LMFDB - Embedded newform 1512.2.c.d.757.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1512,2,Mod(757,1512)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1512, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 1, 0, 0]))

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

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

chi := DirichletCharacter("1512.757");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1512 = 2^{3} \cdot 3^{3} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1512.c (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:	$12.0733807856$
Analytic rank:	$0$
Dimension:	$16$
Coefficient field:	$\Q(\zeta_{40})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - x^{12} + x^{8} - x^{4} + 1 $ x^16 - x^12 + x^8 - x^4 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 2^{8}\cdot 3^{8} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			757.4
Root			$0.453990 - 0.891007i$ of defining polynomial
Character	$\chi$	$=$	1512.757
Dual form			1512.2.c.d.757.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.14412 + 0.831254i) q^{2} +(0.618034 - 1.90211i) q^{4} +1.60758i q^{5} -1.00000 q^{7} +(0.874032 + 2.68999i) q^{8} +O(q^{10})$	\(q+(-1.14412 + 0.831254i) q^{2} +(0.618034 - 1.90211i) q^{4} +1.60758i q^{5} -1.00000 q^{7} +(0.874032 + 2.68999i) q^{8} +(-1.33630 - 1.83927i) q^{10} -0.0549306i q^{11} -3.75621i q^{13} +(1.14412 - 0.831254i) q^{14} +(-3.23607 - 2.35114i) q^{16} -3.16228 q^{17} -0.726543i q^{19} +(3.05779 + 0.993537i) q^{20} +(0.0456612 + 0.0628473i) q^{22} +7.77604 q^{23} +2.41570 q^{25} +(3.12237 + 4.29757i) q^{26} +(-0.618034 + 1.90211i) q^{28} -2.75789i q^{29} -2.14475 q^{31} +5.65685 q^{32} +(3.61803 - 2.62866i) q^{34} -1.60758i q^{35} -0.600848i q^{37} +(0.603941 + 0.831254i) q^{38} +(-4.32437 + 1.40507i) q^{40} +4.53658 q^{41} -6.85004i q^{43} +(-0.104484 - 0.0339490i) q^{44} +(-8.89675 + 6.46386i) q^{46} +0.744883 q^{47} +1.00000 q^{49} +(-2.76385 + 2.00806i) q^{50} +(-7.14475 - 2.32147i) q^{52} +10.5822i q^{53} +0.0883051 q^{55} +(-0.874032 - 2.68999i) q^{56} +(2.29251 + 3.15537i) q^{58} -2.58013i q^{59} +9.80423i q^{61} +(2.45385 - 1.78283i) q^{62} +(-6.47214 + 4.70228i) q^{64} +6.03841 q^{65} -12.2627i q^{67} +(-1.95440 + 6.01501i) q^{68} +(1.33630 + 1.83927i) q^{70} +9.19025 q^{71} +3.85224 q^{73} +(0.499457 + 0.687444i) q^{74} +(-1.38197 - 0.449028i) q^{76} +0.0549306i q^{77} +10.9057 q^{79} +(3.77964 - 5.20223i) q^{80} +(-5.19041 + 3.77105i) q^{82} -13.1624i q^{83} -5.08361i q^{85} +(5.69413 + 7.83729i) q^{86} +(0.147763 - 0.0480111i) q^{88} -7.90356 q^{89} +3.75621i q^{91} +(4.80586 - 14.7909i) q^{92} +(-0.852237 + 0.619187i) q^{94} +1.16797 q^{95} +12.1803 q^{97} +(-1.14412 + 0.831254i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 8 q^{4} - 16 q^{7}+O(q^{10}) $ 16 * q - 8 * q^4 - 16 * q^7	$ 16 q - 8 q^{4} - 16 q^{7} - 20 q^{10} - 16 q^{16} + 20 q^{22} - 32 q^{25} + 8 q^{28} + 40 q^{31} + 40 q^{34} + 40 q^{40} + 4 q^{46} + 16 q^{49} - 40 q^{52} - 72 q^{55} - 32 q^{64} + 20 q^{70} + 24 q^{73} - 40 q^{76} + 24 q^{79} - 28 q^{82} + 40 q^{88} + 24 q^{94} + 16 q^{97}+O(q^{100}) $ 16 * q - 8 * q^4 - 16 * q^7 - 20 * q^10 - 16 * q^16 + 20 * q^22 - 32 * q^25 + 8 * q^28 + 40 * q^31 + 40 * q^34 + 40 * q^40 + 4 * q^46 + 16 * q^49 - 40 * q^52 - 72 * q^55 - 32 * q^64 + 20 * q^70 + 24 * q^73 - 40 * q^76 + 24 * q^79 - 28 * q^82 + 40 * q^88 + 24 * q^94 + 16 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1512\mathbb{Z}\right)^\times$.

$n$	$757$	$785$	$1081$	$1135$
$\chi(n)$	$-1$	$1$	$1$	$1$

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 $

$2$	−1.14412	+	0.831254i	−0.809017	+	0.587785i
$2$	−1.14412	+	0.831254i	−0.809017	+	0.587785i
$3$		0			0
$3$		0			0
$4$	0.618034	−	1.90211i	0.309017	−	0.951057i
$5$			1.60758i			0.718930i	0.933158	+	0.359465i	$0.117041\pi$
$5$			1.60758i			0.718930i	−0.933158	+	0.359465i	$0.882959\pi$
$6$		0			0
$7$	−1.00000			−0.377964
$7$	−1.00000			−0.377964
$8$	0.874032	+	2.68999i	0.309017	+	0.951057i
$9$		0			0
$10$	−1.33630	−	1.83927i	−0.422577	−	0.581627i
$11$		−	0.0549306i		−	0.0165622i	−0.999966	−	0.00828109i	$-0.997364\pi$
$11$		−	0.0549306i		−	0.0165622i	0.999966	−	0.00828109i	$-0.00263598\pi$
$12$		0			0
$13$		−	3.75621i		−	1.04179i	−0.853622	−	0.520893i	$-0.825599\pi$
$13$		−	3.75621i		−	1.04179i	0.853622	−	0.520893i	$-0.174401\pi$
$14$	1.14412	−	0.831254i	0.305780	−	0.222162i
$15$		0			0
$16$	−3.23607	−	2.35114i	−0.809017	−	0.587785i
$17$	−3.16228			−0.766965			−0.383482	−	0.923548i	$-0.625275\pi$
$17$	−3.16228			−0.766965			−0.383482	+	0.923548i	$0.625275\pi$
$18$		0			0
$19$		−	0.726543i		−	0.166680i	−0.996521	−	0.0833401i	$-0.973441\pi$
$19$		−	0.726543i		−	0.166680i	0.996521	−	0.0833401i	$-0.0265588\pi$
$20$	3.05779	+	0.993537i	0.683743	+	0.222162i
$21$		0			0
$22$	0.0456612	+	0.0628473i	0.00973501	+	0.0133991i
$23$	7.77604			1.62142			0.810708	−	0.585450i	$-0.199082\pi$
$23$	7.77604			1.62142			0.810708	+	0.585450i	$0.199082\pi$
$24$		0			0
$25$	2.41570			0.483139
$26$	3.12237	+	4.29757i	0.612347	+	0.842823i
$27$		0			0
$28$	−0.618034	+	1.90211i	−0.116797	+	0.359466i
$29$		−	2.75789i		−	0.512128i	−0.966660	−	0.256064i	$-0.917574\pi$
$29$		−	2.75789i		−	0.512128i	0.966660	−	0.256064i	$-0.0824257\pi$
$30$		0			0
$31$	−2.14475			−0.385208			−0.192604	−	0.981277i	$-0.561693\pi$
$31$	−2.14475			−0.385208			−0.192604	+	0.981277i	$0.561693\pi$
$32$	5.65685			1.00000
$33$		0			0
$34$	3.61803	−	2.62866i	0.620488	−	0.450811i
$35$		−	1.60758i		−	0.271730i
$36$		0			0
$37$		−	0.600848i		−	0.0987788i	−0.998780	−	0.0493894i	$-0.984272\pi$
$37$		−	0.600848i		−	0.0987788i	0.998780	−	0.0493894i	$-0.0157275\pi$
$38$	0.603941	+	0.831254i	0.0979722	+	0.134847i
$39$		0			0
$40$	−4.32437	+	1.40507i	−0.683743	+	0.222162i
$41$	4.53658			0.708495			0.354248	−	0.935152i	$-0.384737\pi$
$41$	4.53658			0.708495			0.354248	+	0.935152i	$0.384737\pi$
$42$		0			0
$43$		−	6.85004i		−	1.04462i	−0.852755	−	0.522311i	$-0.825070\pi$
$43$		−	6.85004i		−	1.04462i	0.852755	−	0.522311i	$-0.174930\pi$
$44$	−0.104484	−	0.0339490i	−0.0157516	−	0.00511800i
$45$		0			0
$46$	−8.89675	+	6.46386i	−1.31175	+	0.953045i
$47$	0.744883			0.108652			0.0543261	−	0.998523i	$-0.482699\pi$
$47$	0.744883			0.108652			0.0543261	+	0.998523i	$0.482699\pi$
$48$		0			0
$49$	1.00000			0.142857
$50$	−2.76385	+	2.00806i	−0.390868	+	0.283982i
$51$		0			0
$52$	−7.14475	−	2.32147i	−0.990798	−	0.321930i
$53$			10.5822i			1.45358i	0.686860	+	0.726790i	$0.258989\pi$
$53$			10.5822i			1.45358i	−0.686860	+	0.726790i	$0.741011\pi$
$54$		0			0
$55$	0.0883051			0.0119071
$56$	−0.874032	−	2.68999i	−0.116797	−	0.359466i
$57$		0			0
$58$	2.29251	+	3.15537i	0.301021	+	0.414320i
$59$		−	2.58013i		−	0.335905i	−0.985795	−	0.167952i	$-0.946285\pi$
$59$		−	2.58013i		−	0.335905i	0.985795	−	0.167952i	$-0.0537155\pi$
$60$		0			0
$61$			9.80423i			1.25530i	0.778495	+	0.627651i	$0.215984\pi$
$61$			9.80423i			1.25530i	−0.778495	+	0.627651i	$0.784016\pi$
$62$	2.45385	−	1.78283i	0.311640	−	0.226419i
$63$		0			0
$64$	−6.47214	+	4.70228i	−0.809017	+	0.587785i
$65$	6.03841			0.748972
$66$		0			0
$67$		−	12.2627i		−	1.49813i	−0.662496	−	0.749065i	$-0.730503\pi$
$67$		−	12.2627i		−	1.49813i	0.662496	−	0.749065i	$-0.269497\pi$
$68$	−1.95440	+	6.01501i	−0.237005	+	0.729427i
$69$		0			0
$70$	1.33630	+	1.83927i	0.159719	+	0.219834i
$71$	9.19025			1.09068			0.545341	−	0.838214i	$-0.316400\pi$
$71$	9.19025			1.09068			0.545341	+	0.838214i	$0.316400\pi$
$72$		0			0
$73$	3.85224			0.450870			0.225435	−	0.974258i	$-0.427620\pi$
$73$	3.85224			0.450870			0.225435	+	0.974258i	$0.427620\pi$
$74$	0.499457	+	0.687444i	0.0580607	+	0.0799137i
$75$		0			0
$76$	−1.38197	−	0.449028i	−0.158522	−	0.0515070i
$77$			0.0549306i			0.00625992i
$78$		0			0
$79$	10.9057			1.22698			0.613491	−	0.789701i	$-0.289765\pi$
$79$	10.9057			1.22698			0.613491	+	0.789701i	$0.289765\pi$
$80$	3.77964	−	5.20223i	0.422577	−	0.581627i
$81$		0			0
$82$	−5.19041	+	3.77105i	−0.573185	+	0.416443i
$83$		−	13.1624i		−	1.44476i	−0.691499	−	0.722378i	$-0.743049\pi$
$83$		−	13.1624i		−	1.44476i	0.691499	−	0.722378i	$-0.256951\pi$
$84$		0			0
$85$		−	5.08361i		−	0.551394i
$86$	5.69413	+	7.83729i	0.614013	+	0.845117i
$87$		0			0
$88$	0.147763	−	0.0480111i	0.0157516	−	0.00511800i
$89$	−7.90356			−0.837776			−0.418888	−	0.908038i	$-0.637580\pi$
$89$	−7.90356			−0.837776			−0.418888	+	0.908038i	$0.637580\pi$
$90$		0			0
$91$			3.75621i			0.393758i
$92$	4.80586	−	14.7909i	0.501045	−	1.54206i
$93$		0			0
$94$	−0.852237	+	0.619187i	−0.0879015	+	0.0638642i
$95$	1.16797			0.119832
$96$		0			0
$97$	12.1803			1.23673			0.618363	−	0.785893i	$-0.287796\pi$
$97$	12.1803			1.23673			0.618363	+	0.785893i	$0.287796\pi$
$98$	−1.14412	+	0.831254i	−0.115574	+	0.0839693i
$99$		0			0
$100$	1.49298	−	4.59493i	0.149298	−	0.459493i
$101$			4.35250i			0.433090i	0.976273	+	0.216545i	$0.0694788\pi$
$101$			4.35250i			0.433090i	−0.976273	+	0.216545i	$0.930521\pi$
$102$		0			0
$103$	17.5574			1.72998			0.864992	−	0.501785i	$-0.167323\pi$
$103$	17.5574			1.72998			0.864992	+	0.501785i	$0.167323\pi$
$104$	10.1042	−	3.28305i	0.990798	−	0.321930i
$105$		0			0
$106$	−8.79651	−	12.1074i	−0.854392	−	1.17597i
$107$			6.44944i			0.623491i	0.950166	+	0.311745i	$0.100914\pi$
$107$			6.44944i			0.623491i	−0.950166	+	0.311745i	$0.899086\pi$
$108$		0			0
$109$		−	2.03559i		−	0.194975i	−0.995237	−	0.0974873i	$-0.968919\pi$
$109$		−	2.03559i		−	0.194975i	0.995237	−	0.0974873i	$-0.0310805\pi$
$110$	−0.101032	+	0.0734040i	−0.00963301	+	0.00699879i
$111$		0			0
$112$	3.23607	+	2.35114i	0.305780	+	0.222162i
$113$	2.61946			0.246418			0.123209	−	0.992381i	$-0.460681\pi$
$113$	2.61946			0.246418			0.123209	+	0.992381i	$0.460681\pi$
$114$		0			0
$115$			12.5006i			1.16569i
$116$	−5.24582	−	1.70447i	−0.487062	−	0.158256i
$117$		0			0
$118$	2.14475	+	2.95199i	0.197440	+	0.271753i
$119$	3.16228			0.289886
$120$		0			0
$121$	10.9970			0.999726
$122$	−8.14980	−	11.2172i	−0.737848	−	1.01556i
$123$		0			0
$124$	−1.32553	+	4.07955i	−0.119036	+	0.366354i
$125$			11.9213i			1.06627i
$126$		0			0
$127$	−13.6733			−1.21331			−0.606656	−	0.794965i	$-0.707489\pi$
$127$	−13.6733			−1.21331			−0.606656	+	0.794965i	$0.707489\pi$
$128$	3.49613	−	10.7600i	0.309017	−	0.951057i
$129$		0			0
$130$	−6.90868	+	5.01945i	−0.605931	+	0.440235i
$131$		−	11.2592i		−	0.983721i	−0.870674	−	0.491861i	$-0.836317\pi$
$131$		−	11.2592i		−	0.983721i	0.870674	−	0.491861i	$-0.163683\pi$
$132$		0			0
$133$			0.726543i			0.0629992i
$134$	10.1934	+	14.0301i	0.880579	+	1.21201i
$135$		0			0
$136$	−2.76393	−	8.50651i	−0.237005	−	0.729427i
$137$	1.00318			0.0857076			0.0428538	−	0.999081i	$-0.486355\pi$
$137$	1.00318			0.0857076			0.0428538	+	0.999081i	$0.486355\pi$
$138$		0			0
$139$		−	2.60253i		−	0.220744i	−0.993890	−	0.110372i	$-0.964796\pi$
$139$		−	2.60253i		−	0.220744i	0.993890	−	0.110372i	$-0.0352042\pi$
$140$	−3.05779	−	0.993537i	−0.258431	−	0.0839692i
$141$		0			0
$142$	−10.5148	+	7.63943i	−0.882381	+	0.641087i
$143$	−0.206331			−0.0172543
$144$		0			0
$145$	4.43352			0.368184
$146$	−4.40743	+	3.20219i	−0.364762	+	0.265015i
$147$		0			0
$148$	−1.14288	−	0.371344i	−0.0939442	−	0.0305243i
$149$			19.1514i			1.56895i	0.620163	+	0.784473i	$0.287066\pi$
$149$			19.1514i			1.56895i	−0.620163	+	0.784473i	$0.712934\pi$
$150$		0			0
$151$	15.8848			1.29269			0.646344	−	0.763046i	$-0.276297\pi$
$151$	15.8848			1.29269			0.646344	+	0.763046i	$0.276297\pi$
$152$	1.95440	−	0.635021i	0.158522	−	0.0515070i
$153$		0			0
$154$	−0.0456612	−	0.0628473i	−0.00367949	−	0.00506438i
$155$		−	3.44784i		−	0.276937i
$156$		0			0
$157$		−	14.7099i		−	1.17398i	−0.809595	−	0.586988i	$-0.800313\pi$
$157$		−	14.7099i		−	1.17398i	0.809595	−	0.586988i	$-0.199687\pi$
$158$	−12.4774	+	9.06537i	−0.992650	+	0.721202i
$159$		0			0
$160$			9.09383i			0.718930i
$161$	−7.77604			−0.612838
$162$		0			0
$163$			9.69687i			0.759517i	0.925086	+	0.379759i	$0.123993\pi$
$163$			9.69687i			0.759517i	−0.925086	+	0.379759i	$0.876007\pi$
$164$	2.80376	−	8.62909i	0.218937	−	0.673819i
$165$		0			0
$166$	10.9413	+	15.0593i	0.849206	+	1.16883i
$167$	2.57013			0.198882			0.0994412	−	0.995043i	$-0.468294\pi$
$167$	2.57013			0.198882			0.0994412	+	0.995043i	$0.468294\pi$
$168$		0			0
$169$	−1.10915			−0.0853193
$170$	4.22577	+	5.81627i	0.324102	+	0.446087i
$171$		0			0
$172$	−13.0296	−	4.23356i	−0.993495	−	0.322806i
$173$		−	1.69460i		−	0.128838i	−0.997923	−	0.0644192i	$-0.979481\pi$
$173$		−	1.69460i		−	0.128838i	0.997923	−	0.0644192i	$-0.0205195\pi$
$174$		0			0
$175$	−2.41570			−0.182609
$176$	−0.129149	+	0.177759i	−0.00973501	+	0.0133991i
$177$		0			0
$178$	9.04264	−	6.56987i	0.677775	−	0.492432i
$179$			11.1383i			0.832518i	0.909246	+	0.416259i	$0.136659\pi$
$179$			11.1383i			0.832518i	−0.909246	+	0.416259i	$0.863341\pi$
$180$		0			0
$181$			6.80203i			0.505591i	0.967520	+	0.252796i	$0.0813500\pi$
$181$			6.80203i			0.505591i	−0.967520	+	0.252796i	$0.918650\pi$
$182$	−3.12237	−	4.29757i	−0.231445	−	0.318557i
$183$		0			0
$184$	6.79651	+	20.9175i	0.501045	+	1.54206i
$185$	0.965909			0.0710151
$186$		0			0
$187$			0.173706i			0.0127026i
$188$	0.460363	−	1.41685i	0.0335754	−	0.103334i
$189$		0			0
$190$	−1.33630	+	0.970882i	−0.0969457	+	0.0704352i
$191$	15.6397			1.13165			0.565824	−	0.824526i	$-0.308558\pi$
$191$	15.6397			1.13165			0.565824	+	0.824526i	$0.308558\pi$
$192$		0			0
$193$	19.5893			1.41007			0.705034	−	0.709174i	$-0.250932\pi$
$193$	19.5893			1.41007			0.705034	+	0.709174i	$0.250932\pi$
$194$	−13.9358	+	10.1250i	−1.00053	+	0.726929i
$195$		0			0
$196$	0.618034	−	1.90211i	0.0441453	−	0.135865i
$197$		−	7.29916i		−	0.520044i	−0.965603	−	0.260022i	$-0.916270\pi$
$197$		−	7.29916i		−	0.520044i	0.965603	−	0.260022i	$-0.0837298\pi$
$198$		0			0
$199$	13.8002			0.978273			0.489136	−	0.872207i	$-0.337312\pi$
$199$	13.8002			0.978273			0.489136	+	0.872207i	$0.337312\pi$
$200$	2.11140	+	6.49821i	0.149298	+	0.459493i
$201$		0			0
$202$	−3.61803	−	4.97980i	−0.254564	−	0.350377i
$203$			2.75789i			0.193566i
$204$		0			0
$205$			7.29291i			0.509359i
$206$	−20.0878	+	14.5947i	−1.39959	+	1.01686i
$207$		0			0
$208$	−8.83139	+	12.1554i	−0.612347	+	0.842823i
$209$	−0.0399094			−0.00276059
$210$		0			0
$211$		−	5.25731i		−	0.361928i	−0.983490	−	0.180964i	$-0.942078\pi$
$211$		−	5.25731i		−	0.361928i	0.983490	−	0.180964i	$-0.0579218\pi$
$212$	20.1286	+	6.54017i	1.38244	+	0.449181i
$213$		0			0
$214$	−5.36112	−	7.37895i	−0.366479	−	0.504415i
$215$	11.0120			0.751011
$216$		0			0
$217$	2.14475			0.145595
$218$	1.69210	+	2.32897i	0.114603	+	0.157738i
$219$		0			0
$220$	0.0545756	−	0.167966i	0.00367948	−	0.0113243i
$221$			11.8782i			0.799014i
$222$		0			0
$223$	4.96512			0.332489			0.166244	−	0.986085i	$-0.446836\pi$
$223$	4.96512			0.332489			0.166244	+	0.986085i	$0.446836\pi$
$224$	−5.65685			−0.377964
$225$		0			0
$226$	−2.99698	+	2.17744i	−0.199356	+	0.144841i
$227$		−	15.1773i		−	1.00735i	−0.863893	−	0.503676i	$-0.831981\pi$
$227$		−	15.1773i		−	1.00735i	0.863893	−	0.503676i	$-0.168019\pi$
$228$		0			0
$229$		−	5.69636i		−	0.376426i	−0.982128	−	0.188213i	$-0.939730\pi$
$229$		−	5.69636i		−	0.376426i	0.982128	−	0.188213i	$-0.0602695\pi$
$230$	−10.3912	−	14.3022i	−0.685173	−	0.943060i
$231$		0			0
$232$	7.41871	−	2.41049i	0.487062	−	0.158256i
$233$	−16.5086			−1.08151			−0.540756	−	0.841179i	$-0.681862\pi$
$233$	−16.5086			−1.08151			−0.540756	+	0.841179i	$0.681862\pi$
$234$		0			0
$235$			1.19746i			0.0781134i
$236$	−4.90770	−	1.59461i	−0.319464	−	0.103800i
$237$		0			0
$238$	−3.61803	+	2.62866i	−0.234522	+	0.170390i
$239$	−15.1437			−0.979564			−0.489782	−	0.871845i	$-0.662924\pi$
$239$	−15.1437			−0.979564			−0.489782	+	0.871845i	$0.662924\pi$
$240$		0			0
$241$	−28.5047			−1.83615			−0.918075	−	0.396407i	$-0.870257\pi$
$241$	−28.5047			−1.83615			−0.918075	+	0.396407i	$0.870257\pi$
$242$	−12.5819	+	9.14128i	−0.808795	+	0.587624i
$243$		0			0
$244$	18.6487	+	6.05934i	1.19386	+	0.387910i
$245$			1.60758i			0.102704i
$246$		0			0
$247$	−2.72905			−0.173645
$248$	−1.87458	−	5.76935i	−0.119036	−	0.366354i
$249$		0			0
$250$	−9.90963	−	13.6394i	−0.626740	−	0.862634i
$251$		−	7.18930i		−	0.453785i	−0.973920	−	0.226892i	$-0.927143\pi$
$251$		−	7.18930i		−	0.453785i	0.973920	−	0.226892i	$-0.0728566\pi$
$252$		0			0
$253$		−	0.427142i		−	0.0268542i
$254$	15.6440	−	11.3660i	0.981589	−	0.713166i
$255$		0			0
$256$	4.94427	+	15.2169i	0.309017	+	0.951057i
$257$	−30.4469			−1.89922			−0.949612	−	0.313427i	$-0.898523\pi$
$257$	−30.4469			−1.89922			−0.949612	+	0.313427i	$0.898523\pi$
$258$		0			0
$259$			0.600848i			0.0373349i
$260$	3.73194	−	11.4857i	0.231445	−	0.712315i
$261$		0			0
$262$	9.35926	+	12.8819i	0.578217	+	0.795847i
$263$	−8.28410			−0.510820			−0.255410	−	0.966833i	$-0.582210\pi$
$263$	−8.28410			−0.510820			−0.255410	+	0.966833i	$0.582210\pi$
$264$		0			0
$265$	−17.0117			−1.04502
$266$	−0.603941	−	0.831254i	−0.0370300	−	0.0509674i
$267$		0			0
$268$	−23.3251	−	7.57878i	−1.42481	−	0.462948i
$269$		−	7.16222i		−	0.436689i	−0.975872	−	0.218344i	$-0.929934\pi$
$269$		−	7.16222i		−	0.436689i	0.975872	−	0.218344i	$-0.0700656\pi$
$270$		0			0
$271$	12.4721			0.757628			0.378814	−	0.925473i	$-0.376332\pi$
$271$	12.4721			0.757628			0.378814	+	0.925473i	$0.376332\pi$
$272$	10.2333	+	7.43496i	0.620488	+	0.450811i
$273$		0			0
$274$	−1.14776	+	0.833899i	−0.0693389	+	0.0503777i
$275$		−	0.132696i		−	0.00800184i
$276$		0			0
$277$		−	8.91531i		−	0.535669i	−0.963465	−	0.267835i	$-0.913692\pi$
$277$		−	8.91531i		−	0.535669i	0.963465	−	0.267835i	$-0.0863081\pi$
$278$	2.16336	+	2.97761i	0.129750	+	0.178585i
$279$		0			0
$280$	4.32437	−	1.40507i	0.258431	−	0.0839692i
$281$	−12.3577			−0.737198			−0.368599	−	0.929589i	$-0.620162\pi$
$281$	−12.3577			−0.737198			−0.368599	+	0.929589i	$0.620162\pi$
$282$		0			0
$283$		−	21.4245i		−	1.27356i	−0.771047	−	0.636778i	$-0.780267\pi$
$283$		−	21.4245i		−	1.27356i	0.771047	−	0.636778i	$-0.219733\pi$
$284$	5.67989	−	17.4809i	0.337039	−	1.03730i
$285$		0			0
$286$	0.236068	−	0.171513i	0.0139590	−	0.0101418i
$287$	−4.53658			−0.267786
$288$		0			0
$289$	−7.00000			−0.411765
$290$	−5.07250	+	3.68538i	−0.297867	+	0.216413i
$291$		0			0
$292$	2.38081	−	7.32739i	0.139327	−	0.428803i
$293$			0.0647976i			0.00378552i	0.999998	+	0.00189276i	$0.000602484\pi$
$293$			0.0647976i			0.00378552i	−0.999998	+	0.00189276i	$0.999398\pi$
$294$		0			0
$295$	4.14776			0.241492
$296$	1.61628	−	0.525160i	0.0939442	−	0.0305243i
$297$		0			0
$298$	−15.9197	−	21.9116i	−0.922203	−	1.26930i
$299$		−	29.2085i		−	1.68917i
$300$		0			0
$301$			6.85004i			0.394830i
$302$	−18.1742	+	13.2043i	−1.04581	+	0.759823i
$303$		0			0
$304$	−1.70820	+	2.35114i	−0.0979722	+	0.134847i
$305$	−15.7611			−0.902475
$306$		0			0
$307$			15.8474i			0.904460i	0.891901	+	0.452230i	$0.149371\pi$
$307$			15.8474i			0.904460i	−0.891901	+	0.452230i	$0.850629\pi$
$308$	0.104484	+	0.0339490i	0.00595354	+	0.00193442i
$309$		0			0
$310$	2.86603	+	3.94476i	0.162780	+	0.224047i
$311$	−13.0254			−0.738602			−0.369301	−	0.929310i	$-0.620403\pi$
$311$	−13.0254			−0.738602			−0.369301	+	0.929310i	$0.620403\pi$
$312$		0			0
$313$	24.0265			1.35806			0.679030	−	0.734110i	$-0.262401\pi$
$313$	24.0265			1.35806			0.679030	+	0.734110i	$0.262401\pi$
$314$	12.2276	+	16.8299i	0.690046	+	0.949767i
$315$		0			0
$316$	6.74007	−	20.7438i	0.379158	−	1.16693i
$317$			3.71438i			0.208620i	0.994545	+	0.104310i	$0.0332635\pi$
$317$			3.71438i			0.208620i	−0.994545	+	0.104310i	$0.966737\pi$
$318$		0			0
$319$	−0.151493			−0.00848195
$320$	−7.55928	−	10.4045i	−0.422577	−	0.581627i
$321$		0			0
$322$	8.89675	−	6.46386i	0.495796	−	0.360217i
$323$			2.29753i			0.127838i
$324$		0			0
$325$		−	9.07387i		−	0.503328i
$326$	−8.06056	−	11.0944i	−0.446433	−	0.614463i
$327$		0			0
$328$	3.96512	+	12.2034i	0.218937	+	0.673819i
$329$	−0.744883			−0.0410667
$330$		0			0
$331$			3.50059i			0.192410i	0.995362	+	0.0962048i	$0.0306704\pi$
$331$			3.50059i			0.192410i	−0.995362	+	0.0962048i	$0.969330\pi$
$332$	−25.0363	−	8.13478i	−1.37404	−	0.446454i
$333$		0			0
$334$	−2.94054	+	2.13643i	−0.160899	+	0.116900i
$335$	19.7133			1.07705
$336$		0			0
$337$	−16.9917			−0.925595			−0.462797	−	0.886464i	$-0.653154\pi$
$337$	−16.9917			−0.925595			−0.462797	+	0.886464i	$0.653154\pi$
$338$	1.26901	−	0.921986i	0.0690248	−	0.0501494i
$339$		0			0
$340$	−9.66959	−	3.14184i	−0.524407	−	0.170390i
$341$			0.117812i			0.00637988i
$342$		0			0
$343$	−1.00000			−0.0539949
$344$	18.4266	−	5.98716i	0.993495	−	0.322806i
$345$		0			0
$346$	1.40865	+	1.93883i	0.0757293	+	0.104232i
$347$		−	36.6651i		−	1.96829i	−0.177373	−	0.984144i	$-0.556760\pi$
$347$		−	36.6651i		−	1.96829i	0.177373	−	0.984144i	$-0.443240\pi$
$348$		0			0
$349$			34.7887i			1.86220i	0.364770	+	0.931098i	$0.381148\pi$
$349$			34.7887i			1.86220i	−0.364770	+	0.931098i	$0.618852\pi$
$350$	2.76385	−	2.00806i	0.147734	−	0.107335i
$351$		0			0
$352$		−	0.310734i		−	0.0165622i
$353$	−12.1913			−0.648876			−0.324438	−	0.945907i	$-0.605175\pi$
$353$	−12.1913			−0.648876			−0.324438	+	0.945907i	$0.605175\pi$
$354$		0			0
$355$			14.7740i			0.784125i
$356$	−4.88467	+	15.0335i	−0.258887	+	0.796772i
$357$		0			0
$358$	−9.25878	−	12.7436i	−0.489342	−	0.673521i
$359$	33.4411			1.76495			0.882477	−	0.470355i	$-0.155874\pi$
$359$	33.4411			1.76495			0.882477	+	0.470355i	$0.155874\pi$
$360$		0			0
$361$	18.4721			0.972218
$362$	−5.65422	−	7.78236i	−0.297179	−	0.409032i
$363$		0			0
$364$	7.14475	+	2.32147i	0.374486	+	0.121678i
$365$			6.19277i			0.324144i
$366$		0			0
$367$	−14.4869			−0.756212			−0.378106	−	0.925762i	$-0.623425\pi$
$367$	−14.4869			−0.756212			−0.378106	+	0.925762i	$0.623425\pi$
$368$	−25.1638	−	18.2826i	−1.31175	−	0.953045i
$369$		0			0
$370$	−1.10512	+	0.802916i	−0.0574524	+	0.0417416i
$371$		−	10.5822i		−	0.549401i
$372$		0			0
$373$		−	28.7612i		−	1.48920i	−0.667512	−	0.744599i	$-0.732641\pi$
$373$		−	28.7612i		−	1.48920i	0.667512	−	0.744599i	$-0.267359\pi$
$374$	−0.144394	−	0.198741i	−0.00746641	−	0.0102766i
$375$		0			0
$376$	0.651051	+	2.00373i	0.0335754	+	0.103334i
$377$	−10.3592			−0.533528
$378$		0			0
$379$		−	16.1036i		−	0.827188i	−0.910461	−	0.413594i	$-0.864273\pi$
$379$		−	16.1036i		−	0.827188i	0.910461	−	0.413594i	$-0.135727\pi$
$380$	0.721847	−	2.22162i	0.0370300	−	0.113967i
$381$		0			0
$382$	−17.8937	+	13.0006i	−0.915523	+	0.665166i
$383$	−25.7602			−1.31629			−0.658143	−	0.752893i	$-0.728658\pi$
$383$	−25.7602			−1.31629			−0.658143	+	0.752893i	$0.728658\pi$
$384$		0			0
$385$	−0.0883051			−0.00450045
$386$	−22.4126	+	16.2837i	−1.14077	+	0.828817i
$387$		0			0
$388$	7.52786	−	23.1684i	0.382169	−	1.17620i
$389$		−	9.82322i		−	0.498057i	−0.968496	−	0.249029i	$-0.919889\pi$
$389$		−	9.82322i		−	0.498057i	0.968496	−	0.249029i	$-0.0801113\pi$
$390$		0			0
$391$	−24.5900			−1.24357
$392$	0.874032	+	2.68999i	0.0441453	+	0.135865i
$393$		0			0
$394$	6.06746	+	8.35114i	0.305674	+	0.420724i
$395$			17.5317i			0.882115i
$396$		0			0
$397$		−	24.1824i		−	1.21368i	−0.794824	−	0.606840i	$-0.792437\pi$
$397$		−	24.1824i		−	1.21368i	0.794824	−	0.606840i	$-0.207563\pi$
$398$	−15.7892	+	11.4715i	−0.791439	+	0.575014i
$399$		0			0
$400$	−7.81736	−	5.67964i	−0.390868	−	0.283982i
$401$	23.4216			1.16962			0.584810	−	0.811170i	$-0.301169\pi$
$401$	23.4216			1.16962			0.584810	+	0.811170i	$0.301169\pi$
$402$		0			0
$403$			8.05613i			0.401304i
$404$	8.27895	+	2.68999i	0.411893	+	0.133832i
$405$		0			0
$406$	−2.29251	−	3.15537i	−0.113775	−	0.156598i
$407$	−0.0330049			−0.00163599
$408$		0			0
$409$	−32.6813			−1.61599			−0.807994	−	0.589191i	$-0.799447\pi$
$409$	−32.6813			−1.61599			−0.807994	+	0.589191i	$0.799447\pi$
$410$	−6.06226	−	8.34398i	−0.299393	−	0.412080i
$411$		0			0
$412$	10.8511	−	33.3962i	0.534595	−	1.64531i
$413$			2.58013i			0.126960i
$414$		0			0
$415$	21.1595			1.03868
$416$		−	21.2484i		−	1.04179i
$417$		0			0
$418$	0.0456612	−	0.0331748i	0.00223336	−	0.00162263i
$419$		−	29.3981i		−	1.43619i	−0.695945	−	0.718095i	$-0.745014\pi$
$419$		−	29.3981i		−	1.43619i	0.695945	−	0.718095i	$-0.254986\pi$
$420$		0			0
$421$			1.59493i			0.0777319i	0.999244	+	0.0388660i	$0.0123745\pi$
$421$			1.59493i			0.0777319i	−0.999244	+	0.0388660i	$0.987625\pi$
$422$	4.37016	+	6.01501i	0.212736	+	0.292806i
$423$		0			0
$424$	−28.4661	+	9.24920i	−1.38244	+	0.449181i
$425$	−7.63910			−0.370551
$426$		0			0
$427$		−	9.80423i		−	0.474460i
$428$	12.2676	+	3.98597i	0.592975	+	0.192669i
$429$		0			0
$430$	−12.5991	+	9.15375i	−0.607580	+	0.441433i
$431$	−10.7336			−0.517020			−0.258510	−	0.966009i	$-0.583232\pi$
$431$	−10.7336			−0.517020			−0.258510	+	0.966009i	$0.583232\pi$
$432$		0			0
$433$	−8.43352			−0.405289			−0.202645	−	0.979252i	$-0.564954\pi$
$433$	−8.43352			−0.405289			−0.202645	+	0.979252i	$0.564954\pi$
$434$	−2.45385	+	1.78283i	−0.117789	+	0.0855785i
$435$		0			0
$436$	−3.87193	−	1.25807i	−0.185432	−	0.0602505i
$437$		−	5.64962i		−	0.270258i
$438$		0			0
$439$	−17.3452			−0.827842			−0.413921	−	0.910313i	$-0.635841\pi$
$439$	−17.3452			−0.827842			−0.413921	+	0.910313i	$0.635841\pi$
$440$	0.0771815	+	0.237540i	0.00367948	+	0.0113243i
$441$		0			0
$442$	−9.87380	−	13.5901i	−0.469649	−	0.646416i
$443$		−	29.8824i		−	1.41976i	−0.704325	−	0.709878i	$-0.748750\pi$
$443$		−	29.8824i		−	1.41976i	0.704325	−	0.709878i	$-0.251250\pi$
$444$		0			0
$445$		−	12.7056i		−	0.602302i
$446$	−5.68070	+	4.12727i	−0.268989	+	0.195432i
$447$		0			0
$448$	6.47214	−	4.70228i	0.305780	−	0.222162i
$449$	18.6303			0.879217			0.439608	−	0.898190i	$-0.355117\pi$
$449$	18.6303			0.879217			0.439608	+	0.898190i	$0.355117\pi$
$450$		0			0
$451$		−	0.249197i		−	0.0117342i
$452$	1.61891	−	4.98251i	0.0761473	−	0.234357i
$453$		0			0
$454$	12.6162	+	17.3647i	0.592106	+	0.814964i
$455$	−6.03841			−0.283085
$456$		0			0
$457$	−6.63702			−0.310466			−0.155233	−	0.987878i	$-0.549613\pi$
$457$	−6.63702			−0.310466			−0.155233	+	0.987878i	$0.549613\pi$
$458$	4.73512	+	6.51734i	0.221258	+	0.304535i
$459$		0			0
$460$	23.7775	+	7.72579i	1.10863	+	0.360217i
$461$			42.1500i			1.96312i	0.191155	+	0.981560i	$0.438777\pi$
$461$			42.1500i			1.96312i	−0.191155	+	0.981560i	$0.561223\pi$
$462$		0			0
$463$	−27.1209			−1.26041			−0.630207	−	0.776427i	$-0.717030\pi$
$463$	−27.1209			−1.26041			−0.630207	+	0.776427i	$0.717030\pi$
$464$	−6.48419	+	8.92473i	−0.301021	+	0.414320i
$465$		0			0
$466$	18.8878	−	13.7228i	0.874962	−	0.635697i
$467$		−	1.06443i		−	0.0492561i	−0.999697	−	0.0246280i	$-0.992160\pi$
$467$		−	1.06443i		−	0.0492561i	0.999697	−	0.0246280i	$-0.00784014\pi$
$468$		0			0
$469$			12.2627i			0.566240i
$470$	−0.995390	−	1.37004i	−0.0459139	−	0.0631951i
$471$		0			0
$472$	6.94054	−	2.25512i	0.319464	−	0.103800i
$473$	−0.376277			−0.0173012
$474$		0			0
$475$		−	1.75511i		−	0.0805298i
$476$	1.95440	−	6.01501i	0.0895796	−	0.275698i
$477$		0			0
$478$	17.3262	−	12.5882i	0.792484	−	0.575773i
$479$	−32.7777			−1.49765			−0.748825	−	0.662767i	$-0.769382\pi$
$479$	−32.7777			−1.49765			−0.748825	+	0.662767i	$0.769382\pi$
$480$		0			0
$481$	−2.25691			−0.102906
$482$	32.6129	−	23.6947i	1.48548	−	1.07926i
$483$		0			0
$484$	6.79651	−	20.9175i	0.308932	−	0.950796i
$485$			19.5808i			0.889120i
$486$		0			0
$487$	−2.44329			−0.110716			−0.0553580	−	0.998467i	$-0.517630\pi$
$487$	−2.44329			−0.110716			−0.0553580	+	0.998467i	$0.517630\pi$
$488$	−26.3733	+	8.56921i	−1.19386	+	0.387910i
$489$		0			0
$490$	−1.33630	−	1.83927i	−0.0603681	−	0.0830896i
$491$			25.5978i			1.15521i	0.816315	+	0.577606i	$0.196013\pi$
$491$			25.5978i			1.15521i	−0.816315	+	0.577606i	$0.803987\pi$
$492$		0			0
$493$			8.72122i			0.392784i
$494$	3.12237	−	2.26853i	0.140482	−	0.102066i
$495$		0			0
$496$	6.94054	+	5.04260i	0.311640	+	0.226419i
$497$	−9.19025			−0.412239
$498$		0			0
$499$		−	7.96720i		−	0.356661i	−0.983971	−	0.178330i	$-0.942930\pi$
$499$		−	7.96720i		−	0.356661i	0.983971	−	0.178330i	$-0.0570696\pi$
$500$	22.6757	+	7.36777i	1.01409	+	0.329497i
$501$		0			0
$502$	5.97614	+	8.22545i	0.266728	+	0.367120i
$503$	31.3158			1.39630			0.698151	−	0.715951i	$-0.254007\pi$
$503$	31.3158			1.39630			0.698151	+	0.715951i	$0.254007\pi$
$504$		0			0
$505$	−6.99698			−0.311362
$506$	0.355064	+	0.488703i	0.0157845	+	0.0217255i
$507$		0			0
$508$	−8.45058	+	26.0082i	−0.374934	+	1.15393i
$509$			40.7362i			1.80560i	0.430061	+	0.902800i	$0.358492\pi$
$509$			40.7362i			1.80560i	−0.430061	+	0.902800i	$0.641508\pi$
$510$		0			0
$511$	−3.85224			−0.170413
$512$	−18.3060	−	13.3001i	−0.809017	−	0.587785i
$513$		0			0
$514$	34.8350	−	25.3091i	1.53651	−	1.11634i
$515$			28.2249i			1.24374i
$516$		0			0
$517$		−	0.0409168i		−	0.00179952i
$518$	−0.499457	−	0.687444i	−0.0219449	−	0.0302045i
$519$		0			0
$520$	5.27776	+	16.2433i	0.231445	+	0.712315i
$521$	−43.3880			−1.90086			−0.950432	−	0.310931i	$-0.899359\pi$
$521$	−43.3880			−1.90086			−0.950432	+	0.310931i	$0.899359\pi$
$522$		0			0
$523$		−	17.9726i		−	0.785887i	−0.919563	−	0.392944i	$-0.871457\pi$
$523$		−	17.9726i		−	0.785887i	0.919563	−	0.392944i	$-0.128543\pi$
$524$	−21.4163	−	6.95857i	−0.935574	−	0.303987i
$525$		0			0
$526$	9.47803	−	6.88619i	0.413262	−	0.300252i
$527$	6.78228			0.295441
$528$		0			0
$529$	37.4668			1.62899
$530$	19.4635	−	14.1411i	0.845441	−	0.614249i
$531$		0			0
$532$	1.38197	+	0.449028i	0.0599158	+	0.0194678i
$533$		−	17.0404i		−	0.738101i
$534$		0			0
$535$	−10.3680			−0.448246
$536$	32.9867	−	10.7180i	1.42481	−	0.462948i
$537$		0			0
$538$	5.95363	+	8.19446i	0.256679	+	0.353288i
$539$		−	0.0549306i		−	0.00236603i
$540$		0			0
$541$			11.5151i			0.495074i	0.968878	+	0.247537i	$0.0796212\pi$
$541$			11.5151i			0.495074i	−0.968878	+	0.247537i	$0.920379\pi$
$542$	−14.2697	+	10.3675i	−0.612934	+	0.445323i
$543$		0			0
$544$	−17.8885			−0.766965
$545$	3.27238			0.140173
$546$		0			0
$547$			14.5265i			0.621107i	0.950556	+	0.310553i	$0.100514\pi$
$547$			14.5265i			0.621107i	−0.950556	+	0.310553i	$0.899486\pi$
$548$	0.620000	−	1.90816i	0.0264851	−	0.0815128i
$549$		0			0
$550$	0.110304	+	0.151820i	0.00470336	+	0.00647362i
$551$	−2.00373			−0.0853616
$552$		0			0
$553$	−10.9057			−0.463756
$554$	7.41089	+	10.2002i	0.314858	+	0.433365i
$555$		0			0
$556$	−4.95031	−	1.60845i	−0.209940	−	0.0682136i
$557$		−	44.6492i		−	1.89185i	−0.324387	−	0.945924i	$-0.605158\pi$
$557$		−	44.6492i		−	1.89185i	0.324387	−	0.945924i	$-0.394842\pi$
$558$		0			0
$559$	−25.7302			−1.08827
$560$	−3.77964	+	5.20223i	−0.159719	+	0.219834i
$561$		0			0
$562$	14.1387	−	10.2724i	0.596406	−	0.433314i
$563$			4.26356i			0.179688i	0.995956	+	0.0898438i	$0.0286368\pi$
$563$			4.26356i			0.179688i	−0.995956	+	0.0898438i	$0.971363\pi$
$564$		0			0
$565$			4.21098i			0.177157i
$566$	17.8092	+	24.5123i	0.748577	+	1.03033i
$567$		0			0
$568$	8.03258	+	24.7217i	0.337039	+	1.03730i
$569$	38.6045			1.61838			0.809192	−	0.587544i	$-0.199905\pi$
$569$	38.6045			1.61838			0.809192	+	0.587544i	$0.199905\pi$
$570$		0			0
$571$		−	28.0556i		−	1.17409i	−0.809554	−	0.587045i	$-0.800291\pi$
$571$		−	28.0556i		−	1.17409i	0.809554	−	0.587045i	$-0.199709\pi$
$572$	−0.127520	+	0.392465i	−0.00533186	+	0.0164098i
$573$		0			0
$574$	5.19041	−	3.77105i	0.216643	−	0.157401i
$575$	18.7845			0.783370
$576$		0			0
$577$	−2.46468			−0.102606			−0.0513029	−	0.998683i	$-0.516337\pi$
$577$	−2.46468			−0.102606			−0.0513029	+	0.998683i	$0.516337\pi$
$578$	8.00886	−	5.81878i	0.333125	−	0.242029i
$579$		0			0
$580$	2.74007	−	8.43306i	0.113775	−	0.350164i
$581$			13.1624i			0.546066i
$582$		0			0
$583$	0.581287			0.0240745
$584$	3.36698	+	10.3625i	0.139327	+	0.428803i
$585$		0			0
$586$	−0.0538633	−	0.0741364i	−0.00222507	−	0.00306255i
$587$			42.7523i			1.76458i	0.470710	+	0.882288i	$0.343998\pi$
$587$			42.7523i			1.76458i	−0.470710	+	0.882288i	$0.656002\pi$
$588$		0			0
$589$			1.55825i			0.0642065i
$590$	−4.74555	+	3.44784i	−0.195371	+	0.141945i
$591$		0			0
$592$	−1.41268	+	1.94438i	−0.0580607	+	0.0799137i
$593$	−17.7945			−0.730733			−0.365367	−	0.930864i	$-0.619056\pi$
$593$	−17.7945			−0.730733			−0.365367	+	0.930864i	$0.619056\pi$
$594$		0			0
$595$			5.08361i			0.208408i
$596$	36.4282	+	11.8362i	1.49216	+	0.484831i
$597$		0			0
$598$	24.2797	+	33.4181i	0.992869	+	1.36657i
$599$	14.5626			0.595011			0.297506	−	0.954720i	$-0.403845\pi$
$599$	14.5626			0.595011			0.297506	+	0.954720i	$0.403845\pi$
$600$		0			0
$601$	−27.1497			−1.10746			−0.553730	−	0.832696i	$-0.686796\pi$
$601$	−27.1497			−1.10746			−0.553730	+	0.832696i	$0.686796\pi$
$602$	−5.69413	−	7.83729i	−0.232075	−	0.319424i
$603$		0			0
$604$	9.81736	−	30.2147i	0.399463	−	1.22942i
$605$			17.6785i			0.718733i
$606$		0			0
$607$	10.8708			0.441231			0.220616	−	0.975361i	$-0.429193\pi$
$607$	10.8708			0.441231			0.220616	+	0.975361i	$0.429193\pi$
$608$		−	4.10995i		−	0.166680i
$609$		0			0
$610$	18.0326	−	13.1014i	0.730118	−	0.530462i
$611$		−	2.79794i		−	0.113192i
$612$		0			0
$613$			26.1387i			1.05573i	0.849327	+	0.527866i	$0.177008\pi$
$613$			26.1387i			1.05573i	−0.849327	+	0.527866i	$0.822992\pi$
$614$	−13.1732	−	18.1314i	−0.531628	−	0.731724i
$615$		0			0
$616$	−0.147763	+	0.0480111i	−0.00595354	+	0.00193442i
$617$	42.5464			1.71285			0.856427	−	0.516269i	$-0.172679\pi$
$617$	42.5464			1.71285			0.856427	+	0.516269i	$0.172679\pi$
$618$		0			0
$619$			41.0012i			1.64798i	0.566606	+	0.823989i	$0.308256\pi$
$619$			41.0012i			1.64798i	−0.566606	+	0.823989i	$0.691744\pi$
$620$	−6.55819	−	2.13088i	−0.263383	−	0.0855784i
$621$		0			0
$622$	14.9026	−	10.8274i	0.597542	−	0.434139i
$623$	7.90356			0.316649
$624$		0			0
$625$	−7.08594			−0.283437
$626$	−27.4893	+	19.9722i	−1.09869	+	0.798248i
$627$		0			0
$628$	−27.9799	−	9.09121i	−1.11652	−	0.362779i
$629$			1.90005i			0.0757599i
$630$		0			0
$631$	−29.8045			−1.18650			−0.593249	−	0.805019i	$-0.702155\pi$
$631$	−29.8045			−1.18650			−0.593249	+	0.805019i	$0.702155\pi$
$632$	9.53190	+	29.3362i	0.379158	+	1.16693i
$633$		0			0
$634$	−3.08759	−	4.24971i	−0.122624	−	0.168777i
$635$		−	21.9809i		−	0.872286i
$636$		0			0
$637$		−	3.75621i		−	0.148827i
$638$	0.173326	−	0.125929i	0.00686204	−	0.00498557i
$639$		0			0
$640$	17.2975	+	5.62030i	0.683743	+	0.222162i
$641$	−18.1768			−0.717941			−0.358971	−	0.933349i	$-0.616872\pi$
$641$	−18.1768			−0.717941			−0.358971	+	0.933349i	$0.616872\pi$
$642$		0			0
$643$			20.8490i			0.822203i	0.911590	+	0.411101i	$0.134856\pi$
$643$			20.8490i			0.822203i	−0.911590	+	0.411101i	$0.865144\pi$
$644$	−4.80586	+	14.7909i	−0.189377	+	0.582843i
$645$		0			0
$646$	−1.90983	−	2.62866i	−0.0751413	−	0.103423i
$647$	18.7706			0.737948			0.368974	−	0.929440i	$-0.379709\pi$
$647$	18.7706			0.737948			0.368974	+	0.929440i	$0.379709\pi$
$648$		0			0
$649$	−0.141728			−0.00556332
$650$	7.54269	+	10.3816i	0.295849	+	0.407201i
$651$		0			0
$652$	18.4445	+	5.99300i	0.722344	+	0.234704i
$653$			25.5220i			0.998751i	0.866386	+	0.499376i	$0.166437\pi$
$653$			25.5220i			0.998751i	−0.866386	+	0.499376i	$0.833563\pi$
$654$		0			0
$655$	18.1000			0.707227
$656$	−14.6807	−	10.6661i	−0.573185	−	0.416443i
$657$		0			0
$658$	0.852237	−	0.619187i	0.0332237	−	0.0241384i
$659$			18.8249i			0.733314i	0.930356	+	0.366657i	$0.119498\pi$
$659$			18.8249i			0.733314i	−0.930356	+	0.366657i	$0.880502\pi$
$660$		0			0
$661$			25.1764i			0.979247i	0.871934	+	0.489623i	$0.162866\pi$
$661$			25.1764i			0.979247i	−0.871934	+	0.489623i	$0.837134\pi$
$662$	−2.90988	−	4.00510i	−0.113096	−	0.155663i
$663$		0			0
$664$	35.4066	−	11.5043i	1.37404	−	0.446454i
$665$	−1.16797			−0.0452921
$666$		0			0
$667$		−	21.4455i		−	0.830372i
$668$	1.58843	−	4.88867i	0.0614581	−	0.189148i
$669$		0			0
$670$	−22.5544	+	16.3867i	−0.871353	+	0.633075i
$671$	0.538552			0.0207906
$672$		0			0
$673$	8.29322			0.319680			0.159840	−	0.987143i	$-0.448902\pi$
$673$	8.29322			0.319680			0.159840	+	0.987143i	$0.448902\pi$
$674$	19.4405	−	14.1244i	0.748822	−	0.544051i
$675$		0			0
$676$	−0.685493	+	2.10973i	−0.0263651	+	0.0811435i
$677$		−	11.6825i		−	0.448993i	−0.974475	−	0.224497i	$-0.927926\pi$
$677$		−	11.6825i		−	0.448993i	0.974475	−	0.224497i	$-0.0720738\pi$
$678$		0			0
$679$	−12.1803			−0.467439
$680$	13.6749	−	4.44323i	0.524407	−	0.170390i
$681$		0			0
$682$	−0.0979317	−	0.134791i	−0.00375000	−	0.00516143i
$683$		−	22.9388i		−	0.877727i	−0.898554	−	0.438864i	$-0.855381\pi$
$683$		−	22.9388i		−	0.877727i	0.898554	−	0.438864i	$-0.144619\pi$
$684$		0			0
$685$			1.61269i			0.0616178i
$686$	1.14412	−	0.831254i	0.0436828	−	0.0317374i
$687$		0			0
$688$	−16.1054	+	22.1672i	−0.614013	+	0.845117i
$689$	39.7491			1.51432
$690$		0			0
$691$			41.2800i			1.57036i	0.619265	+	0.785182i	$0.287431\pi$
$691$			41.2800i			1.57036i	−0.619265	+	0.785182i	$0.712569\pi$
$692$	−3.22333	−	1.04732i	−0.122533	−	0.0398132i
$693$		0			0
$694$	30.4780	+	41.9494i	1.15693	+	1.59238i
$695$	4.18377			0.158699
$696$		0			0
$697$	−14.3459			−0.543391
$698$	−28.9182	−	39.8025i	−1.09457	−	1.50655i
$699$		0			0
$700$	−1.49298	+	4.59493i	−0.0564294	+	0.173672i
$701$		−	22.9596i		−	0.867174i	−0.901112	−	0.433587i	$-0.857248\pi$
$701$		−	22.9596i		−	0.867174i	0.901112	−	0.433587i	$-0.142752\pi$
$702$		0			0
$703$	−0.436542			−0.0164645
$704$	0.258299	+	0.355518i	0.00973501	+	0.0133991i
$705$		0			0
$706$	13.9483	−	10.1340i	0.524951	−	0.381399i
$707$		−	4.35250i		−	0.163693i
$708$		0			0
$709$			22.0831i			0.829348i	0.909970	+	0.414674i	$0.136104\pi$
$709$			22.0831i			0.829348i	−0.909970	+	0.414674i	$0.863896\pi$
$710$	−12.2810	−	16.9033i	−0.460897	−	0.634370i
$711$		0			0
$712$	−6.90797	−	21.2605i	−0.258887	−	0.796772i
$713$	−16.6776			−0.624582
$714$		0			0
$715$		−	0.331693i		−	0.0124046i
$716$	21.1864	+	6.88387i	0.791771	+	0.257262i
$717$		0			0
$718$	−38.2607	+	27.7981i	−1.42788	+	1.03741i
$719$	29.4594			1.09865			0.549325	−	0.835609i	$-0.314885\pi$
$719$	29.4594			1.09865			0.549325	+	0.835609i	$0.314885\pi$
$720$		0			0
$721$	−17.5574			−0.653873
$722$	−21.1344	+	15.3550i	−0.786541	+	0.571455i
$723$		0			0
$724$	12.9382	+	4.20389i	0.480846	+	0.156236i
$725$		−	6.66223i		−	0.247429i
$726$		0			0
$727$	−25.5893			−0.949054			−0.474527	−	0.880241i	$-0.657381\pi$
$727$	−25.5893			−0.949054			−0.474527	+	0.880241i	$0.657381\pi$
$728$	−10.1042	+	3.28305i	−0.374486	+	0.121678i
$729$		0			0
$730$	−5.14776	−	7.08529i	−0.190527	−	0.262238i
$731$			21.6617i			0.801189i
$732$		0			0
$733$			24.3587i			0.899711i	0.893101	+	0.449855i	$0.148524\pi$
$733$			24.3587i			0.899711i	−0.893101	+	0.449855i	$0.851476\pi$
$734$	16.5748	−	12.0423i	0.611789	−	0.444491i
$735$		0			0
$736$	43.9879			1.62142
$737$	−0.673598			−0.0248123
$738$		0			0
$739$			18.8064i			0.691805i	0.938270	+	0.345903i	$0.112427\pi$
$739$			18.8064i			0.691805i	−0.938270	+	0.345903i	$0.887573\pi$
$740$	0.596965	−	1.83727i	0.0219449	−	0.0675393i
$741$		0			0
$742$	8.79651	+	12.1074i	0.322930	+	0.444475i
$743$	−29.4039			−1.07873			−0.539363	−	0.842074i	$-0.681335\pi$
$743$	−29.4039			−1.07873			−0.539363	+	0.842074i	$0.681335\pi$
$744$		0			0
$745$	−30.7874			−1.12796
$746$	23.9079	+	32.9063i	0.875329	+	1.20479i
$747$		0			0
$748$	0.330408	+	0.107356i	0.0120809	+	0.00392532i
$749$		−	6.44944i		−	0.235657i
$750$		0			0
$751$	−16.9057			−0.616896			−0.308448	−	0.951241i	$-0.599810\pi$
$751$	−16.9057			−0.616896			−0.308448	+	0.951241i	$0.599810\pi$
$752$	−2.41049	−	1.75132i	−0.0879015	−	0.0638642i
$753$		0			0
$754$	11.8522	−	8.61115i	0.431633	−	0.313600i
$755$			25.5361i			0.929353i
$756$		0			0
$757$			30.3657i			1.10366i	0.833957	+	0.551830i	$0.186070\pi$
$757$			30.3657i			1.10366i	−0.833957	+	0.551830i	$0.813930\pi$
$758$	13.3862	+	18.4245i	0.486209	+	0.669209i
$759$		0			0
$760$	1.02085	+	3.14184i	0.0370300	+	0.113967i
$761$	18.0960			0.655979			0.327990	−	0.944681i	$-0.393629\pi$
$761$	18.0960			0.655979			0.327990	+	0.944681i	$0.393629\pi$
$762$		0			0
$763$			2.03559i			0.0736935i
$764$	9.66586	−	29.7485i	0.349699	−	1.07626i
$765$		0			0
$766$	29.4728	−	21.4133i	1.06490	−	0.773693i
$767$	−9.69153			−0.349941
$768$		0			0
$769$	15.4944			0.558743			0.279371	−	0.960183i	$-0.409874\pi$
$769$	15.4944			0.558743			0.279371	+	0.960183i	$0.409874\pi$
$770$	0.101032	−	0.0734040i	0.00364094	−	0.00264530i
$771$		0			0
$772$	12.1068	−	37.2610i	0.435735	−	1.34105i
$773$		−	33.1186i		−	1.19119i	−0.803284	−	0.595597i	$-0.796916\pi$
$773$		−	33.1186i		−	1.19119i	0.803284	−	0.595597i	$-0.203084\pi$
$774$		0			0
$775$	−5.18105			−0.186109
$776$	10.6460	+	32.7650i	0.382169	+	1.17620i
$777$		0			0
$778$	8.16559	+	11.2390i	0.292751	+	0.402937i
$779$		−	3.29602i		−	0.118092i
$780$		0			0
$781$		−	0.504826i		−	0.0180641i
$782$	28.1340	−	20.4405i	1.00607	−	0.730952i
$783$		0			0
$784$	−3.23607	−	2.35114i	−0.115574	−	0.0839693i
$785$	23.6473			0.844008
$786$		0			0
$787$			13.8484i			0.493641i	0.969061	+	0.246820i	$0.0793858\pi$
$787$			13.8484i			0.493641i	−0.969061	+	0.246820i	$0.920614\pi$
$788$	−13.8838	−	4.51113i	−0.494591	−	0.160702i
$789$		0			0
$790$	−14.5733	−	20.0584i	−0.518494	−	0.713646i
$791$	−2.61946			−0.0931372
$792$		0			0
$793$	36.8268			1.30776
$794$	20.1017	+	27.6677i	0.713384	+	0.981888i
$795$		0			0
$796$	8.52902	−	26.2496i	0.302303	−	0.930393i
$797$		−	27.5510i		−	0.975908i	−0.872869	−	0.487954i	$-0.837743\pi$
$797$		−	27.5510i		−	0.975908i	0.872869	−	0.487954i	$-0.162257\pi$
$798$		0			0
$799$	−2.35553			−0.0833325
$800$	13.6652			0.483139
$801$		0			0
$802$	−26.7972	+	19.4693i	−0.946243	+	0.687486i
$803$		−	0.211606i		−	0.00746740i
$804$		0			0
$805$		−	12.5006i		−	0.440588i
$806$	−6.69669	−	9.21720i	−0.235881	−	0.324662i
$807$		0			0
$808$	−11.7082	+	3.80423i	−0.411893	+	0.133832i
$809$	−0.181117			−0.00636775			−0.00318388	−	0.999995i	$-0.501013\pi$
$809$	−0.181117			−0.00636775			−0.00318388	+	0.999995i	$0.501013\pi$
$810$		0			0
$811$		−	23.7508i		−	0.834003i	−0.908906	−	0.417002i	$-0.863081\pi$
$811$		−	23.7508i		−	0.834003i	0.908906	−	0.417002i	$-0.136919\pi$
$812$	5.24582	+	1.70447i	0.184092	+	0.0598152i
$813$		0			0
$814$	0.0377617	−	0.0274355i	0.00132355	−	0.000961612i
$815$	−15.5885			−0.546040
$816$		0			0
$817$	−4.97685			−0.174118
$818$	37.3914	−	27.1665i	1.30736	−	0.949854i
$819$		0			0
$820$	13.8719	+	4.50726i	0.484429	+	0.157400i
$821$		−	8.16381i		−	0.284919i	−0.989801	−	0.142460i	$-0.954499\pi$
$821$		−	8.16381i		−	0.284919i	0.989801	−	0.142460i	$-0.0455011\pi$
$822$		0			0
$823$	39.6984			1.38380			0.691900	−	0.721993i	$-0.256774\pi$
$823$	39.6984			1.38380			0.691900	+	0.721993i	$0.256774\pi$
$824$	15.3458	+	47.2294i	0.534595	+	1.64531i
$825$		0			0
$826$	−2.14475	−	2.95199i	−0.0746252	−	0.102713i
$827$			46.0390i			1.60093i	0.599377	+	0.800467i	$0.295415\pi$
$827$			46.0390i			1.60093i	−0.599377	+	0.800467i	$0.704585\pi$
$828$		0			0
$829$			14.1434i			0.491220i	0.969369	+	0.245610i	$0.0789882\pi$
$829$			14.1434i			0.491220i	−0.969369	+	0.245610i	$0.921012\pi$
$830$	−24.2091	+	17.5889i	−0.840309	+	0.610520i
$831$		0			0
$832$	17.6628	+	24.3107i	0.612347	+	0.842823i
$833$	−3.16228			−0.109566
$834$		0			0
$835$			4.13168i			0.142983i
$836$	−0.0246654	+	0.0759122i	−0.000853069	+	0.00262548i
$837$		0			0
$838$	24.4373	+	33.6350i	0.844171	+	1.16190i
$839$	31.0217			1.07099			0.535494	−	0.844539i	$-0.320125\pi$
$839$	31.0217			1.07099			0.535494	+	0.844539i	$0.320125\pi$
$840$		0			0
$841$	21.3940			0.737725
$842$	−1.32579	−	1.82479i	−0.0456897	−	0.0628865i
$843$		0			0
$844$	−10.0000	−	3.24920i	−0.344214	−	0.111842i
$845$		−	1.78305i		−	0.0613386i
$846$		0			0
$847$	−10.9970			−0.377861
$848$	24.8803	−	34.2448i	0.854392	−	1.17597i
$849$		0			0
$850$	8.74007	−	6.35003i	0.299782	−	0.217804i
$851$		−	4.67222i		−	0.160162i
$852$		0			0
$853$		−	36.2812i		−	1.24224i	−0.783714	−	0.621121i	$-0.786677\pi$
$853$		−	36.2812i		−	1.24224i	0.783714	−	0.621121i	$-0.213323\pi$
$854$	8.14980	+	11.2172i	0.278880	+	0.383846i
$855$		0			0
$856$	−17.3489	+	5.63702i	−0.592975	+	0.192669i
$857$	27.6532			0.944616			0.472308	−	0.881434i	$-0.343421\pi$
$857$	27.6532			0.944616			0.472308	+	0.881434i	$0.343421\pi$
$858$		0			0
$859$		−	27.0733i		−	0.923729i	−0.886950	−	0.461865i	$-0.847181\pi$
$859$		−	27.0733i		−	0.923729i	0.886950	−	0.461865i	$-0.152819\pi$
$860$	6.80578	−	20.9460i	0.232075	−	0.714253i
$861$		0			0
$862$	12.2806	−	8.92236i	0.418278	−	0.303897i
$863$	8.98203			0.305752			0.152876	−	0.988245i	$-0.451147\pi$
$863$	8.98203			0.305752			0.152876	+	0.988245i	$0.451147\pi$
$864$		0			0
$865$	2.72421			0.0926258
$866$	9.64899	−	7.01040i	0.327886	−	0.238223i
$867$		0			0
$868$	1.32553	−	4.07955i	0.0449913	−	0.138469i
$869$		−	0.599054i		−	0.0203215i
$870$		0			0
$871$	−46.0614			−1.56073
$872$	5.47574	−	1.77917i	0.185432	−	0.0602505i
$873$		0			0
$874$	4.69627	+	6.46386i	0.158854	+	0.218643i
$875$		−	11.9213i		−	0.403014i
$876$		0			0
$877$		−	27.9552i		−	0.943980i	−0.881604	−	0.471990i	$-0.843536\pi$
$877$		−	27.9552i		−	0.943980i	0.881604	−	0.471990i	$-0.156464\pi$
$878$	19.8451	−	14.4183i	0.669738	−	0.486593i
$879$		0			0
$880$	−0.285761	−	0.207618i	−0.00963301	−	0.00699879i
$881$	−33.0213			−1.11252			−0.556258	−	0.831010i	$-0.687763\pi$
$881$	−33.0213			−1.11252			−0.556258	+	0.831010i	$0.687763\pi$
$882$		0			0
$883$			19.1451i			0.644283i	0.946692	+	0.322141i	$0.104403\pi$
$883$			19.1451i			0.644283i	−0.946692	+	0.322141i	$0.895597\pi$
$884$	22.5937	+	7.34113i	0.759907	+	0.246909i
$885$		0			0
$886$	24.8399	+	34.1891i	0.834512	+	1.14861i
$887$	8.99598			0.302056			0.151028	−	0.988530i	$-0.451742\pi$
$887$	8.99598			0.302056			0.151028	+	0.988530i	$0.451742\pi$
$888$		0			0
$889$	13.6733			0.458588
$890$	10.5616	+	14.5367i	0.354024	+	0.487273i
$891$		0			0
$892$	3.06861	−	9.44422i	0.102745	−	0.316216i
$893$		−	0.541189i		−	0.0181102i
$894$		0			0
$895$	−17.9057			−0.598522
$896$	−3.49613	+	10.7600i	−0.116797	+	0.359466i
$897$		0			0
$898$	−21.3153	+	15.4865i	−0.711301	+	0.516791i
$899$			5.91498i			0.197276i
$900$		0			0
$901$		−	33.4639i		−	1.11484i
$902$	0.207146	+	0.285112i	0.00689721	+	0.00949319i
$903$		0			0
$904$	2.28949	+	7.04633i	0.0761473	+	0.234357i
$905$	−10.9348			−0.363485
$906$		0			0
$907$		−	53.5978i		−	1.77969i	−0.456267	−	0.889843i	$-0.650814\pi$
$907$		−	53.5978i		−	1.77969i	0.456267	−	0.889843i	$-0.349186\pi$
$908$	−28.8689	−	9.38007i	−0.958048	−	0.311289i
$909$		0			0
$910$	6.90868	−	5.01945i	0.229020	−	0.166393i
$911$	−47.1958			−1.56367			−0.781833	−	0.623487i	$-0.785715\pi$
$911$	−47.1958			−1.56367			−0.781833	+	0.623487i	$0.785715\pi$
$912$		0			0
$913$	−0.723015			−0.0239283
$914$	7.59356	−	5.51704i	0.251173	−	0.182488i
$915$		0			0
$916$	−10.8351	−	3.52054i	−0.358002	−	0.116322i
$917$			11.2592i			0.371812i
$918$		0			0
$919$	22.6942			0.748612			0.374306	−	0.927305i	$-0.377881\pi$
$919$	22.6942			0.748612			0.374306	+	0.927305i	$0.377881\pi$
$920$	−33.6265	+	10.9259i	−1.10863	+	0.360217i
$921$		0			0
$922$	−35.0373	−	48.2247i	−1.15389	−	1.58820i
$923$		−	34.5206i		−	1.13626i
$924$		0			0
$925$		−	1.45147i		−	0.0477239i
$926$	31.0296	−	22.5443i	1.01970	−	0.740853i
$927$		0			0
$928$		−	15.6010i		−	0.512128i
$929$	31.0001			1.01708			0.508541	−	0.861038i	$-0.330185\pi$
$929$	31.0001			1.01708			0.508541	+	0.861038i	$0.330185\pi$
$930$		0			0
$931$		−	0.726543i		−	0.0238115i
$932$	−10.2029	+	31.4012i	−0.334206	+	1.02858i
$933$		0			0
$934$	0.884814	+	1.21784i	0.0289520	+	0.0398490i
$935$	−0.279245			−0.00913230
$936$		0			0
$937$	−49.0011			−1.60080			−0.800398	−	0.599469i	$-0.795378\pi$
$937$	−49.0011			−1.60080			−0.800398	+	0.599469i	$0.795378\pi$
$938$	−10.1934	−	14.0301i	−0.332827	−	0.458098i
$939$		0			0
$940$	2.27770	+	0.740069i	0.0742903	+	0.0241384i
$941$		−	49.2485i		−	1.60546i	−0.596345	−	0.802728i	$-0.703381\pi$
$941$		−	49.2485i		−	1.60546i	0.596345	−	0.802728i	$-0.296619\pi$
$942$		0			0
$943$	35.2766			1.14877
$944$	−6.06626	+	8.34949i	−0.197440	+	0.271753i
$945$		0			0
$946$	0.430507	−	0.312782i	0.0139970	−	0.0101694i
$947$			9.28008i			0.301562i	0.988567	+	0.150781i	$0.0481788\pi$
$947$			9.28008i			0.301562i	−0.988567	+	0.150781i	$0.951821\pi$
$948$		0			0
$949$		−	14.4698i		−	0.469711i
$950$	1.45894	+	2.00806i	0.0473342	+	0.0651499i
$951$		0			0
$952$	2.76393	+	8.50651i	0.0895796	+	0.275698i
$953$	50.1855			1.62567			0.812834	−	0.582496i	$-0.197924\pi$
$953$	50.1855			1.62567			0.812834	+	0.582496i	$0.197924\pi$
$954$		0			0
$955$			25.1420i			0.813576i
$956$	−9.35931	+	28.8050i	−0.302702	+	0.931620i
$957$		0			0
$958$	37.5017	−	27.2466i	1.21162	−	0.880297i
$959$	−1.00318			−0.0323944
$960$		0			0
$961$	−26.4001			−0.851615
$962$	2.58219	−	1.87607i	0.0832530	−	0.0604869i
$963$		0			0
$964$	−17.6169	+	54.2192i	−0.567402	+	1.74628i
$965$			31.4913i			1.01374i
$966$		0			0
$967$	−7.81736			−0.251389			−0.125695	−	0.992069i	$-0.540116\pi$
$967$	−7.81736			−0.251389			−0.125695	+	0.992069i	$0.540116\pi$
$968$	9.61172	+	29.5818i	0.308932	+	0.950796i
$969$		0			0
$970$	−16.2766	−	22.4029i	−0.522612	−	0.719313i
$971$		−	7.60460i		−	0.244043i	−0.992527	−	0.122022i	$-0.961062\pi$
$971$		−	7.60460i		−	0.244043i	0.992527	−	0.122022i	$-0.0389377\pi$
$972$		0			0
$973$			2.60253i			0.0834333i
$974$	2.79542	−	2.03099i	0.0895711	−	0.0650772i
$975$		0			0
$976$	23.0511	−	31.7271i	0.737848	−	1.01556i
$977$	37.9179			1.21310			0.606551	−	0.795044i	$-0.292553\pi$
$977$	37.9179			1.21310			0.606551	+	0.795044i	$0.292553\pi$
$978$		0			0
$979$			0.434147i			0.0138754i
$980$	3.05779	+	0.993537i	0.0976776	+	0.0317374i
$981$		0			0
$982$	−21.2783	−	29.2870i	−0.679017	−	0.934587i
$983$	−33.7230			−1.07560			−0.537798	−	0.843074i	$-0.680744\pi$
$983$	−33.7230			−1.07560			−0.537798	+	0.843074i	$0.680744\pi$
$984$		0			0
$985$	11.7340			0.373875
$986$	−7.24955	−	9.97815i	−0.230873	−	0.317769i
$987$		0			0
$988$	−1.68665	+	5.19096i	−0.0536593	+	0.165146i
$989$		−	53.2662i		−	1.69377i
$990$		0			0
$991$	46.3137			1.47120			0.735602	−	0.677414i	$-0.236899\pi$
$991$	46.3137			1.47120			0.735602	+	0.677414i	$0.236899\pi$
$992$	−12.1325			−0.385208
$993$		0			0
$994$	10.5148	−	7.63943i	0.333509	−	0.242308i
$995$			22.1849i			0.703310i
$996$		0			0
$997$			5.20068i			0.164707i	0.996603	+	0.0823535i	$0.0262437\pi$
$997$			5.20068i			0.164707i	−0.996603	+	0.0823535i	$0.973756\pi$
$998$	6.62276	+	9.11545i	0.209640	+	0.288545i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1512.2.c.d.757.4	yes	16
3.2	odd	2	inner	1512.2.c.d.757.13	yes	16
4.3	odd	2		6048.2.c.d.3025.11		16
8.3	odd	2		6048.2.c.d.3025.6		16
8.5	even	2	inner	1512.2.c.d.757.1	✓	16
12.11	even	2		6048.2.c.d.3025.5		16
24.5	odd	2	inner	1512.2.c.d.757.16	yes	16
24.11	even	2		6048.2.c.d.3025.12		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1512.2.c.d.757.1	✓	16	8.5	even	2	inner
1512.2.c.d.757.4	yes	16	1.1	even	1	trivial
1512.2.c.d.757.13	yes	16	3.2	odd	2	inner
1512.2.c.d.757.16	yes	16	24.5	odd	2	inner
6048.2.c.d.3025.5		16	12.11	even	2
6048.2.c.d.3025.6		16	8.3	odd	2
6048.2.c.d.3025.11		16	4.3	odd	2
6048.2.c.d.3025.12		16	24.11	even	2

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:	\( N \)	\(=\)	\( 1512 = 2^{3} \cdot 3^{3} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1512.c (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.14412 + 0.831254i) q^{2} +(0.618034 - 1.90211i) q^{4} +1.60758i q^{5} -1.00000 q^{7} +(0.874032 + 2.68999i) q^{8} +O(q^{10})\)	\(q+(-1.14412 + 0.831254i) q^{2} +(0.618034 - 1.90211i) q^{4} +1.60758i q^{5} -1.00000 q^{7} +(0.874032 + 2.68999i) q^{8} +(-1.33630 - 1.83927i) q^{10} -0.0549306i q^{11} -3.75621i q^{13} +(1.14412 - 0.831254i) q^{14} +(-3.23607 - 2.35114i) q^{16} -3.16228 q^{17} -0.726543i q^{19} +(3.05779 + 0.993537i) q^{20} +(0.0456612 + 0.0628473i) q^{22} +7.77604 q^{23} +2.41570 q^{25} +(3.12237 + 4.29757i) q^{26} +(-0.618034 + 1.90211i) q^{28} -2.75789i q^{29} -2.14475 q^{31} +5.65685 q^{32} +(3.61803 - 2.62866i) q^{34} -1.60758i q^{35} -0.600848i q^{37} +(0.603941 + 0.831254i) q^{38} +(-4.32437 + 1.40507i) q^{40} +4.53658 q^{41} -6.85004i q^{43} +(-0.104484 - 0.0339490i) q^{44} +(-8.89675 + 6.46386i) q^{46} +0.744883 q^{47} +1.00000 q^{49} +(-2.76385 + 2.00806i) q^{50} +(-7.14475 - 2.32147i) q^{52} +10.5822i q^{53} +0.0883051 q^{55} +(-0.874032 - 2.68999i) q^{56} +(2.29251 + 3.15537i) q^{58} -2.58013i q^{59} +9.80423i q^{61} +(2.45385 - 1.78283i) q^{62} +(-6.47214 + 4.70228i) q^{64} +6.03841 q^{65} -12.2627i q^{67} +(-1.95440 + 6.01501i) q^{68} +(1.33630 + 1.83927i) q^{70} +9.19025 q^{71} +3.85224 q^{73} +(0.499457 + 0.687444i) q^{74} +(-1.38197 - 0.449028i) q^{76} +0.0549306i q^{77} +10.9057 q^{79} +(3.77964 - 5.20223i) q^{80} +(-5.19041 + 3.77105i) q^{82} -13.1624i q^{83} -5.08361i q^{85} +(5.69413 + 7.83729i) q^{86} +(0.147763 - 0.0480111i) q^{88} -7.90356 q^{89} +3.75621i q^{91} +(4.80586 - 14.7909i) q^{92} +(-0.852237 + 0.619187i) q^{94} +1.16797 q^{95} +12.1803 q^{97} +(-1.14412 + 0.831254i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 8 q^{4} - 16 q^{7}+O(q^{10}) \) 16 * q - 8 * q^4 - 16 * q^7	\( 16 q - 8 q^{4} - 16 q^{7} - 20 q^{10} - 16 q^{16} + 20 q^{22} - 32 q^{25} + 8 q^{28} + 40 q^{31} + 40 q^{34} + 40 q^{40} + 4 q^{46} + 16 q^{49} - 40 q^{52} - 72 q^{55} - 32 q^{64} + 20 q^{70} + 24 q^{73} - 40 q^{76} + 24 q^{79} - 28 q^{82} + 40 q^{88} + 24 q^{94} + 16 q^{97}+O(q^{100}) \) 16 * q - 8 * q^4 - 16 * q^7 - 20 * q^10 - 16 * q^16 + 20 * q^22 - 32 * q^25 + 8 * q^28 + 40 * q^31 + 40 * q^34 + 40 * q^40 + 4 * q^46 + 16 * q^49 - 40 * q^52 - 72 * q^55 - 32 * q^64 + 20 * q^70 + 24 * q^73 - 40 * q^76 + 24 * q^79 - 28 * q^82 + 40 * q^88 + 24 * q^94 + 16 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more