LMFDB - Embedded newform 648.2.f.c.323.9

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

$q$-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	$-0.650630\pi$
$7$		−	4.71000i		−	1.78021i	0.455754	−	0.890106i	$-0.349370\pi$
$8$	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	$0.224219\pi$
$11$			4.29556i			1.29516i	−0.761997	+	0.647581i	$0.775781\pi$
$12$		0			0
$13$		−	4.06857i		−	1.12842i	−0.825632	−	0.564210i	$-0.809181\pi$
$13$		−	4.06857i		−	1.12842i	0.825632	−	0.564210i	$-0.190819\pi$
$14$	−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	$-0.953835\pi$
$17$		−	1.19178i		−	0.289049i	0.989501	−	0.144524i	$-0.0461652\pi$
$18$		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	$0.0164091\pi$
$31$			0.573791i			0.103056i	−0.998672	+	0.0515279i	$0.983591\pi$
$32$	−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	$0.131189\pi$
$37$			4.87320i			0.801148i	−0.916264	+	0.400574i	$0.868811\pi$
$38$	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	$-0.724202\pi$
$41$		−	9.75877i		−	1.52406i	0.647539	−	0.762032i	$-0.275798\pi$
$42$		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	$0.0364312\pi$
$59$			1.75441i			0.228405i	−0.993458	+	0.114202i	$0.963569\pi$
$60$		0			0
$61$		−	9.92114i		−	1.27027i	−0.772400	−	0.635136i	$-0.780944\pi$
$61$		−	9.92114i		−	1.27027i	0.772400	−	0.635136i	$-0.219056\pi$
$62$	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	$0.104761\pi$
$79$			5.74545i			0.646414i	−0.946328	+	0.323207i	$0.895239\pi$
$80$	−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	$0.240730\pi$
$83$			12.5035i			1.37243i	−0.727397	+	0.686217i	$0.759270\pi$
$84$		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	$-0.819319\pi$
$89$		−	10.1440i		−	1.07527i	0.843179	−	0.537633i	$-0.180681\pi$
$90$		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	$-0.961420\pi$
$103$		−	2.45412i		−	0.241812i	0.992664	−	0.120906i	$-0.0385800\pi$
$104$	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	$0.00435760\pi$
$107$			0.283208i			0.0273788i	−0.999906	+	0.0136894i	$0.995642\pi$
$108$		0			0
$109$		−	9.74716i		−	0.933609i	−0.884361	−	0.466805i	$-0.845405\pi$
$109$		−	9.74716i		−	0.933609i	0.884361	−	0.466805i	$-0.154595\pi$
$110$	−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	$-0.928625\pi$
$113$		−	4.72734i		−	0.444711i	0.974966	−	0.222356i	$-0.0713746\pi$
$114$		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	$-0.790179\pi$
$127$		−	13.8042i		−	1.22492i	0.790500	−	0.612462i	$-0.209821\pi$
$128$	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	$-0.933684\pi$
$131$		−	4.73463i		−	0.413666i	0.978376	−	0.206833i	$-0.0663157\pi$
$132$		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	$-0.768667\pi$
$137$		−	15.5543i		−	1.32890i	0.747334	−	0.664448i	$-0.231333\pi$
$138$		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	$0.0236391\pi$
$151$			1.82348i			0.148392i	−0.997244	+	0.0741962i	$0.976361\pi$
$152$	−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	$-0.695310\pi$
$157$		−	20.4887i		−	1.63518i	0.575802	−	0.817589i	$-0.304690\pi$
$158$	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	$0.278338\pi$
$179$			20.5282i			1.53435i	−0.641439	+	0.767174i	$0.721662\pi$
$180$		0			0
$181$			9.96062i			0.740367i	0.928959	+	0.370184i	$0.120705\pi$
$181$			9.96062i			0.740367i	−0.928959	+	0.370184i	$0.879295\pi$
$182$	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	$0.00711567\pi$
$199$			0.630646i			0.0447053i	−0.999750	+	0.0223527i	$0.992884\pi$
$200$	−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	$-0.923518\pi$
$223$		−	7.10727i		−	0.475938i	0.971273	−	0.237969i	$-0.0764816\pi$
$224$	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	$-0.864282\pi$
$227$		−	12.4621i		−	0.827138i	0.910473	−	0.413569i	$-0.135718\pi$
$228$		0			0
$229$			9.76872i			0.645535i	0.946478	+	0.322768i	$0.104613\pi$
$229$			9.76872i			0.645535i	−0.946478	+	0.322768i	$0.895387\pi$
$230$	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	$-0.951180\pi$
$233$		−	4.66388i		−	0.305541i	0.988262	−	0.152771i	$-0.0488196\pi$
$234$		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	$-0.779523\pi$
$251$		−	20.2340i		−	1.27716i	0.769556	−	0.638579i	$-0.220477\pi$
$252$		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	$0.0116791\pi$
$257$			1.17614i			0.0733655i	−0.999327	+	0.0366828i	$0.988321\pi$
$258$		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	$0.108335\pi$
$271$			10.9905i			0.667625i	−0.942639	+	0.333813i	$0.891665\pi$
$272$	−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	$-0.965490\pi$
$277$		−	3.60170i		−	0.216405i	0.994129	−	0.108203i	$-0.0345096\pi$
$278$	−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	$0.119309\pi$
$281$			12.2741i			0.732209i	−0.930574	+	0.366104i	$0.880691\pi$
$282$		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	$0.0588062\pi$
$347$			6.84376i			0.367392i	−0.982983	+	0.183696i	$0.941194\pi$
$348$		0			0
$349$		−	14.4443i		−	0.773183i	−0.922251	−	0.386592i	$-0.873652\pi$
$349$		−	14.4443i		−	0.773183i	0.922251	−	0.386592i	$-0.126348\pi$
$350$	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	$-0.861092\pi$
$353$		−	15.8826i		−	0.845343i	0.906283	−	0.422671i	$-0.138908\pi$
$354$		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	$0.255717\pi$
$367$			27.5746i			1.43938i	−0.694294	+	0.719692i	$0.744283\pi$
$368$	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	$0.0671808\pi$
$373$			8.09190i			0.418982i	−0.977811	+	0.209491i	$0.932819\pi$
$374$	−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	$0.230303\pi$
$397$			26.3815i			1.32405i	−0.749481	+	0.662026i	$0.769697\pi$
$398$	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	$0.0102641\pi$
$401$			1.29121i			0.0644801i	−0.999480	+	0.0322401i	$0.989736\pi$
$402$		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	$-0.881164\pi$
$419$		−	14.9313i		−	0.729444i	0.931116	−	0.364722i	$-0.118836\pi$
$420$		0			0
$421$		−	14.8896i		−	0.725673i	−0.931853	−	0.362836i	$-0.881808\pi$
$421$		−	14.8896i		−	0.725673i	0.931853	−	0.362836i	$-0.118192\pi$
$422$	−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	$-0.990506\pi$
$439$		−	1.24969i		−	0.0596443i	0.999555	−	0.0298221i	$-0.00949409\pi$
$440$	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	$-0.774124\pi$
$443$		−	27.4266i		−	1.30308i	0.758616	−	0.651538i	$-0.225876\pi$
$444$		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	$-0.874696\pi$
$449$		−	16.2552i		−	0.767132i	0.923513	−	0.383566i	$-0.125304\pi$
$450$		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	$0.0173313\pi$
$463$			2.34200i			0.108842i	−0.998518	+	0.0544209i	$0.982669\pi$
$464$	−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	$0.0911153\pi$
$467$			12.2034i			0.564708i	−0.959310	+	0.282354i	$0.908885\pi$
$468$		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	$-0.860056\pi$
$487$		−	18.7853i		−	0.851242i	0.904902	−	0.425621i	$-0.139944\pi$
$488$	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	$0.00883110\pi$
$491$			1.22936i			0.0554803i	−0.999615	+	0.0277402i	$0.991169\pi$
$492$		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	$0.0631136\pi$
$521$			8.99232i			0.393961i	−0.980407	+	0.196980i	$0.936886\pi$
$522$		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	$-0.689136\pi$
$541$		−	38.5456i		−	1.65721i	0.559836	−	0.828603i	$-0.310864\pi$
$542$	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	$-0.664417\pi$
$563$		−	41.2641i		−	1.73907i	0.493867	−	0.869537i	$-0.335583\pi$
$564$		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	$0.203596\pi$
$569$			28.4760i			1.19378i	−0.802325	+	0.596888i	$0.796404\pi$
$570$		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	$0.125836\pi$
$587$			18.6609i			0.770217i	−0.922871	+	0.385109i	$0.874164\pi$
$588$		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	$0.00442175\pi$
$593$			0.676531i			0.0277818i	−0.999904	+	0.0138909i	$0.995578\pi$
$594$		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	$0.0152381\pi$
$607$			2.35798i			0.0957075i	−0.998854	+	0.0478537i	$0.984762\pi$
$608$	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	$-0.840546\pi$
$613$		−	23.7808i		−	0.960497i	0.877132	−	0.480249i	$-0.159454\pi$
$614$	−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	$-0.976489\pi$
$617$		−	3.66608i		−	0.147591i	0.997273	−	0.0737954i	$-0.0235112\pi$
$618$		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	$-0.856251\pi$
$631$		−	21.9248i		−	0.872811i	0.899750	−	0.436405i	$-0.143749\pi$
$632$	−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	$-0.864916\pi$
$641$		−	20.8495i		−	0.823507i	0.911295	−	0.411754i	$-0.135084\pi$
$642$		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	$-0.916024\pi$
$659$		−	13.3884i		−	0.521538i	0.965401	−	0.260769i	$-0.0839760\pi$
$660$		0			0
$661$			16.7021i			0.649635i	0.945777	+	0.324818i	$0.105303\pi$
$661$			16.7021i			0.649635i	−0.945777	+	0.324818i	$0.894697\pi$
$662$	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	$-0.754217\pi$
$683$		−	36.4666i		−	1.39536i	0.716412	−	0.697678i	$-0.245783\pi$
$684$		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	$-0.776951\pi$
$709$		−	34.3370i		−	1.28955i	0.764371	−	0.644776i	$-0.223049\pi$
$710$	−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	$0.257179\pi$
$727$			38.9815i			1.44575i	−0.690981	+	0.722873i	$0.742821\pi$
$728$	−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	$0.234642\pi$
$733$			36.3971i			1.34436i	−0.740388	+	0.672179i	$0.765358\pi$
$734$	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	$0.0288304\pi$
$751$			4.95743i			0.180899i	−0.995901	+	0.0904496i	$0.971170\pi$
$752$	−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	$-0.999214\pi$
$757$		−	0.135856i		−	0.00493778i	0.999997	−	0.00246889i	$-0.000785872\pi$
$758$	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	$-0.987608\pi$
$761$		−	2.14729i		−	0.0778390i	0.999242	−	0.0389195i	$-0.0123916\pi$
$762$		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	$0.156286\pi$
$809$			26.8216i			0.942996i	−0.881867	+	0.471498i	$0.843714\pi$
$810$		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	$-0.814921\pi$
$823$		−	31.5126i		−	1.09846i	0.835671	−	0.549230i	$-0.185079\pi$
$824$	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	$0.0892077\pi$
$827$			15.9087i			0.553200i	−0.960985	+	0.276600i	$0.910792\pi$
$828$		0			0
$829$			40.2678i			1.39856i	0.714848	+	0.699280i	$0.246496\pi$
$829$			40.2678i			1.39856i	−0.714848	+	0.699280i	$0.753504\pi$
$830$	−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	$-0.812237\pi$
$853$		−	32.4923i		−	1.11252i	0.831009	−	0.556258i	$-0.187763\pi$
$854$	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	$0.136709\pi$
$857$			24.3799i			0.832801i	−0.909181	+	0.416400i	$0.863291\pi$
$858$		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	$0.0371093\pi$
$877$			6.88935i			0.232637i	−0.993212	+	0.116318i	$0.962891\pi$
$878$	−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	$-0.731696\pi$
$881$		−	44.3192i		−	1.49315i	0.665300	−	0.746576i	$-0.268304\pi$
$882$		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	$-0.877816\pi$
$919$		−	22.7057i		−	0.748991i	0.927229	−	0.374495i	$-0.122184\pi$
$920$	−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	$0.239402\pi$
$929$			41.6457i			1.36635i	−0.730254	+	0.683176i	$0.760598\pi$
$930$		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	$0.0697462\pi$
$947$			13.3781i			0.434730i	−0.976090	+	0.217365i	$0.930254\pi$
$948$		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	$-0.798511\pi$
$953$		−	36.5239i		−	1.18313i	0.806259	−	0.591563i	$-0.201489\pi$
$954$		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	$0.117297\pi$
$967$			22.4030i			0.720430i	−0.932869	+	0.360215i	$0.882703\pi$
$968$	−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	$-0.817633\pi$
$971$		−	33.7841i		−	1.08418i	0.840320	−	0.542091i	$-0.182367\pi$
$972$		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	$-0.924803\pi$
$977$		−	14.6312i		−	0.468094i	0.972225	−	0.234047i	$-0.0751969\pi$
$978$		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	$0.134036\pi$
$991$			25.7352i			0.817504i	−0.912645	+	0.408752i	$0.865964\pi$
$992$	−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	$0.209129\pi$
$997$			38.5688i			1.22149i	−0.791829	+	0.610743i	$0.790871\pi$
$998$	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.323.9	✓	24
3.2	odd	2	inner	648.2.f.c.323.16	yes	24
4.3	odd	2		2592.2.f.c.1295.11		24
8.3	odd	2	inner	648.2.f.c.323.15	yes	24
8.5	even	2		2592.2.f.c.1295.14		24
9.2	odd	6		648.2.l.g.539.18		48
9.4	even	3		648.2.l.g.107.23		48
9.5	odd	6		648.2.l.g.107.2		48
9.7	even	3		648.2.l.g.539.7		48
12.11	even	2		2592.2.f.c.1295.13		24
24.5	odd	2		2592.2.f.c.1295.12		24
24.11	even	2	inner	648.2.f.c.323.10	yes	24
36.7	odd	6		2592.2.p.g.2159.13		48
36.11	even	6		2592.2.p.g.2159.11		48
36.23	even	6		2592.2.p.g.431.12		48
36.31	odd	6		2592.2.p.g.431.14		48
72.5	odd	6		2592.2.p.g.431.13		48
72.11	even	6		648.2.l.g.539.23		48
72.13	even	6		2592.2.p.g.431.11		48
72.29	odd	6		2592.2.p.g.2159.14		48
72.43	odd	6		648.2.l.g.539.2		48
72.59	even	6		648.2.l.g.107.7		48
72.61	even	6		2592.2.p.g.2159.12		48
72.67	odd	6		648.2.l.g.107.18		48

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

Properties

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