	0.858913	−	2.09189i
$855$		0			0
$856$	−0.313399	−	0.737181i	−0.0107118	−	0.0251963i
$857$		−	24.3799i		−	0.832801i	−0.909181	−	0.416400i	$-0.863291\pi$
$857$		−	24.3799i		−	0.832801i	0.909181	−	0.416400i	$-0.136709\pi$
$858$		0			0
$859$	−12.0962			−0.412719			−0.206359	−	0.978476i	$-0.566162\pi$
$859$	−12.0962			−0.412719			−0.206359	+	0.978476i	$0.566162\pi$
$860$	−7.18279	−	7.09443i	−0.244931	−	0.241918i
$861$		0			0
$862$	−16.5677	+	40.3506i	−0.564297	+	1.37435i
$863$	−39.4505			−1.34291			−0.671456	−	0.741044i	$-0.734331\pi$
$863$	−39.4505			−1.34291			−0.671456	+	0.741044i	$0.734331\pi$
$864$		0			0
$865$	11.9966			0.407897
$866$	15.6790	−	38.1863i	0.532794	−	1.29762i
$867$		0			0
$868$	−3.84557	−	3.79826i	−0.130527	−	0.128921i
$869$	−24.6800			−0.837210
$870$		0			0
$871$			44.6188i			1.51185i
$872$	10.7862	+	25.3715i	0.365268	+	0.859188i
$873$		0			0
$874$	1.28098	−	3.11982i	0.0433297	−	0.105530i
$875$			40.6953i			1.37575i
$876$		0			0
$877$		−	6.88935i		−	0.232637i	−0.993212	−	0.116318i	$-0.962891\pi$
$877$		−	6.88935i		−	0.232637i	0.993212	−	0.116318i	$-0.0371093\pi$
$878$	−1.63488	−	0.671270i	−0.0551745	−	0.0226543i
$879$		0			0
$880$	−16.3162	+	0.201968i	−0.550018	+	0.00680833i
$881$			44.3192i			1.49315i	0.665300	+	0.746576i	$0.268304\pi$
$881$			44.3192i			1.49315i	−0.665300	+	0.746576i	$0.731696\pi$
$882$		0			0
$883$	48.0579			1.61728			0.808639	−	0.588305i	$-0.200205\pi$
$883$	48.0579			1.61728			0.808639	+	0.588305i	$0.200205\pi$
$884$	6.89960	+	6.81472i	0.232059	+	0.229204i
$885$		0			0
$886$	−35.8803	−	14.7322i	−1.20542	−	0.494938i
$887$	−27.0292			−0.907550			−0.453775	−	0.891116i	$-0.649923\pi$
$887$	−27.0292			−0.907550			−0.453775	+	0.891116i	$0.649923\pi$
$888$		0			0
$889$	−65.0177			−2.18062
$890$	12.6028	+	5.17461i	0.422446	+	0.173453i
$891$		0			0
$892$	9.98879	−	10.1132i	0.334450	−	0.338615i
$893$	31.1982			1.04401
$894$		0			0
$895$			19.4949i			0.651643i
$896$	−48.7780	+	21.4538i	−1.62956	+	0.716721i
$897$		0			0
$898$	−21.2656	−	8.73151i	−0.709643	−	0.291374i
$899$			4.44322i			0.148190i
$900$		0			0
$901$			1.04600i			0.0348474i
$902$	−22.5170	+	54.8403i	−0.749736	+	1.82598i
$903$		0			0
$904$	5.23130	+	12.3051i	0.173990	+	0.409262i
$905$			9.45927i			0.314437i
$906$		0			0
$907$	5.43993			0.180630			0.0903149	−	0.995913i	$-0.471213\pi$
$907$	5.43993			0.180630			0.0903149	+	0.995913i	$0.471213\pi$
$908$	17.5147	−	17.7328i	0.581244	−	0.588484i
$909$		0			0
$910$	−9.77529	+	23.8077i	−0.324048	+	0.789219i
$911$	−39.5517			−1.31041			−0.655203	−	0.755453i	$-0.727417\pi$
$911$	−39.5517			−1.31041			−0.655203	+	0.755453i	$0.727417\pi$
$912$		0			0
$913$	−53.7094			−1.77752
$914$	−10.1447	+	24.7074i	−0.335557	+	0.817249i
$915$		0			0
$916$	−13.7293	+	13.9003i	−0.453629	+	0.459279i
$917$	−22.3001			−0.736414
$918$		0			0
$919$			22.7057i			0.748991i	0.927229	+	0.374495i	$0.122184\pi$
$919$			22.7057i			0.748991i	−0.927229	+	0.374495i	$0.877816\pi$
$920$	−1.85557	+	0.788862i	−0.0611763	+	0.0260080i
$921$		0			0
$922$	−10.3696	+	25.2551i	−0.341504	+	0.831734i
$923$		−	40.3215i		−	1.32720i
$924$		0			0
$925$			19.9710i			0.656643i
$926$	3.06388	+	1.25801i	0.100685	+	0.0413406i
$927$		0			0
$928$	40.7246	+	16.1351i	1.33685	+	0.529661i
$929$		−	41.6457i		−	1.36635i	−0.730254	−	0.683176i	$-0.760598\pi$
$929$		−	41.6457i		−	1.36635i	0.730254	−	0.683176i	$-0.239402\pi$
$930$		0			0
$931$	48.2387			1.58096
$932$	6.55478	−	6.63642i	0.214709	−	0.217383i
$933$		0			0
$934$	15.9649	+	6.55509i	0.522389	+	0.214489i
$935$	−4.86169			−0.158994
$936$		0			0
$937$	54.4421			1.77855			0.889274	−	0.457376i	$-0.151211\pi$
$937$	54.4421			1.77855			0.889274	+	0.457376i	$0.151211\pi$
$938$	−67.5743	−	27.7455i	−2.20638	−	0.905923i
$939$		0			0
$940$	−13.2703	−	13.1070i	−0.432828	−	0.427503i
$941$	−43.6434			−1.42274			−0.711368	−	0.702820i	$-0.751924\pi$
$941$	−43.6434			−1.42274			−0.711368	+	0.702820i	$0.751924\pi$
$942$		0			0
$943$			7.32543i			0.238549i
$944$	7.01710	−	0.0868604i	0.228387	−	0.00282706i
$945$		0			0
$946$	−29.8704	−	12.2646i	−0.971170	−	0.398755i
$947$		−	13.3781i		−	0.434730i	−0.976090	−	0.217365i	$-0.930254\pi$
$947$		−	13.3781i		−	0.434730i	0.976090	−	0.217365i	$-0.0697462\pi$
$948$		0			0
$949$			35.5977i			1.15555i
$950$	−6.99342	+	17.0325i	−0.226896	+	0.552607i
$951$		0			0
$952$	−14.6112	+	6.21167i	−0.473551	+	0.201321i
$953$			36.5239i			1.18313i	0.806259	+	0.591563i	$0.201489\pi$
$953$			36.5239i			1.18313i	−0.806259	+	0.591563i	$0.798511\pi$
$954$		0			0
$955$	−21.8422			−0.706796
$956$	4.87402	+	4.81406i	0.157637	+	0.155698i
$957$		0			0
$958$	−19.0406	+	46.3733i	−0.615172	+	1.49825i
$959$	−73.2609			−2.36572
$960$		0			0
$961$	30.6708			0.989379
$962$	−10.6501	+	25.9382i	−0.343372	+	0.836282i
$963$		0			0
$964$	−1.78681	−	1.76483i	−0.0575493	−	0.0568414i
$965$	0.949666			0.0305708
$966$		0			0
$967$		−	22.4030i		−	0.720430i	−0.932869	−	0.360215i	$-0.882703\pi$
$967$		−	22.4030i		−	0.720430i	0.932869	−	0.360215i	$-0.117297\pi$
$968$	−19.3970	+	8.24627i	−0.623442	+	0.265045i
$969$		0			0
$970$	3.99431	−	9.72814i	0.128249	−	0.312352i
$971$			33.7841i			1.08418i	0.840320	+	0.542091i	$0.182367\pi$
$971$			33.7841i			1.08418i	−0.840320	+	0.542091i	$0.817633\pi$
$972$		0			0
$973$			37.1609i			1.19132i
$974$	−24.5755	−	10.0905i	−0.787449	−	0.323321i
$975$		0			0
$976$	−39.6815	+	0.491194i	−1.27017	+	0.0157227i
$977$			14.6312i			0.468094i	0.972225	+	0.234047i	$0.0751969\pi$
$977$			14.6312i			0.468094i	−0.972225	+	0.234047i	$0.924803\pi$
$978$		0			0
$979$	43.5744			1.39264
$980$	−20.5185	−	20.2661i	−0.655440	−	0.647376i
$981$		0			0
$982$	1.60829	+	0.660352i	0.0513226	+	0.0210727i
$983$	37.6759			1.20167			0.600837	−	0.799372i	$-0.294834\pi$
$983$	37.6759			1.20167			0.600837	+	0.799372i	$0.294834\pi$
$984$		0			0
$985$	−0.493484			−0.0157237
$986$	12.0733	+	4.95719i	0.384491	+	0.157869i
$987$		0			0
$988$	−18.1660	+	18.3923i	−0.577938	+	0.585136i
$989$	−3.99001			−0.126875
$990$		0			0
$991$		−	25.7352i		−	0.817504i	−0.912645	−	0.408752i	$-0.865964\pi$
$991$		−	25.7352i		−	0.817504i	0.912645	−	0.408752i	$-0.134036\pi$
$992$	−1.19559	+	3.01763i	−0.0379600	+	0.0958099i
$993$		0			0
$994$	61.0661	+	25.0733i	1.93690	+	0.795276i
$995$			0.598903i			0.0189865i
$996$		0			0
$997$		−	38.5688i		−	1.22149i	−0.791829	−	0.610743i	$-0.790871\pi$
$997$		−	38.5688i		−	1.22149i	0.791829	−	0.610743i	$-0.209129\pi$
$998$	1.86564	−	4.54377i	0.0590558	−	0.143831i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	648.2.f.c.323.10	yes	24
3.2	odd	2	inner	648.2.f.c.323.15	yes	24
4.3	odd	2		2592.2.f.c.1295.12		24
8.3	odd	2	inner	648.2.f.c.323.16	yes	24
8.5	even	2		2592.2.f.c.1295.13		24
9.2	odd	6		648.2.l.g.539.2		48
9.4	even	3		648.2.l.g.107.7		48
9.5	odd	6		648.2.l.g.107.18		48
9.7	even	3		648.2.l.g.539.23		48
12.11	even	2		2592.2.f.c.1295.14		24
24.5	odd	2		2592.2.f.c.1295.11		24
24.11	even	2	inner	648.2.f.c.323.9	✓	24
36.7	odd	6		2592.2.p.g.2159.14		48
36.11	even	6		2592.2.p.g.2159.12		48
36.23	even	6		2592.2.p.g.431.11		48
36.31	odd	6		2592.2.p.g.431.13		48
72.5	odd	6		2592.2.p.g.431.14		48
72.11	even	6		648.2.l.g.539.7		48
72.13	even	6		2592.2.p.g.431.12		48
72.29	odd	6		2592.2.p.g.2159.13		48
72.43	odd	6		648.2.l.g.539.18		48
72.59	even	6		648.2.l.g.107.23		48
72.61	even	6		2592.2.p.g.2159.11		48
72.67	odd	6		648.2.l.g.107.2		48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
648.2.f.c.323.9	✓	24	24.11	even	2	inner
648.2.f.c.323.10	yes	24	1.1	even	1	trivial
648.2.f.c.323.15	yes	24	3.2	odd	2	inner
648.2.f.c.323.16	yes	24	8.3	odd	2	inner
648.2.l.g.107.2		48	72.67	odd	6
648.2.l.g.107.7		48	9.4	even	3
648.2.l.g.107.18		48	9.5	odd	6
648.2.l.g.107.23		48	72.59	even	6
648.2.l.g.539.2		48	9.2	odd	6
648.2.l.g.539.7		48	72.11	even	6
648.2.l.g.539.18		48	72.43	odd	6
648.2.l.g.539.23		48	9.7	even	3
2592.2.f.c.1295.11		24	24.5	odd	2
2592.2.f.c.1295.12		24	4.3	odd	2
2592.2.f.c.1295.13		24	8.5	even	2
2592.2.f.c.1295.14		24	12.11	even	2
2592.2.p.g.431.11		48	36.23	even	6
2592.2.p.g.431.12		48	72.13	even	6
2592.2.p.g.431.13		48	36.31	odd	6
2592.2.p.g.431.14		48	72.5	odd	6
2592.2.p.g.2159.11		48	72.61	even	6
2592.2.p.g.2159.12		48	36.11	even	6
2592.2.p.g.2159.13		48	72.29	odd	6
2592.2.p.g.2159.14		48	36.7	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:	\( N \)	\(=\)	\( 648 = 2^{3} \cdot 3^{4} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	648.f (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.537150 + 1.30823i) q^{2} +(-1.42294 - 1.40543i) q^{4} -0.949666 q^{5} +4.71000i q^{7} +(2.60297 - 1.10660i) q^{8} +O(q^{10})\)	\(q+(-0.537150 + 1.30823i) q^{2} +(-1.42294 - 1.40543i) q^{4} -0.949666 q^{5} +4.71000i q^{7} +(2.60297 - 1.10660i) q^{8} +(0.510114 - 1.24238i) q^{10} -4.29556i q^{11} +4.06857i q^{13} +(-6.16177 - 2.52998i) q^{14} +(0.0495098 + 3.99969i) q^{16} +1.19178i q^{17} -3.17693 q^{19} +(1.35132 + 1.33469i) q^{20} +(5.61959 + 2.30736i) q^{22} +0.750651 q^{23} -4.09813 q^{25} +(-5.32263 - 2.18544i) q^{26} +(6.61959 - 6.70204i) q^{28} -7.74362 q^{29} -0.573791i q^{31} +(-5.25912 - 2.08367i) q^{32} +(-1.55912 - 0.640165i) q^{34} -4.47293i q^{35} -4.87320i q^{37} +(1.70649 - 4.15616i) q^{38} +(-2.47195 + 1.05090i) q^{40} +9.75877i q^{41} -5.31540 q^{43} +(-6.03713 + 6.11233i) q^{44} +(-0.403212 + 0.982025i) q^{46} -9.82024 q^{47} -15.1841 q^{49} +(2.20131 - 5.36131i) q^{50} +(5.71811 - 5.78933i) q^{52} +0.877682 q^{53} +4.07935i q^{55} +(5.21210 + 12.2600i) q^{56} +(4.15949 - 10.1304i) q^{58} -1.75441i q^{59} +9.92114i q^{61} +(0.750651 + 0.308212i) q^{62} +(5.55086 - 5.76090i) q^{64} -3.86379i q^{65} +10.9667 q^{67} +(1.67497 - 1.69583i) q^{68} +(5.85162 + 2.40263i) q^{70} -9.91048 q^{71} +8.74944 q^{73} +(6.37527 + 2.61764i) q^{74} +(4.52057 + 4.46496i) q^{76} +20.2321 q^{77} -5.74545i q^{79} +(-0.0470178 - 3.79837i) q^{80} +(-12.7667 - 5.24193i) q^{82} -12.5035i q^{83} -1.13179i q^{85} +(2.85517 - 6.95377i) q^{86} +(-4.75349 - 11.1812i) q^{88} +10.1440i q^{89} -19.1630 q^{91} +(-1.06813 - 1.05499i) q^{92} +(5.27494 - 12.8471i) q^{94} +3.01702 q^{95} +7.83023 q^{97} +(8.15614 - 19.8643i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q+O(q^{10}) \) 24 * q	\( 24 q + 12 q^{16} - 12 q^{22} + 24 q^{25} + 12 q^{28} - 24 q^{34} - 24 q^{40} - 12 q^{46} - 24 q^{49} - 12 q^{58} + 24 q^{64} + 48 q^{67} - 36 q^{70} - 60 q^{76} - 36 q^{82} - 60 q^{88} + 48 q^{94}+O(q^{100}) \) 24 * q + 12 * q^16 - 12 * q^22 + 24 * q^25 + 12 * q^28 - 24 * q^34 - 24 * q^40 - 12 * q^46 - 24 * q^49 - 12 * q^58 + 24 * q^64 + 48 * q^67 - 36 * q^70 - 60 * q^76 - 36 * q^82 - 60 * q^88 + 48 * q^94

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

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