LMFDB - Embedded newform 360.2.x.a.53.11

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [360,2,Mod(53,360)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(360, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([0, 2, 2, 3]))

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

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

chi := DirichletCharacter("360.53");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 360 = 2^{3} \cdot 3^{2} \cdot 5 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	360.x (of order $4$, degree $2$, 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:	$2.87461447277$
Analytic rank:	$0$
Dimension:	$48$
Relative dimension:	$24$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			53.11
Character	$\chi$	$=$	360.53
Dual form			360.2.x.a.197.11

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.319115 - 1.37774i) q^{2} +(-1.79633 + 0.879316i) q^{4} +(-1.42597 + 1.72238i) q^{5} +(3.11972 - 3.11972i) q^{7} +(1.78470 + 2.19427i) q^{8} +O(q^{10})$	\(q+(-0.319115 - 1.37774i) q^{2} +(-1.79633 + 0.879316i) q^{4} +(-1.42597 + 1.72238i) q^{5} +(3.11972 - 3.11972i) q^{7} +(1.78470 + 2.19427i) q^{8} +(2.82804 + 1.41498i) q^{10} +1.17794 q^{11} +(2.15100 - 2.15100i) q^{13} +(-5.29371 - 3.30261i) q^{14} +(2.45361 - 3.15908i) q^{16} +(-1.33507 - 1.33507i) q^{17} +0.322444 q^{19} +(1.04700 - 4.34785i) q^{20} +(-0.375899 - 1.62290i) q^{22} +(4.71347 - 4.71347i) q^{23} +(-0.933209 - 4.91214i) q^{25} +(-3.64993 - 2.27710i) q^{26} +(-2.86083 + 8.34726i) q^{28} -6.63043i q^{29} -0.0675826 q^{31} +(-5.13538 - 2.37232i) q^{32} +(-1.41334 + 2.26543i) q^{34} +(0.924721 + 9.82198i) q^{35} +(7.60938 + 7.60938i) q^{37} +(-0.102897 - 0.444244i) q^{38} +(-6.32432 - 0.0550251i) q^{40} +3.19684i q^{41} +(-6.70505 + 6.70505i) q^{43} +(-2.11597 + 1.03578i) q^{44} +(-7.99807 - 4.98979i) q^{46} +(7.34279 + 7.34279i) q^{47} -12.4653i q^{49} +(-6.46985 + 2.85326i) q^{50} +(-1.97250 + 5.75531i) q^{52} +(-5.73432 - 5.73432i) q^{53} +(-1.67971 + 2.02887i) q^{55} +(12.4133 + 1.27774i) q^{56} +(-9.13501 + 2.11587i) q^{58} +8.68448i q^{59} -12.5620i q^{61} +(0.0215666 + 0.0931112i) q^{62} +(-1.62966 + 7.83225i) q^{64} +(0.637580 + 6.77210i) q^{65} +(1.87740 + 1.87740i) q^{67} +(3.57219 + 1.22428i) q^{68} +(13.2370 - 4.40837i) q^{70} -4.18221i q^{71} +(3.97893 + 3.97893i) q^{73} +(8.05547 - 12.9120i) q^{74} +(-0.579216 + 0.283530i) q^{76} +(3.67485 - 3.67485i) q^{77} +9.66644i q^{79} +(1.94238 + 8.73082i) q^{80} +(4.40441 - 1.02016i) q^{82} +(0.585119 + 0.585119i) q^{83} +(4.20329 - 0.395732i) q^{85} +(11.3775 + 7.09813i) q^{86} +(2.10228 + 2.58473i) q^{88} +0.557322 q^{89} -13.4210i q^{91} +(-4.32232 + 12.6116i) q^{92} +(7.77325 - 12.4596i) q^{94} +(-0.459796 + 0.555372i) q^{95} +(-10.5772 + 10.5772i) q^{97} +(-17.1739 + 3.97786i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q+O(q^{10}) $ 48 * q	$ 48 q + 16 q^{10} - 8 q^{16} + 16 q^{22} - 32 q^{28} + 32 q^{31} - 56 q^{40} - 16 q^{46} - 56 q^{52} - 80 q^{58} - 64 q^{70} + 48 q^{76} - 48 q^{82} + 64 q^{88} - 32 q^{97}+O(q^{100}) $ 48 * q + 16 * q^10 - 8 * q^16 + 16 * q^22 - 32 * q^28 + 32 * q^31 - 56 * q^40 - 16 * q^46 - 56 * q^52 - 80 * q^58 - 64 * q^70 + 48 * q^76 - 48 * q^82 + 64 * q^88 - 32 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/360\mathbb{Z}\right)^\times$.

$n$	$181$	$217$	$271$	$281$
$\chi(n)$	$-1$	$e\left(\frac{3}{4}\right)$	$1$	$-1$

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 $

$2$	−0.319115	−	1.37774i	−0.225649	−	0.974209i
$2$	−0.319115	−	1.37774i	−0.225649	−	0.974209i
$3$		0			0
$3$		0			0
$4$	−1.79633	+	0.879316i	−0.898165	+	0.439658i
$5$	−1.42597	+	1.72238i	−0.637714	+	0.770273i
$5$	−1.42597	+	1.72238i	−0.637714	+	0.770273i
$6$		0			0
$7$	3.11972	−	3.11972i	1.17914	−	1.17914i	0.199179	−	0.979963i	$-0.436172\pi$
$7$	3.11972	−	3.11972i	1.17914	−	1.17914i	0.979963	−	0.199179i	$-0.0638277\pi$
$8$	1.78470	+	2.19427i	0.630988	+	0.775792i
$9$		0			0
$10$	2.82804	+	1.41498i	0.894306	+	0.447455i
$11$	1.17794			0.355163			0.177581	−	0.984106i	$-0.443173\pi$
$11$	1.17794			0.355163			0.177581	+	0.984106i	$0.443173\pi$
$12$		0			0
$13$	2.15100	−	2.15100i	0.596579	−	0.596579i	−0.342822	−	0.939401i	$-0.611383\pi$
$13$	2.15100	−	2.15100i	0.596579	−	0.596579i	0.939401	+	0.342822i	$0.111383\pi$
$14$	−5.29371	−	3.30261i	−1.41480	−	0.882659i
$15$		0			0
$16$	2.45361	−	3.15908i	0.613402	−	0.789771i
$17$	−1.33507	−	1.33507i	−0.323803	−	0.323803i	0.526421	−	0.850224i	$-0.323534\pi$
$17$	−1.33507	−	1.33507i	−0.323803	−	0.323803i	−0.850224	+	0.526421i	$0.823534\pi$
$18$		0			0
$19$	0.322444			0.0739738			0.0369869	−	0.999316i	$-0.488224\pi$
$19$	0.322444			0.0739738			0.0369869	+	0.999316i	$0.488224\pi$
$20$	1.04700	−	4.34785i	0.234116	−	0.972209i
$21$		0			0
$22$	−0.375899	−	1.62290i	−0.0801420	−	0.346003i
$23$	4.71347	−	4.71347i	0.982826	−	0.982826i	−0.0170294	−	0.999855i	$-0.505421\pi$
$23$	4.71347	−	4.71347i	0.982826	−	0.982826i	0.999855	+	0.0170294i	$0.00542088\pi$
$24$		0			0
$25$	−0.933209	−	4.91214i	−0.186642	−	0.982428i
$26$	−3.64993	−	2.27710i	−0.715810	−	0.446575i
$27$		0			0
$28$	−2.86083	+	8.34726i	−0.540646	+	1.57748i
$29$		−	6.63043i		−	1.23124i	−0.788043	−	0.615620i	$-0.788906\pi$
$29$		−	6.63043i		−	1.23124i	0.788043	−	0.615620i	$-0.211094\pi$
$30$		0			0
$31$	−0.0675826			−0.0121382			−0.00606909	−	0.999982i	$-0.501932\pi$
$31$	−0.0675826			−0.0121382			−0.00606909	+	0.999982i	$0.501932\pi$
$32$	−5.13538	−	2.37232i	−0.907815	−	0.419371i
$33$		0			0
$34$	−1.41334	+	2.26543i	−0.242386	+	0.388518i
$35$	0.924721	+	9.82198i	0.156306	+	1.66022i
$36$		0			0
$37$	7.60938	+	7.60938i	1.25097	+	1.25097i	0.955284	+	0.295690i	$0.0955496\pi$
$37$	7.60938	+	7.60938i	1.25097	+	1.25097i	0.295690	+	0.955284i	$0.404450\pi$
$38$	−0.102897	−	0.444244i	−0.0166921	−	0.0720659i
$39$		0			0
$40$	−6.32432	−	0.0550251i	−0.999962	−	0.00870023i
$41$			3.19684i			0.499262i	0.968341	+	0.249631i	$0.0803093\pi$
$41$			3.19684i			0.499262i	−0.968341	+	0.249631i	$0.919691\pi$
$42$		0			0
$43$	−6.70505	+	6.70505i	−1.02251	+	1.02251i	−0.0227703	+	0.999741i	$0.507249\pi$
$43$	−6.70505	+	6.70505i	−1.02251	+	1.02251i	−0.999741	+	0.0227703i	$0.992751\pi$
$44$	−2.11597	+	1.03578i	−0.318995	+	0.156150i
$45$		0			0
$46$	−7.99807	−	4.98979i	−1.17925	−	0.735704i
$47$	7.34279	+	7.34279i	1.07106	+	1.07106i	0.997274	+	0.0737817i	$0.0235068\pi$
$47$	7.34279	+	7.34279i	1.07106	+	1.07106i	0.0737817	+	0.997274i	$0.476493\pi$
$48$		0			0
$49$		−	12.4653i		−	1.78075i
$50$	−6.46985	+	2.85326i	−0.914975	+	0.403512i
$51$		0			0
$52$	−1.97250	+	5.75531i	−0.273536	+	0.798117i
$53$	−5.73432	−	5.73432i	−0.787669	−	0.787669i	0.193442	−	0.981112i	$-0.438035\pi$
$53$	−5.73432	−	5.73432i	−0.787669	−	0.787669i	−0.981112	+	0.193442i	$0.938035\pi$
$54$		0			0
$55$	−1.67971	+	2.02887i	−0.226492	+	0.273572i
$56$	12.4133	+	1.27774i	1.65879	+	0.170745i
$57$		0			0
$58$	−9.13501	+	2.11587i	−1.19949	+	0.277828i
$59$			8.68448i			1.13062i	0.824877	+	0.565312i	$0.191244\pi$
$59$			8.68448i			1.13062i	−0.824877	+	0.565312i	$0.808756\pi$
$60$		0			0
$61$		−	12.5620i		−	1.60840i	−0.594359	−	0.804199i	$-0.702594\pi$
$61$		−	12.5620i		−	1.60840i	0.594359	−	0.804199i	$-0.297406\pi$
$62$	0.0215666	+	0.0931112i	0.00273897	+	0.0118251i
$63$		0			0
$64$	−1.62966	+	7.83225i	−0.203708	+	0.979032i
$65$	0.637580	+	6.77210i	0.0790821	+	0.839976i
$66$		0			0
$67$	1.87740	+	1.87740i	0.229360	+	0.229360i	0.812425	−	0.583065i	$-0.198147\pi$
$67$	1.87740	+	1.87740i	0.229360	+	0.229360i	−0.583065	+	0.812425i	$0.698147\pi$
$68$	3.57219	+	1.22428i	0.433191	+	0.148466i
$69$		0			0
$70$	13.2370	−	4.40837i	1.58213	−	0.526901i
$71$		−	4.18221i		−	0.496337i	−0.968717	−	0.248168i	$-0.920171\pi$
$71$		−	4.18221i		−	0.496337i	0.968717	−	0.248168i	$-0.0798286\pi$
$72$		0			0
$73$	3.97893	+	3.97893i	0.465699	+	0.465699i	0.900518	−	0.434819i	$-0.143188\pi$
$73$	3.97893	+	3.97893i	0.465699	+	0.465699i	−0.434819	+	0.900518i	$0.643188\pi$
$74$	8.05547	−	12.9120i	0.936429	−	1.50099i
$75$		0			0
$76$	−0.579216	+	0.283530i	−0.0664407	+	0.0325231i
$77$	3.67485	−	3.67485i	0.418788	−	0.418788i
$78$		0			0
$79$			9.66644i			1.08756i	0.839228	+	0.543780i	$0.183007\pi$
$79$			9.66644i			1.08756i	−0.839228	+	0.543780i	$0.816993\pi$
$80$	1.94238	+	8.73082i	0.217164	+	0.976135i
$81$		0			0
$82$	4.40441	−	1.02016i	0.486385	−	0.112658i
$83$	0.585119	+	0.585119i	0.0642251	+	0.0642251i	0.738490	−	0.674265i	$-0.235539\pi$
$83$	0.585119	+	0.585119i	0.0642251	+	0.0642251i	−0.674265	+	0.738490i	$0.735539\pi$
$84$		0			0
$85$	4.20329	−	0.395732i	0.455911	−	0.0429231i
$86$	11.3775	+	7.09813i	1.22687	+	0.765411i
$87$		0			0
$88$	2.10228	+	2.58473i	0.224104	+	0.275533i
$89$	0.557322			0.0590760			0.0295380	−	0.999564i	$-0.490596\pi$
$89$	0.557322			0.0590760			0.0295380	+	0.999564i	$0.490596\pi$
$90$		0			0
$91$		−	13.4210i		−	1.40690i
$92$	−4.32232	+	12.6116i	−0.450633	+	1.31485i
$93$		0			0
$94$	7.77325	−	12.4596i	0.801750	−	1.28511i
$95$	−0.459796	+	0.555372i	−0.0471741	+	0.0569800i
$96$		0			0
$97$	−10.5772	+	10.5772i	−1.07395	+	1.07395i	−0.0769138	+	0.997038i	$0.524507\pi$
$97$	−10.5772	+	10.5772i	−1.07395	+	1.07395i	−0.997038	+	0.0769138i	$0.975493\pi$
$98$	−17.1739	+	3.97786i	−1.73483	+	0.401825i
$99$		0			0
$100$	5.99567	+	8.00324i	0.599567	+	0.800324i
$101$	−9.52870			−0.948141			−0.474071	−	0.880487i	$-0.657216\pi$
$101$	−9.52870			−0.948141			−0.474071	+	0.880487i	$0.657216\pi$
$102$		0			0
$103$	−0.162450	−	0.162450i	−0.0160066	−	0.0160066i	0.699058	−	0.715065i	$-0.253603\pi$
$103$	−0.162450	−	0.162450i	−0.0160066	−	0.0160066i	−0.715065	+	0.699058i	$0.753603\pi$
$104$	8.55876	+	0.880979i	0.839256	+	0.0863871i
$105$		0			0
$106$	−6.07049	+	9.73030i	−0.589618	+	0.945091i
$107$	11.7955	−	11.7955i	1.14032	−	1.14032i	0.151925	−	0.988392i	$-0.451453\pi$
$107$	11.7955	−	11.7955i	1.14032	−	1.14032i	0.988392	−	0.151925i	$-0.0485471\pi$
$108$		0			0
$109$	−10.8601			−1.04021			−0.520105	−	0.854102i	$-0.674107\pi$
$109$	−10.8601			−1.04021			−0.520105	+	0.854102i	$0.674107\pi$
$110$	3.33127	+	1.66676i	0.317624	+	0.158920i
$111$		0			0
$112$	−2.20088	−	17.5100i	−0.207964	−	1.65454i
$113$	−8.74476	+	8.74476i	−0.822637	+	0.822637i	−0.986486	−	0.163848i	$-0.947609\pi$
$113$	−8.74476	+	8.74476i	−0.822637	+	0.822637i	0.163848	+	0.986486i	$0.447609\pi$
$114$		0			0
$115$	1.39713	+	14.8397i	0.130283	+	1.38381i
$116$	5.83024	+	11.9105i	0.541325	+	1.10586i
$117$		0			0
$118$	11.9650	−	2.77135i	1.10146	−	0.255124i
$119$	−8.33011			−0.763620
$120$		0			0
$121$	−9.61245			−0.873859
$122$	−17.3072	+	4.00873i	−1.56692	+	0.362933i
$123$		0			0
$124$	0.121401	−	0.0594264i	0.0109021	−	0.00533665i
$125$	9.79132	+	5.39723i	0.875762	+	0.482743i
$126$		0			0
$127$	−3.83755	+	3.83755i	−0.340528	+	0.340528i	−0.856566	−	0.516038i	$-0.827406\pi$
$127$	−3.83755	+	3.83755i	−0.340528	+	0.340528i	0.516038	+	0.856566i	$0.327406\pi$
$128$	11.3109	−	0.254145i	0.999748	−	0.0224635i
$129$		0			0
$130$	9.12673	−	3.03950i	0.800467	−	0.266582i
$131$	−1.85715			−0.162260			−0.0811298	−	0.996704i	$-0.525853\pi$
$131$	−1.85715			−0.162260			−0.0811298	+	0.996704i	$0.525853\pi$
$132$		0			0
$133$	1.00593	−	1.00593i	0.0872256	−	0.0872256i
$134$	1.98746	−	3.18567i	0.171690	−	0.275200i
$135$		0			0
$136$	0.546804	−	5.31223i	0.0468880	−	0.455520i
$137$	−1.89240	−	1.89240i	−0.161678	−	0.161678i	0.621631	−	0.783310i	$-0.286470\pi$
$137$	−1.89240	−	1.89240i	−0.161678	−	0.161678i	−0.783310	+	0.621631i	$0.786470\pi$
$138$		0			0
$139$	−18.4370			−1.56380			−0.781902	−	0.623401i	$-0.785750\pi$
$139$	−18.4370			−1.56380			−0.781902	+	0.623401i	$0.785750\pi$
$140$	−10.2977	−	16.8304i	−0.870316	−	1.42243i
$141$		0			0
$142$	−5.76199	+	1.33461i	−0.483536	+	0.111998i
$143$	2.53375	−	2.53375i	0.211883	−	0.211883i
$144$		0			0
$145$	11.4201	+	9.45481i	0.948392	+	0.785179i
$146$	4.21219	−	6.75167i	0.348603	−	0.558772i
$147$		0			0
$148$	−20.3600	−	6.97791i	−1.67358	−	0.573581i
$149$		−	1.24573i		−	0.102054i	−0.998697	−	0.0510272i	$-0.983750\pi$
$149$		−	1.24573i		−	0.102054i	0.998697	−	0.0510272i	$-0.0162495\pi$
$150$		0			0
$151$	16.7587			1.36380			0.681902	−	0.731444i	$-0.261153\pi$
$151$	16.7587			1.36380			0.681902	+	0.731444i	$0.261153\pi$
$152$	0.575468	+	0.707530i	0.0466766	+	0.0573883i
$153$		0			0
$154$	−6.23568	−	3.89028i	−0.502485	−	0.313488i
$155$	0.0963708	−	0.116403i	0.00774069	−	0.00934972i
$156$		0			0
$157$	6.90784	+	6.90784i	0.551306	+	0.551306i	0.926818	−	0.375512i	$-0.122533\pi$
$157$	6.90784	+	6.90784i	0.551306	+	0.551306i	−0.375512	+	0.926818i	$0.622533\pi$
$158$	13.3178	−	3.08471i	1.05951	−	0.245406i
$159$		0			0
$160$	11.4089	−	5.46223i	0.901956	−	0.431827i
$161$		−	29.4094i		−	2.31778i
$162$		0			0
$163$	6.07821	−	6.07821i	0.476082	−	0.476082i	−0.427794	−	0.903876i	$-0.640709\pi$
$163$	6.07821	−	6.07821i	0.476082	−	0.476082i	0.903876	+	0.427794i	$0.140709\pi$
$164$	−2.81103	−	5.74257i	−0.219504	−	0.448420i
$165$		0			0
$166$	0.619421	−	0.992861i	0.0480764	−	0.0770610i
$167$	−2.82159	−	2.82159i	−0.218341	−	0.218341i	0.589458	−	0.807799i	$-0.299341\pi$
$167$	−2.82159	−	2.82159i	−0.218341	−	0.218341i	−0.807799	+	0.589458i	$0.799341\pi$
$168$		0			0
$169$			3.74643i			0.288187i
$170$	−1.88655	−	5.66475i	−0.144692	−	0.434467i
$171$		0			0
$172$	6.14864	−	17.9404i	0.468829	−	1.36794i
$173$	−7.27921	−	7.27921i	−0.553428	−	0.553428i	0.374001	−	0.927428i	$-0.377986\pi$
$173$	−7.27921	−	7.27921i	−0.553428	−	0.553428i	−0.927428	+	0.374001i	$0.877986\pi$
$174$		0			0
$175$	−18.2358	−	12.4131i	−1.37850	−	0.938345i
$176$	2.89021	−	3.72122i	0.217858	−	0.280497i
$177$		0			0
$178$	−0.177850	−	0.767845i	−0.0133304	−	0.0575524i
$179$			9.56604i			0.714999i	0.933913	+	0.357500i	$0.116371\pi$
$179$			9.56604i			0.714999i	−0.933913	+	0.357500i	$0.883629\pi$
$180$		0			0
$181$			4.44857i			0.330659i	0.986238	+	0.165330i	$0.0528688\pi$
$181$			4.44857i			0.330659i	−0.986238	+	0.165330i	$0.947131\pi$
$182$	−18.4906	+	4.28285i	−1.37062	+	0.317466i
$183$		0			0
$184$	18.7548	+	1.93048i	1.38262	+	0.142317i
$185$	−23.9570	+	2.25551i	−1.76136	+	0.165828i
$186$		0			0
$187$	−1.57264	−	1.57264i	−0.115003	−	0.115003i
$188$	−19.6467	−	6.73345i	−1.43288	−	0.491087i
$189$		0			0
$190$	0.911887	+	0.456251i	0.0661552	+	0.0331000i
$191$			3.16704i			0.229159i	0.993414	+	0.114579i	$0.0365521\pi$
$191$			3.16704i			0.229159i	−0.993414	+	0.114579i	$0.963448\pi$
$192$		0			0
$193$	1.07726	+	1.07726i	0.0775426	+	0.0775426i	0.744814	−	0.667272i	$-0.232538\pi$
$193$	1.07726	+	1.07726i	0.0775426	+	0.0775426i	−0.667272	+	0.744814i	$0.732538\pi$
$194$	17.9480	+	11.1973i	1.28859	+	0.803917i
$195$		0			0
$196$	10.9609	+	22.3918i	0.782922	+	1.59941i
$197$	5.59062	−	5.59062i	0.398315	−	0.398315i	−0.479323	−	0.877638i	$-0.659118\pi$
$197$	5.59062	−	5.59062i	0.398315	−	0.398315i	0.877638	+	0.479323i	$0.159118\pi$
$198$		0			0
$199$			15.7707i			1.11796i	0.829182	+	0.558978i	$0.188806\pi$
$199$			15.7707i			1.11796i	−0.829182	+	0.558978i	$0.811194\pi$
$200$	9.11307	−	10.8144i	0.644391	−	0.764696i
$201$		0			0
$202$	3.04076	+	13.1281i	0.213947	+	0.923688i
$203$	−20.6851	−	20.6851i	−1.45181	−	1.45181i
$204$		0			0
$205$	−5.50618	−	4.55860i	−0.384568	−	0.318386i
$206$	−0.171973	+	0.275653i	−0.0119819	+	0.0192057i
$207$		0			0
$208$	−1.51747	−	12.0729i	−0.105218	−	0.837104i
$209$	0.379820			0.0262727
$210$		0			0
$211$		−	10.9274i		−	0.752273i	−0.926564	−	0.376137i	$-0.877252\pi$
$211$		−	10.9274i		−	0.752273i	0.926564	−	0.376137i	$-0.122748\pi$
$212$	15.3430	+	5.25846i	1.05376	+	0.361152i
$213$		0			0
$214$	−20.0153	−	12.4870i	−1.36822	−	0.853596i
$215$	−1.98746	−	21.1099i	−0.135543	−	1.43968i
$216$		0			0
$217$	−0.210839	+	0.210839i	−0.0143127	+	0.0143127i
$218$	3.46563	+	14.9624i	0.234722	+	1.01338i
$219$		0			0
$220$	1.23330	−	5.12151i	0.0831493	−	0.345292i
$221$	−5.74348			−0.386348
$222$		0			0
$223$	0.947865	+	0.947865i	0.0634737	+	0.0634737i	0.738131	−	0.674657i	$-0.235709\pi$
$223$	0.947865	+	0.947865i	0.0634737	+	0.0634737i	−0.674657	+	0.738131i	$0.735709\pi$
$224$	−23.4219	+	8.61996i	−1.56494	+	0.575945i
$225$		0			0
$226$	14.8386	+	9.25741i	0.987048	+	0.615794i
$227$	−4.87410	+	4.87410i	−0.323506	+	0.323506i	−0.850110	−	0.526605i	$-0.823465\pi$
$227$	−4.87410	+	4.87410i	−0.323506	+	0.323506i	0.526605	+	0.850110i	$0.323465\pi$
$228$		0			0
$229$	−17.1740			−1.13489			−0.567444	−	0.823412i	$-0.692068\pi$
$229$	−17.1740			−1.13489			−0.567444	+	0.823412i	$0.692068\pi$
$230$	19.9993	−	6.66044i	1.31872	−	0.439176i
$231$		0			0
$232$	14.5490	−	11.8334i	0.955187	−	0.776898i
$233$	17.1696	−	17.1696i	1.12482	−	1.12482i	0.133811	−	0.991007i	$-0.457278\pi$
$233$	17.1696	−	17.1696i	1.12482	−	1.12482i	0.991007	−	0.133811i	$-0.0427216\pi$
$234$		0			0
$235$	−23.1177	+	2.17649i	−1.50803	+	0.141978i
$236$	−7.63640	−	15.6002i	−0.497087	−	1.01549i
$237$		0			0
$238$	2.65827	+	11.4767i	0.172310	+	0.743926i
$239$	−19.8347			−1.28300			−0.641501	−	0.767122i	$-0.721688\pi$
$239$	−19.8347			−1.28300			−0.641501	+	0.767122i	$0.721688\pi$
$240$		0			0
$241$	−2.89615			−0.186557			−0.0932787	−	0.995640i	$-0.529735\pi$
$241$	−2.89615			−0.186557			−0.0932787	+	0.995640i	$0.529735\pi$
$242$	3.06748	+	13.2435i	0.197185	+	0.851321i
$243$		0			0
$244$	11.0460	+	22.5655i	0.707145	+	1.44461i
$245$	21.4700	+	17.7751i	1.37167	+	1.13561i
$246$		0			0
$247$	0.693576	−	0.693576i	0.0441312	−	0.0441312i
$248$	−0.120615	−	0.148295i	−0.00765905	−	0.00941671i
$249$		0			0
$250$	4.31141	−	15.2122i	0.272678	−	0.962105i
$251$	8.93270			0.563827			0.281914	−	0.959440i	$-0.409031\pi$
$251$	8.93270			0.563827			0.281914	+	0.959440i	$0.409031\pi$
$252$		0			0
$253$	5.55219	−	5.55219i	0.349063	−	0.349063i
$254$	6.51177	+	4.06252i	0.408584	+	0.254905i
$255$		0			0
$256$	−3.95961	−	15.5023i	−0.247476	−	0.968894i
$257$	12.4301	+	12.4301i	0.775367	+	0.775367i	0.979039	−	0.203672i	$-0.0652877\pi$
$257$	12.4301	+	12.4301i	0.775367	+	0.775367i	−0.203672	+	0.979039i	$0.565288\pi$
$258$		0			0
$259$	47.4782			2.95015
$260$	−7.10012	−	11.6043i	−0.440331	−	0.719668i
$261$		0			0
$262$	0.592644	+	2.55866i	0.0366137	+	0.158075i
$263$	−12.1529	+	12.1529i	−0.749383	+	0.749383i	−0.974363	−	0.224981i	$-0.927768\pi$
$263$	−12.1529	+	12.1529i	−0.749383	+	0.749383i	0.224981	+	0.974363i	$0.427768\pi$
$264$		0			0
$265$	18.0537	−	1.69972i	1.10903	−	0.104413i
$266$	−1.70693	−	1.06491i	−0.104658	−	0.0652936i
$267$		0			0
$268$	−5.02325	−	1.72160i	−0.306844	−	0.105163i
$269$			19.0912i			1.16401i	0.813185	+	0.582005i	$0.197732\pi$
$269$			19.0912i			1.16401i	−0.813185	+	0.582005i	$0.802268\pi$
$270$		0			0
$271$	13.6087			0.826670			0.413335	−	0.910579i	$-0.364364\pi$
$271$	13.6087			0.826670			0.413335	+	0.910579i	$0.364364\pi$
$272$	−7.49336	+	0.941862i	−0.454352	+	0.0571088i
$273$		0			0
$274$	−2.00334	+	3.21112i	−0.121026	+	0.193991i
$275$	−1.09927	−	5.78622i	−0.0662882	−	0.348922i
$276$		0			0
$277$	−13.9103	−	13.9103i	−0.835788	−	0.835788i	0.152514	−	0.988301i	$-0.451263\pi$
$277$	−13.9103	−	13.9103i	−0.835788	−	0.835788i	−0.988301	+	0.152514i	$0.951263\pi$
$278$	5.88353	+	25.4014i	0.352870	+	1.52347i
$279$		0			0
$280$	−19.9017	+	19.5584i	−1.18936	+	1.16884i
$281$			13.9435i			0.831799i	0.909411	+	0.415899i	$0.136533\pi$
$281$			13.9435i			0.831799i	−0.909411	+	0.415899i	$0.863467\pi$
$282$		0			0
$283$	14.3526	−	14.3526i	0.853174	−	0.853174i	−0.137349	−	0.990523i	$-0.543858\pi$
$283$	14.3526	−	14.3526i	0.853174	−	0.853174i	0.990523	+	0.137349i	$0.0438582\pi$
$284$	3.67748	+	7.51263i	0.218218	+	0.445793i
$285$		0			0
$286$	−4.29940	−	2.68229i	−0.254229	−	0.158607i
$287$	9.97323	+	9.97323i	0.588701	+	0.588701i
$288$		0			0
$289$		−	13.4352i		−	0.790303i
$290$	9.38192	−	18.7512i	0.550925	−	1.10111i
$291$		0			0
$292$	−10.6462	−	3.64874i	−0.623022	−	0.213526i
$293$	12.4180	+	12.4180i	0.725465	+	0.725465i	0.969713	−	0.244248i	$-0.0785411\pi$
$293$	12.4180	+	12.4180i	0.725465	+	0.725465i	−0.244248	+	0.969713i	$0.578541\pi$
$294$		0			0
$295$	−14.9580	−	12.3838i	−0.870889	−	0.721014i
$296$	−3.11656	+	30.2775i	−0.181146	+	1.75985i
$297$		0			0
$298$	−1.71630	+	0.397533i	−0.0994224	+	0.0230285i
$299$		−	20.2773i		−	1.17267i
$300$		0			0
$301$			41.8357i			2.41137i
$302$	−5.34796	−	23.0891i	−0.307740	−	1.32863i
$303$		0			0
$304$	0.791152	−	1.01863i	0.0453757	−	0.0584223i
$305$	21.6366	+	17.9131i	1.23891	+	1.02570i
$306$		0			0
$307$	14.9940	+	14.9940i	0.855753	+	0.855753i	0.990834	−	0.135082i	$-0.0431297\pi$
$307$	14.9940	+	14.9940i	0.855753	+	0.855753i	−0.135082	+	0.990834i	$0.543130\pi$
$308$	−3.36989	+	9.83259i	−0.192017	+	0.560264i
$309$		0			0
$310$	−0.191127	−	0.0956279i	−0.0108553	−	0.00543130i
$311$			32.7316i			1.85604i	0.372534	+	0.928019i	$0.378489\pi$
$311$			32.7316i			1.85604i	−0.372534	+	0.928019i	$0.621511\pi$
$312$		0			0
$313$	8.25286	+	8.25286i	0.466479	+	0.466479i	0.900772	−	0.434293i	$-0.143002\pi$
$313$	8.25286	+	8.25286i	0.466479	+	0.466479i	−0.434293	+	0.900772i	$0.643002\pi$
$314$	7.31281	−	11.7216i	0.412686	−	0.661488i
$315$		0			0
$316$	−8.49985	−	17.3641i	−0.478154	−	0.976808i
$317$	−8.30940	+	8.30940i	−0.466702	+	0.466702i	−0.900844	−	0.434142i	$-0.857052\pi$
$317$	−8.30940	+	8.30940i	−0.466702	+	0.466702i	0.434142	+	0.900844i	$0.357052\pi$
$318$		0			0
$319$		−	7.81027i		−	0.437291i
$320$	−11.1663	−	13.9755i	−0.624215	−	0.781253i
$321$		0			0
$322$	−40.5184	+	9.38498i	−2.25800	+	0.523005i
$323$	−0.430487	−	0.430487i	−0.0239529	−	0.0239529i
$324$		0			0
$325$	−12.5733	−	8.55867i	−0.697443	−	0.474749i
$326$	−10.3138	−	6.43454i	−0.571231	−	0.356376i
$327$		0			0
$328$	−7.01473	+	5.70541i	−0.387324	+	0.315028i
$329$	45.8149			2.52586
$330$		0			0
$331$			7.43429i			0.408626i	0.978906	+	0.204313i	$0.0654960\pi$
$331$			7.43429i			0.408626i	−0.978906	+	0.204313i	$0.934504\pi$
$332$	−1.56557	−	0.536563i	−0.0859219	−	0.0294477i
$333$		0			0
$334$	−2.98700	+	4.78782i	−0.163441	+	0.261978i
$335$	−5.91071	+	0.556482i	−0.322936	+	0.0304038i
$336$		0			0
$337$	−3.88868	+	3.88868i	−0.211830	+	0.211830i	−0.805044	−	0.593215i	$-0.797859\pi$
$337$	−3.88868	+	3.88868i	−0.211830	+	0.211830i	0.593215	+	0.805044i	$0.297859\pi$
$338$	5.16160	−	1.19554i	0.280754	−	0.0650290i
$339$		0			0
$340$	−7.20253	+	4.40688i	−0.390612	+	0.238997i
$341$	−0.0796083			−0.00431103
$342$		0			0
$343$	−17.0501	−	17.0501i	−0.920620	−	0.920620i
$344$	−26.6793	−	2.74617i	−1.43845	−	0.148064i
$345$		0			0
$346$	−7.70594	+	12.3518i	−0.414274	+	0.664034i
$347$	20.7432	−	20.7432i	1.11355	−	1.11355i	0.120889	−	0.992666i	$-0.461426\pi$
$347$	20.7432	−	20.7432i	1.11355	−	1.11355i	0.992666	−	0.120889i	$-0.0385744\pi$
$348$		0			0
$349$	−3.04055			−0.162757			−0.0813783	−	0.996683i	$-0.525932\pi$
$349$	−3.04055			−0.162757			−0.0813783	+	0.996683i	$0.525932\pi$
$350$	−11.2827	+	29.0855i	−0.603088	+	1.55468i
$351$		0			0
$352$	−6.04918	−	2.79446i	−0.322422	−	0.148945i
$353$	−3.46489	+	3.46489i	−0.184417	+	0.184417i	−0.793278	−	0.608860i	$-0.791627\pi$
$353$	−3.46489	+	3.46489i	−0.184417	+	0.184417i	0.608860	+	0.793278i	$0.291627\pi$
$354$		0			0
$355$	7.20337	+	5.96371i	0.382315	+	0.316521i
$356$	−1.00113	+	0.490062i	−0.0530600	+	0.0259732i
$357$		0			0
$358$	13.1795	−	3.05267i	0.696558	−	0.161339i
$359$	8.63299			0.455632			0.227816	−	0.973704i	$-0.426842\pi$
$359$	8.63299			0.455632			0.227816	+	0.973704i	$0.426842\pi$
$360$		0			0
$361$	−18.8960			−0.994528
$362$	6.12897	−	1.41961i	0.322131	−	0.0746129i
$363$		0			0
$364$	11.8013	+	24.1086i	0.618556	+	1.26363i
$365$	−12.5271	+	1.17940i	−0.655698	+	0.0617327i
$366$		0			0
$367$	15.3844	−	15.3844i	0.803060	−	0.803060i	−0.180512	−	0.983573i	$-0.557776\pi$
$367$	15.3844	−	15.3844i	0.803060	−	0.803060i	0.983573	+	0.180512i	$0.0577756\pi$
$368$	−3.32523	−	26.4552i	−0.173340	−	1.37907i
$369$		0			0
$370$	10.7526	+	32.2868i	0.558999	+	1.67851i
$371$	−35.7789			−1.85755
$372$		0			0
$373$	7.40616	−	7.40616i	0.383476	−	0.383476i	−0.488877	−	0.872353i	$-0.662593\pi$
$373$	7.40616	−	7.40616i	0.383476	−	0.383476i	0.872353	+	0.488877i	$0.162593\pi$
$374$	−1.66483	+	2.66854i	−0.0860866	+	0.137987i
$375$		0			0
$376$	−3.00737	+	29.2168i	−0.155093	+	1.50674i
$377$	−14.2620	−	14.2620i	−0.734532	−	0.734532i
$378$		0			0
$379$	6.54952			0.336426			0.168213	−	0.985751i	$-0.446200\pi$
$379$	6.54952			0.336426			0.168213	+	0.985751i	$0.446200\pi$
$380$	0.337599	−	1.40194i	0.0173184	−	0.0719179i
$381$		0			0
$382$	4.36336	−	1.01065i	0.223249	−	0.0517094i
$383$	14.8778	−	14.8778i	0.760222	−	0.760222i	−0.216140	−	0.976362i	$-0.569347\pi$
$383$	14.8778	−	14.8778i	0.760222	−	0.760222i	0.976362	+	0.216140i	$0.0693468\pi$
$384$		0			0
$385$	1.08927	+	11.5697i	0.0555142	+	0.589648i
$386$	1.14041	−	1.82795i	0.0580453	−	0.0930401i
$387$		0			0
$388$	9.69945	−	28.3008i	0.492415	−	1.43676i
$389$			0.254115i			0.0128842i	0.999979	+	0.00644208i	$0.00205059\pi$
$389$			0.254115i			0.0128842i	−0.999979	+	0.00644208i	$0.997949\pi$
$390$		0			0
$391$	−12.5857			−0.636484
$392$	27.3522	−	22.2468i	1.38150	−	1.12363i
$393$		0			0
$394$	−9.48647	−	5.91836i	−0.477921	−	0.298163i
$395$	−16.6493	−	13.7841i	−0.837718	−	0.693552i
$396$		0			0
$397$	20.6584	+	20.6584i	1.03682	+	1.03682i	0.999296	+	0.0375215i	$0.0119463\pi$
$397$	20.6584	+	20.6584i	1.03682	+	1.03682i	0.0375215	+	0.999296i	$0.488054\pi$
$398$	21.7279	−	5.03268i	1.08912	−	0.252265i
$399$		0			0
$400$	−17.8076	−	9.10438i	−0.890379	−	0.455219i
$401$		−	20.6863i		−	1.03303i	−0.856279	−	0.516513i	$-0.827230\pi$
$401$		−	20.6863i		−	1.03303i	0.856279	−	0.516513i	$-0.172770\pi$
$402$		0			0
$403$	−0.145370	+	0.145370i	−0.00724139	+	0.00724139i
$404$	17.1167	−	8.37874i	0.851588	−	0.416858i
$405$		0			0
$406$	−21.8977	+	35.0996i	−1.08677	+	1.74196i
$407$	8.96340	+	8.96340i	0.444299	+	0.444299i
$408$		0			0
$409$		−	26.9787i		−	1.33401i	−0.745053	−	0.667005i	$-0.767576\pi$
$409$		−	26.9787i		−	1.33401i	0.745053	−	0.667005i	$-0.232424\pi$
$410$	−4.52345	+	9.04079i	−0.223397	+	0.446493i
$411$		0			0
$412$	0.434658	+	0.148969i	0.0214140	+	0.00733916i
$413$	27.0931	+	27.0931i	1.33317	+	1.33317i
$414$		0			0
$415$	−1.84216	+	0.173436i	−0.0904282	+	0.00851364i
$416$	−16.1490	+	5.94333i	−0.791771	+	0.291395i
$417$		0			0
$418$	−0.121207	−	0.523294i	−0.00592841	−	0.0255951i
$419$			34.3778i			1.67946i	0.543001	+	0.839732i	$0.317288\pi$
$419$			34.3778i			1.67946i	−0.543001	+	0.839732i	$0.682712\pi$
$420$		0			0
$421$		−	4.05773i		−	0.197762i	−0.995099	−	0.0988809i	$-0.968474\pi$
$421$		−	4.05773i		−	0.197762i	0.995099	−	0.0988809i	$-0.0315263\pi$
$422$	−15.0551	+	3.48710i	−0.732871	+	0.169749i
$423$		0			0
$424$	2.34859	−	22.8167i	0.114058	−	1.10808i
$425$	−5.31217	+	7.80398i	−0.257678	+	0.378549i
$426$		0			0
$427$	−39.1899	−	39.1899i	−1.89653	−	1.89653i
$428$	−10.8167	+	31.5607i	−0.522844	+	1.52554i
$429$		0			0
$430$	−28.4497	+	9.47469i	−1.37197	+	0.456910i
$431$		−	16.0853i		−	0.774800i	−0.921912	−	0.387400i	$-0.873373\pi$
$431$		−	16.0853i		−	0.774800i	0.921912	−	0.387400i	$-0.126627\pi$
$432$		0			0
$433$	−3.04812	−	3.04812i	−0.146483	−	0.146483i	0.630062	−	0.776545i	$-0.283030\pi$
$433$	−3.04812	−	3.04812i	−0.146483	−	0.146483i	−0.776545	+	0.630062i	$0.783030\pi$
$434$	0.357762	+	0.223199i	0.0171731	+	0.0107139i
$435$		0			0
$436$	19.5084	−	9.54947i	0.934281	−	0.457337i
$437$	1.51983	−	1.51983i	0.0727033	−	0.0727033i
$438$		0			0
$439$		−	4.78470i		−	0.228361i	−0.993460	−	0.114181i	$-0.963576\pi$
$439$		−	4.78470i		−	0.228361i	0.993460	−	0.114181i	$-0.0364243\pi$
$440$	−7.44968	−	0.0648164i	−0.355149	−	0.00309000i
$441$		0			0
$442$	1.83283	+	7.91302i	0.0871790	+	0.376384i
$443$	11.2608	+	11.2608i	0.535019	+	0.535019i	0.922062	−	0.387043i	$-0.126503\pi$
$443$	11.2608	+	11.2608i	0.535019	+	0.535019i	−0.387043	+	0.922062i	$0.626503\pi$
$444$		0			0
$445$	−0.794726	+	0.959922i	−0.0376736	+	0.0455047i
$446$	1.00343	−	1.60839i	0.0475139	−	0.0761594i
$447$		0			0
$448$	19.3503	+	29.5185i	0.914218	+	1.39462i
$449$	−7.49133			−0.353538			−0.176769	−	0.984252i	$-0.556565\pi$
$449$	−7.49133			−0.353538			−0.176769	+	0.984252i	$0.556565\pi$
$450$		0			0
$451$			3.76569i			0.177319i
$452$	8.01907	−	23.3979i	0.377185	−	1.10054i
$453$		0			0
$454$	8.27065	+	5.15984i	0.388161	+	0.242163i
$455$	23.1161	+	19.1380i	1.08370	+	0.897202i
$456$		0			0
$457$	−14.2198	+	14.2198i	−0.665173	+	0.665173i	−0.956595	−	0.291422i	$-0.905872\pi$
$457$	−14.2198	+	14.2198i	−0.665173	+	0.665173i	0.291422	+	0.956595i	$0.405872\pi$
$458$	5.48048	+	23.6613i	0.256086	+	1.10562i
$459$		0			0
$460$	−15.5584	−	25.4284i	−0.725416	−	1.18561i
$461$	−19.4366			−0.905254			−0.452627	−	0.891700i	$-0.649513\pi$
$461$	−19.4366			−0.905254			−0.452627	+	0.891700i	$0.649513\pi$
$462$		0			0
$463$	−2.18789	−	2.18789i	−0.101680	−	0.101680i	0.654437	−	0.756117i	$-0.272906\pi$
$463$	−2.18789	−	2.18789i	−0.101680	−	0.101680i	−0.756117	+	0.654437i	$0.772906\pi$
$464$	−20.9461	−	16.2685i	−0.972398	−	0.755246i
$465$		0			0
$466$	−29.1343	−	18.1762i	−1.34962	−	0.841994i
$467$	−2.06992	+	2.06992i	−0.0957845	+	0.0957845i	−0.753375	−	0.657591i	$-0.771576\pi$
$467$	−2.06992	+	2.06992i	−0.0957845	+	0.0957845i	0.657591	+	0.753375i	$0.271576\pi$
$468$		0			0
$469$	11.7139			0.540897
$470$	10.3759	+	31.1556i	0.478602	+	1.43710i
$471$		0			0
$472$	−19.0561	+	15.4992i	−0.877129	+	0.713410i
$473$	−7.89816	+	7.89816i	−0.363158	+	0.363158i
$474$		0			0
$475$	−0.300908	−	1.58389i	−0.0138066	−	0.0726739i
$476$	14.9636	−	7.32480i	0.685857	−	0.335732i
$477$		0			0
$478$	6.32957	+	27.3271i	0.289508	+	1.24991i
$479$	−27.5481			−1.25871			−0.629353	−	0.777120i	$-0.716680\pi$
$479$	−27.5481			−1.25871			−0.629353	+	0.777120i	$0.716680\pi$
$480$		0			0
$481$	32.7355			1.49261
$482$	0.924206	+	3.99014i	0.0420964	+	0.181746i
$483$		0			0
$484$	17.2671	−	8.45238i	0.784870	−	0.384199i
$485$	−3.13520	−	33.3008i	−0.142362	−	1.51211i
$486$		0			0
$487$	27.7336	−	27.7336i	1.25673	−	1.25673i	0.304083	−	0.952646i	$-0.401650\pi$
$487$	27.7336	−	27.7336i	1.25673	−	1.25673i	0.952646	−	0.304083i	$-0.0983500\pi$
$488$	27.5644	−	22.4195i	1.24778	−	1.01488i
$489$		0			0
$490$	17.6381	−	35.2524i	0.796808	−	1.59254i
$491$	2.58679			0.116740			0.0583700	−	0.998295i	$-0.481410\pi$
$491$	2.58679			0.116740			0.0583700	+	0.998295i	$0.481410\pi$
$492$		0			0
$493$	−8.85213	+	8.85213i	−0.398680	+	0.398680i
$494$	−1.17690	−	0.734236i	−0.0529511	−	0.0330349i
$495$		0			0
$496$	−0.165821	+	0.213499i	−0.00744559	+	0.00958639i
$497$	−13.0473	−	13.0473i	−0.585252	−	0.585252i
$498$		0			0
$499$	25.5951			1.14579			0.572897	−	0.819627i	$-0.305819\pi$
$499$	25.5951			1.14579			0.572897	+	0.819627i	$0.305819\pi$
$500$	−22.3343	−	1.08555i	−0.998821	−	0.0485473i
$501$		0			0
$502$	−2.85056	−	12.3069i	−0.127227	−	0.549285i
$503$	9.39909	−	9.39909i	0.419085	−	0.419085i	−0.465804	−	0.884888i	$-0.654235\pi$
$503$	9.39909	−	9.39909i	0.419085	−	0.419085i	0.884888	+	0.465804i	$0.154235\pi$
$504$		0			0
$505$	13.5877	−	16.4121i	0.604643	−	0.730328i
$506$	−9.42126	−	5.87768i	−0.418826	−	0.261295i
$507$		0			0
$508$	3.51909	−	10.2679i	0.156134	−	0.455566i
$509$		−	11.5075i		−	0.510059i	−0.966933	−	0.255030i	$-0.917915\pi$
$509$		−	11.5075i		−	0.510059i	0.966933	−	0.255030i	$-0.0820852\pi$
$510$		0			0
$511$	24.8263			1.09825
$512$	−20.0946	+	10.4023i	−0.888062	+	0.459723i
$513$		0			0
$514$	13.1588	−	21.0920i	0.580409	−	0.930329i
$515$	0.511449	−	0.0481519i	0.0225371	−	0.00212183i
$516$		0			0
$517$	8.64938	+	8.64938i	0.380399	+	0.380399i
$518$	−15.1510	−	65.4126i	−0.665698	−	2.87406i
$519$		0			0
$520$	−13.7219	+	13.4852i	−0.601747	+	0.591366i
$521$			8.12668i			0.356036i	0.984027	+	0.178018i	$0.0569686\pi$
$521$			8.12668i			0.356036i	−0.984027	+	0.178018i	$0.943031\pi$
$522$		0			0
$523$	−23.2646	+	23.2646i	−1.01729	+	1.01729i	−0.0174440	+	0.999848i	$0.505553\pi$
$523$	−23.2646	+	23.2646i	−1.01729	+	1.01729i	−0.999848	+	0.0174440i	$0.994447\pi$
$524$	3.33605	−	1.63302i	0.145736	−	0.0713387i
$525$		0			0
$526$	20.6218	+	12.8654i	0.899152	+	0.560958i
$527$	0.0902278	+	0.0902278i	0.00393038	+	0.00393038i
$528$		0			0
$529$		−	21.4335i		−	0.931892i
$530$	−8.10297	−	24.3308i	−0.351971	−	1.05686i
$531$		0			0
$532$	−0.922457	+	2.69153i	−0.0399936	+	0.116692i
$533$	6.87638	+	6.87638i	0.297849	+	0.297849i
$534$		0			0
$535$	3.49633	+	37.1365i	0.151160	+	1.60555i
$536$	−0.768921	+	7.47011i	−0.0332123	+	0.322660i
$537$		0			0
$538$	26.3027	−	6.09229i	1.13399	−	0.262657i
$539$		−	14.6834i		−	0.632458i
$540$		0			0
$541$		−	21.6496i		−	0.930787i	−0.885104	−	0.465393i	$-0.845913\pi$
$541$		−	21.6496i		−	0.930787i	0.885104	−	0.465393i	$-0.154087\pi$
$542$	−4.34275	−	18.7492i	−0.186537	−	0.805349i
$543$		0			0
$544$	3.68889	+	10.0233i	0.158160	+	0.429747i
$545$	15.4862	−	18.7053i	0.663357	−	0.801246i
$546$		0			0
$547$	15.4574	+	15.4574i	0.660912	+	0.660912i	0.955595	−	0.294683i	$-0.0952141\pi$
$547$	15.4574	+	15.4574i	0.660912	+	0.660912i	−0.294683	+	0.955595i	$0.595214\pi$
$548$	5.06339	+	1.73536i	0.216297	+	0.0741308i
$549$		0			0
$550$	−7.62110	+	3.36097i	−0.324965	+	0.143312i
$551$		−	2.13794i		−	0.0910795i
$552$		0			0
$553$	30.1566	+	30.1566i	1.28239	+	1.28239i
$554$	−14.7258	+	23.6037i	−0.625637	+	1.00283i
$555$		0			0
$556$	33.1189	−	16.2119i	1.40456	−	0.687539i
$557$	−10.9318	+	10.9318i	−0.463194	+	0.463194i	−0.899701	−	0.436507i	$-0.856215\pi$
$557$	−10.9318	+	10.9318i	−0.463194	+	0.463194i	0.436507	+	0.899701i	$0.356215\pi$
$558$		0			0
$559$			28.8451i			1.22002i
$560$	33.2974	+	21.1780i	1.40707	+	0.894935i
$561$		0			0
$562$	19.2105	−	4.44958i	0.810346	−	0.187694i
$563$	13.9005	+	13.9005i	0.585835	+	0.585835i	0.936501	−	0.350666i	$-0.114045\pi$
$563$	13.9005	+	13.9005i	0.585835	+	0.585835i	−0.350666	+	0.936501i	$0.614045\pi$
$564$		0			0
$565$	−2.59205	−	27.5316i	−0.109048	−	1.15826i
$566$	−24.3543	−	15.1940i	−1.02369	−	0.638652i
$567$		0			0
$568$	9.17690	−	7.46401i	0.385054	−	0.313183i
$569$	3.03632			0.127289			0.0636446	−	0.997973i	$-0.479728\pi$
$569$	3.03632			0.127289			0.0636446	+	0.997973i	$0.479728\pi$
$570$		0			0
$571$			1.26119i			0.0527792i	0.999652	+	0.0263896i	$0.00840105\pi$
$571$			1.26119i			0.0527792i	−0.999652	+	0.0263896i	$0.991599\pi$
$572$	−2.32349	+	6.77942i	−0.0971498	+	0.283462i
$573$		0			0
$574$	10.5579	−	16.9231i	0.440678	−	0.706357i
$575$	−27.5519	−	18.7546i	−1.14899	−	0.782119i
$576$		0			0
$577$	−5.10444	+	5.10444i	−0.212501	+	0.212501i	−0.805329	−	0.592828i	$-0.798011\pi$
$577$	−5.10444	+	5.10444i	−0.212501	+	0.212501i	0.592828	+	0.805329i	$0.298011\pi$
$578$	−18.5101	+	4.28736i	−0.769920	+	0.178331i
$579$		0			0
$580$	−28.8281	−	6.94205i	−1.19702	−	0.288253i
$581$	3.65081			0.151461
$582$		0			0
$583$	−6.75469	−	6.75469i	−0.279751	−	0.279751i
$584$	−1.62964	+	15.8321i	−0.0674351	+	0.655136i
$585$		0			0
$586$	13.1459	−	21.0715i	0.543054	−	0.870454i
$587$	2.16591	−	2.16591i	0.0893966	−	0.0893966i	−0.660994	−	0.750391i	$-0.729865\pi$
$587$	2.16591	−	2.16591i	0.0893966	−	0.0893966i	0.750391	+	0.660994i	$0.229865\pi$
$588$		0			0
$589$	−0.0217916			−0.000897908
$590$	−12.2884	+	24.5601i	−0.505904	+	1.01112i
$591$		0			0
$592$	42.7091	−	5.36823i	1.75533	−	0.220633i
$593$	−14.8495	+	14.8495i	−0.609795	+	0.609795i	−0.942892	−	0.333097i	$-0.891906\pi$
$593$	−14.8495	+	14.8495i	−0.609795	+	0.609795i	0.333097	+	0.942892i	$0.391906\pi$
$594$		0			0
$595$	11.8785	−	14.3476i	0.486971	−	0.588196i
$596$	1.09539	+	2.23775i	0.0448690	+	0.0916618i
$597$		0			0
$598$	−27.9368	+	6.47080i	−1.14242	+	0.264611i
$599$	−20.1979			−0.825262			−0.412631	−	0.910898i	$-0.635390\pi$
$599$	−20.1979			−0.825262			−0.412631	+	0.910898i	$0.635390\pi$
$600$		0			0
$601$	−30.9787			−1.26365			−0.631823	−	0.775113i	$-0.717693\pi$
$601$	−30.9787			−1.26365			−0.631823	+	0.775113i	$0.717693\pi$
$602$	57.6388	−	13.3504i	2.34918	−	0.544123i
$603$		0			0
$604$	−30.1042	+	14.7362i	−1.22492	+	0.599607i
$605$	13.7071	−	16.5563i	0.557272	−	0.673110i
$606$		0			0
$607$	−7.72619	+	7.72619i	−0.313596	+	0.313596i	−0.846301	−	0.532705i	$-0.821176\pi$
$607$	−7.72619	+	7.72619i	−0.313596	+	0.313596i	0.532705	+	0.846301i	$0.321176\pi$
$608$	−1.65587	−	0.764941i	−0.0671545	−	0.0310224i
$609$		0			0
$610$	17.7750	−	35.5259i	0.719687	−	1.43840i
$611$	31.5886			1.27794
$612$		0			0
$613$	−7.56398	+	7.56398i	−0.305506	+	0.305506i	−0.843164	−	0.537657i	$-0.819309\pi$
$613$	−7.56398	+	7.56398i	−0.305506	+	0.305506i	0.537657	+	0.843164i	$0.319309\pi$
$614$	15.8730	−	25.4426i	0.640582	−	1.02678i
$615$		0			0
$616$	14.6221	+	1.50510i	0.589142	+	0.0606422i
$617$	−20.1379	−	20.1379i	−0.810722	−	0.810722i	0.174020	−	0.984742i	$-0.444324\pi$
$617$	−20.1379	−	20.1379i	−0.810722	−	0.810722i	−0.984742	+	0.174020i	$0.944324\pi$
$618$		0			0
$619$	−26.5448			−1.06692			−0.533462	−	0.845824i	$-0.679109\pi$
$619$	−26.5448			−1.06692			−0.533462	+	0.845824i	$0.679109\pi$
$620$	−0.0707588	+	0.293839i	−0.00284174	+	0.0118009i
$621$		0			0
$622$	45.0956	−	10.4451i	1.80817	−	0.418812i
$623$	1.73869	−	1.73869i	0.0696591	−	0.0696591i
$624$		0			0
$625$	−23.2582	+	9.16811i	−0.930330	+	0.366724i
$626$	8.73667	−	14.0039i	0.349188	−	0.559708i
$627$		0			0
$628$	−18.4829	−	6.33460i	−0.737550	−	0.252778i
$629$		−	20.3182i		−	0.810139i
$630$		0			0
$631$	−38.2805			−1.52392			−0.761961	−	0.647623i	$-0.775763\pi$
$631$	−38.2805			−1.52392			−0.761961	+	0.647623i	$0.775763\pi$
$632$	−21.2108	+	17.2517i	−0.843720	+	0.686237i
$633$		0			0
$634$	14.0998	+	8.79653i	0.559976	+	0.349355i
$635$	−1.13749	−	12.0820i	−0.0451401	−	0.479458i
$636$		0			0
$637$	−26.8128	−	26.8128i	−1.06236	−	1.06236i
$638$	−10.7605	+	2.49238i	−0.426013	+	0.0986741i
$639$		0			0
$640$	−15.6912	+	19.8440i	−0.620250	+	0.784404i
$641$			24.4013i			0.963792i	0.876228	+	0.481896i	$0.160052\pi$
$641$			24.4013i			0.963792i	−0.876228	+	0.481896i	$0.839948\pi$
$642$		0			0
$643$	1.08062	−	1.08062i	0.0426157	−	0.0426157i	−0.685478	−	0.728094i	$-0.740407\pi$
$643$	1.08062	−	1.08062i	0.0426157	−	0.0426157i	0.728094	+	0.685478i	$0.240407\pi$
$644$	25.8601	+	52.8289i	1.01903	+	2.08175i
$645$		0			0
$646$	−0.455724	+	0.730474i	−0.0179302	+	0.0287401i
$647$	−22.0445	−	22.0445i	−0.866659	−	0.866659i	0.125442	−	0.992101i	$-0.459965\pi$
$647$	−22.0445	−	22.0445i	−0.866659	−	0.866659i	−0.992101	+	0.125442i	$0.959965\pi$
$648$		0			0
$649$			10.2298i			0.401556i
$650$	−7.77927	+	20.0540i	−0.305128	+	0.786581i
$651$		0			0
$652$	−5.57381	+	16.2631i	−0.218287	+	0.636914i
$653$	−20.9241	−	20.9241i	−0.818823	−	0.818823i	0.167115	−	0.985937i	$-0.446555\pi$
$653$	−20.9241	−	20.9241i	−0.818823	−	0.818823i	−0.985937	+	0.167115i	$0.946555\pi$
$654$		0			0
$655$	2.64824	−	3.19872i	0.103475	−	0.124984i
$656$	10.0991	+	7.84378i	0.394302	+	0.306248i
$657$		0			0
$658$	−14.6202	−	63.1209i	−0.569956	−	2.46071i
$659$			7.22520i			0.281454i	0.990048	+	0.140727i	$0.0449440\pi$
$659$			7.22520i			0.281454i	−0.990048	+	0.140727i	$0.955056\pi$
$660$		0			0
$661$			20.3836i			0.792830i	0.918071	+	0.396415i	$0.129746\pi$
$661$			20.3836i			0.792830i	−0.918071	+	0.396415i	$0.870254\pi$
$662$	10.2425	−	2.37240i	0.398087	−	0.0922059i
$663$		0			0
$664$	−0.239646	+	2.32817i	−0.00930006	+	0.0903507i
$665$	0.298171	+	3.16704i	0.0115626	+	0.122813i
$666$		0			0
$667$	−31.2523	−	31.2523i	−1.21009	−	1.21009i
$668$	7.54957	+	2.58744i	0.292102	+	0.100111i
$669$		0			0
$670$	2.65288	+	7.96583i	0.102490	+	0.307747i
$671$		−	14.7973i		−	0.571244i
$672$		0			0
$673$	−19.4517	−	19.4517i	−0.749807	−	0.749807i	0.224636	−	0.974443i	$-0.427881\pi$
$673$	−19.4517	−	19.4517i	−0.749807	−	0.749807i	−0.974443	+	0.224636i	$0.927881\pi$
$674$	6.59852	+	4.11664i	0.254165	+	0.158567i
$675$		0			0
$676$	−3.29429	−	6.72983i	−0.126704	−	0.258839i
$677$	−24.8145	+	24.8145i	−0.953698	+	0.953698i	−0.998974	−	0.0452768i	$-0.985583\pi$
$677$	−24.8145	+	24.8145i	−0.953698	+	0.953698i	0.0452768	+	0.998974i	$0.485583\pi$
$678$		0			0
$679$			65.9957i			2.53268i
$680$	8.36997	+	8.51690i	0.320974	+	0.326608i
$681$		0			0
$682$	0.0254042	+	0.109680i	0.000972779	+	0.00419985i
$683$	7.85886	+	7.85886i	0.300711	+	0.300711i	0.841292	−	0.540581i	$-0.181796\pi$
$683$	7.85886	+	7.85886i	0.300711	+	0.300711i	−0.540581	+	0.841292i	$0.681796\pi$
$684$		0			0
$685$	5.95794	−	0.560928i	0.227641	−	0.0214320i
$686$	−18.0497	+	28.9316i	−0.689139	+	1.10461i
$687$		0			0
$688$	4.73025	+	37.6334i	0.180339	+	1.43476i
$689$	−24.6690			−0.939814
$690$		0			0
$691$			49.6748i			1.88972i	0.327479	+	0.944858i	$0.393801\pi$
$691$			49.6748i			1.88972i	−0.327479	+	0.944858i	$0.606199\pi$
$692$	19.4766	+	6.67514i	0.740389	+	0.253751i
$693$		0			0
$694$	−35.1982	−	21.9593i	−1.33611	−	0.833563i
$695$	26.2906	−	31.7556i	0.997260	−	1.20456i
$696$		0			0
$697$	4.26802	−	4.26802i	0.161663	−	0.161663i
$698$	0.970285	+	4.18908i	0.0367258	+	0.158559i
$699$		0			0
$700$	43.6727	+	6.26305i	1.65067	+	0.236721i
$701$	30.5703			1.15462			0.577312	−	0.816524i	$-0.304102\pi$
$701$	30.5703			1.15462			0.577312	+	0.816524i	$0.304102\pi$
$702$		0			0
$703$	2.45360	+	2.45360i	0.0925393	+	0.0925393i
$704$	−1.91965	+	9.22594i	−0.0723494	+	0.347716i
$705$		0			0
$706$	5.87941	+	3.66801i	0.221275	+	0.138047i
$707$	−29.7269	+	29.7269i	−1.11799	+	1.11799i
$708$		0			0
$709$	−11.1384			−0.418310			−0.209155	−	0.977882i	$-0.567071\pi$
$709$	−11.1384			−0.418310			−0.209155	+	0.977882i	$0.567071\pi$
$710$	5.91773	−	11.8275i	0.222089	−	0.443877i
$711$		0			0
$712$	0.994655	+	1.22292i	0.0372763	+	0.0458307i
$713$	−0.318548	+	0.318548i	−0.0119297	+	0.0119297i
$714$		0			0
$715$	0.751033	+	7.97714i	0.0280870	+	0.298328i
$716$	−8.41157	−	17.1838i	−0.314355	−	0.642188i
$717$		0			0
$718$	−2.75492	−	11.8940i	−0.102813	−	0.443880i
$719$	41.0316			1.53022			0.765111	−	0.643899i	$-0.222684\pi$
$719$	41.0316			1.53022			0.765111	+	0.643899i	$0.222684\pi$
$720$		0			0
$721$	−1.01359			−0.0377482
$722$	6.03001	+	26.0338i	0.224414	+	0.968878i
$723$		0			0
$724$	−3.91169	−	7.99110i	−0.145377	−	0.296987i
$725$	−32.5696	+	6.18758i	−1.20961	+	0.229801i
$726$		0			0
$727$	−4.35975	+	4.35975i	−0.161694	+	0.161694i	−0.783317	−	0.621623i	$-0.786474\pi$
$727$	−4.35975	+	4.35975i	−0.161694	+	0.161694i	0.621623	+	0.783317i	$0.286474\pi$
$728$	29.4493	−	23.9525i	1.09146	−	0.887740i
$729$		0			0
$730$	5.62249	+	16.8827i	0.208098	+	0.624857i
$731$	17.9035			0.662185
$732$		0			0
$733$	28.3786	−	28.3786i	1.04819	−	1.04819i	0.0494094	−	0.998779i	$-0.484266\pi$
$733$	28.3786	−	28.3786i	1.04819	−	1.04819i	0.998779	−	0.0494094i	$-0.0157339\pi$
$734$	−26.1051	−	16.2863i	−0.963558	−	0.601139i
$735$		0			0
$736$	−35.3873	+	13.0236i	−1.30439	+	0.480055i
$737$	2.21146	+	2.21146i	0.0814603	+	0.0814603i
$738$		0			0
$739$	−6.53862			−0.240527			−0.120264	−	0.992742i	$-0.538374\pi$
$739$	−6.53862			−0.240527			−0.120264	+	0.992742i	$0.538374\pi$
$740$	41.0514	−	25.1174i	1.50908	−	0.923335i
$741$		0			0
$742$	11.4176	+	49.2940i	0.419153	+	1.80964i
$743$	−20.0409	+	20.0409i	−0.735230	+	0.735230i	−0.971651	−	0.236421i	$-0.924026\pi$
$743$	−20.0409	+	20.0409i	−0.735230	+	0.735230i	0.236421	+	0.971651i	$0.424026\pi$
$744$		0			0
$745$	2.14563	+	1.77638i	0.0786098	+	0.0650816i
$746$	−12.5672	−	7.84033i	−0.460117	−	0.287055i
$747$		0			0
$748$	4.20783	+	1.44214i	0.153854	+	0.0527297i
$749$		−	73.5974i		−	2.68919i
$750$		0			0
$751$	7.89337			0.288033			0.144017	−	0.989575i	$-0.453998\pi$
$751$	7.89337			0.288033			0.144017	+	0.989575i	$0.453998\pi$
$752$	41.2128	−	5.18016i	1.50288	−	0.188901i
$753$		0			0
$754$	−15.0981	+	24.2006i	−0.549842	+	0.881334i
$755$	−23.8974	+	28.8649i	−0.869717	+	1.05050i
$756$		0			0
$757$	5.76852	+	5.76852i	0.209660	+	0.209660i	0.804123	−	0.594463i	$-0.202635\pi$
$757$	5.76852	+	5.76852i	0.209660	+	0.209660i	−0.594463	+	0.804123i	$0.702635\pi$
$758$	−2.09005	−	9.02352i	−0.0759141	−	0.327749i
$759$		0			0
$760$	−2.03924	−	0.0177425i	−0.0739710	−	0.000643589i
$761$			11.7806i			0.427045i	0.976938	+	0.213522i	$0.0684936\pi$
$761$			11.7806i			0.427045i	−0.976938	+	0.213522i	$0.931506\pi$
$762$		0			0
$763$	−33.8805	+	33.8805i	−1.22656	+	1.22656i
$764$	−2.78483	−	5.68905i	−0.100752	−	0.205823i
$765$		0			0
$766$	−25.2455	−	15.7500i	−0.912158	−	0.569072i
$767$	18.6803	+	18.6803i	0.674506	+	0.674506i
$768$		0			0
$769$			34.7788i			1.25416i	0.778956	+	0.627078i	$0.215749\pi$
$769$			34.7788i			1.25416i	−0.778956	+	0.627078i	$0.784251\pi$
$770$	15.5925	−	5.19280i	0.561913	−	0.187136i
$771$		0			0
$772$	−2.88236	−	0.987861i	−0.103738	−	0.0355539i
$773$	−27.6201	−	27.6201i	−0.993426	−	0.993426i	0.00655287	−	0.999979i	$-0.497914\pi$
$773$	−27.6201	−	27.6201i	−0.993426	−	0.993426i	−0.999979	+	0.00655287i	$0.997914\pi$
$774$		0			0
$775$	0.0630687	+	0.331975i	0.00226549	+	0.0119249i
$776$	−42.0864	−	4.33208i	−1.51081	−	0.155513i
$777$		0			0
$778$	0.350105	−	0.0810921i	0.0125519	−	0.00290729i
$779$			1.03080i			0.0369323i
$780$		0			0
$781$		−	4.92640i		−	0.176280i
$782$	4.01628	+	17.3398i	0.143622	+	0.620068i
$783$		0			0
$784$	−39.3788	−	30.5849i	−1.40639	−	1.09232i
$785$	−21.7483	+	2.04756i	−0.776232	+	0.0730807i
$786$		0			0
$787$	−18.2310	−	18.2310i	−0.649864	−	0.649864i	0.303096	−	0.952960i	$-0.401980\pi$
$787$	−18.2310	−	18.2310i	−0.649864	−	0.649864i	−0.952960	+	0.303096i	$0.901980\pi$
$788$	−5.12668	+	14.9585i	−0.182631	+	0.532875i
$789$		0			0
$790$	−13.6778	+	27.3371i	−0.486634	+	0.972611i
$791$			54.5623i			1.94001i
$792$		0			0
$793$	−27.0208	−	27.0208i	−0.959537	−	0.959537i
$794$	21.8695	−	35.0544i	0.776120	−	1.24403i
$795$		0			0
$796$	−13.8674	−	28.3294i	−0.491518	−	1.00411i
$797$	11.4983	−	11.4983i	0.407290	−	0.407290i	−0.473502	−	0.880793i	$-0.657010\pi$
$797$	11.4983	−	11.4983i	0.407290	−	0.407290i	0.880793	+	0.473502i	$0.157010\pi$
$798$		0			0
$799$		−	19.6064i		−	0.693623i
$800$	−6.86079	+	27.4396i	−0.242566	+	0.970135i
$801$		0			0
$802$	−28.5004	+	6.60133i	−1.00638	+	0.233101i
$803$	4.68695	+	4.68695i	0.165399	+	0.165399i
$804$		0			0
$805$	50.6542	+	41.9369i	1.78533	+	1.47808i
$806$	0.246672	+	0.153892i	0.00868863	+	0.00542061i
$807$		0			0
$808$	−17.0059	−	20.9086i	−0.598266	−	0.735561i
$809$	−17.8481			−0.627506			−0.313753	−	0.949505i	$-0.601586\pi$
$809$	−17.8481			−0.627506			−0.313753	+	0.949505i	$0.601586\pi$
$810$		0			0
$811$		−	41.5242i		−	1.45811i	−0.684454	−	0.729056i	$-0.739959\pi$
$811$		−	41.5242i		−	1.45811i	0.684454	−	0.729056i	$-0.260041\pi$
$812$	55.3460	+	18.9685i	1.94226	+	0.665665i
$813$		0			0
$814$	9.48887	−	15.2096i	0.332585	−	0.533096i
$815$	1.80165	+	19.1364i	0.0631091	+	0.670317i
$816$		0			0
$817$	−2.16201	+	2.16201i	−0.0756390	+	0.0756390i
$818$	−37.1696	+	8.60931i	−1.29960	+	0.301017i
$819$		0			0
$820$	13.8994	+	3.34708i	0.485387	+	0.116885i
$821$	28.9849			1.01158			0.505790	−	0.862657i	$-0.331201\pi$
$821$	28.9849			1.01158			0.505790	+	0.862657i	$0.331201\pi$
$822$		0			0
$823$	20.6586	+	20.6586i	0.720112	+	0.720112i	0.968628	−	0.248516i	$-0.0799428\pi$
$823$	20.6586	+	20.6586i	0.720112	+	0.720112i	−0.248516	+	0.968628i	$0.579943\pi$
$824$	0.0665341	−	0.646383i	0.00231783	−	0.0225178i
$825$		0			0
$826$	28.6814	−	45.9731i	0.997955	−	1.59961i
$827$	−25.4075	+	25.4075i	−0.883504	+	0.883504i	−0.993889	−	0.110385i	$-0.964792\pi$
$827$	−25.4075	+	25.4075i	−0.883504	+	0.883504i	0.110385	+	0.993889i	$0.464792\pi$
$828$		0			0
$829$	24.7882			0.860931			0.430465	−	0.902607i	$-0.358349\pi$
$829$	24.7882			0.860931			0.430465	+	0.902607i	$0.358349\pi$
$830$	0.826812	+	2.48267i	0.0286991	+	0.0861748i
$831$		0			0
$832$	13.3418	+	20.3525i	0.462542	+	0.705598i
$833$	−16.6421	+	16.6421i	−0.576614	+	0.576614i
$834$		0			0
$835$	8.88336	−	0.836351i	0.307421	−	0.0289431i
$836$	−0.682283	+	0.333982i	−0.0235973	+	0.0115510i
$837$		0			0
$838$	47.3636	−	10.9705i	1.63615	−	0.378969i
$839$	52.8553			1.82477			0.912383	−	0.409338i	$-0.134240\pi$
$839$	52.8553			1.82477			0.912383	+	0.409338i	$0.134240\pi$
$840$		0			0
$841$	−14.9627			−0.515954
$842$	−5.59050	+	1.29488i	−0.192661	+	0.0446247i
$843$		0			0
$844$	9.60864	+	19.6292i	0.330743	+	0.675666i
$845$	−6.45279	−	5.34230i	−0.221983	−	0.183781i
$846$		0			0
$847$	−29.9881	+	29.9881i	−1.03040	+	1.03040i
$848$	−32.1850	+	4.04542i	−1.10524	+	0.138920i
$849$		0			0
$850$	12.4470	+	4.82842i	0.426930	+	0.165613i
$851$	71.7331			2.45898
$852$		0			0
$853$	7.39491	−	7.39491i	0.253197	−	0.253197i	−0.569083	−	0.822280i	$-0.692702\pi$
$853$	7.39491	−	7.39491i	0.253197	−	0.253197i	0.822280	+	0.569083i	$0.192702\pi$
$854$	−41.4873	+	66.4995i	−1.41967	+	2.27557i
$855$		0			0
$856$	46.9341	+	4.83107i	1.60418	+	0.165123i
$857$	6.82308	+	6.82308i	0.233072	+	0.233072i	0.813974	−	0.580902i	$-0.197300\pi$
$857$	6.82308	+	6.82308i	0.233072	+	0.233072i	−0.580902	+	0.813974i	$0.697300\pi$
$858$		0			0
$859$	−43.6736			−1.49012			−0.745061	−	0.666996i	$-0.767580\pi$
$859$	−43.6736			−1.49012			−0.745061	+	0.666996i	$0.767580\pi$
$860$	22.1324	+	36.1727i	0.754708	+	1.23348i
$861$		0			0
$862$	−22.1613	+	5.13306i	−0.754817	+	0.174833i
$863$	13.1338	−	13.1338i	0.447080	−	0.447080i	−0.447303	−	0.894383i	$-0.647615\pi$
$863$	13.1338	−	13.1338i	0.447080	−	0.447080i	0.894383	+	0.447303i	$0.147615\pi$
$864$		0			0
$865$	22.9175	−	2.15764i	0.779219	−	0.0733620i
$866$	−3.22681	+	5.17221i	−0.109651	+	0.175759i
$867$		0			0
$868$	0.193342	−	0.564129i	0.00656246	−	0.0191478i
$869$			11.3865i			0.386261i
$870$		0			0
$871$	8.07654			0.273663
$872$	−19.3821	−	23.8301i	−0.656361	−	0.806987i
$873$		0			0
$874$	−2.57893	−	1.60893i	−0.0872336	−	0.0544228i
$875$	47.3840	−	13.7083i	1.60187	−	0.463426i
$876$		0			0
$877$	−28.9437	−	28.9437i	−0.977360	−	0.977360i	0.0223891	−	0.999749i	$-0.492873\pi$
$877$	−28.9437	−	28.9437i	−0.977360	−	0.977360i	−0.999749	+	0.0223891i	$0.992873\pi$
$878$	−6.59207	+	1.52687i	−0.222472	+	0.0515294i
$879$		0			0
$880$	2.28801	+	10.2844i	0.0771287	+	0.346687i
$881$		−	7.23302i		−	0.243687i	−0.992549	−	0.121843i	$-0.961119\pi$
$881$		−	7.23302i		−	0.243687i	0.992549	−	0.121843i	$-0.0388805\pi$
$882$		0			0
$883$	7.01625	−	7.01625i	0.236116	−	0.236116i	−0.579124	−	0.815239i	$-0.696605\pi$
$883$	7.01625	−	7.01625i	0.236116	−	0.236116i	0.815239	+	0.579124i	$0.196605\pi$
$884$	10.3172	−	5.05033i	0.347005	−	0.169861i
$885$		0			0
$886$	11.9210	−	19.1080i	0.400494	−	0.641946i
$887$	−15.2597	−	15.2597i	−0.512371	−	0.512371i	0.402881	−	0.915252i	$-0.368009\pi$
$887$	−15.2597	−	15.2597i	−0.512371	−	0.512371i	−0.915252	+	0.402881i	$0.868009\pi$
$888$		0			0
$889$			23.9441i			0.803061i
$890$	1.57613	+	0.788599i	0.0528321	+	0.0264339i
$891$		0			0
$892$	−2.53615	−	0.869206i	−0.0849166	−	0.0291032i
$893$	2.36764	+	2.36764i	0.0792301	+	0.0792301i
$894$		0			0
$895$	−16.4764	−	13.6409i	−0.550745	−	0.455965i
$896$	34.4938	−	36.0795i	1.15236	−	1.20533i
$897$		0			0
$898$	2.39060	+	10.3211i	0.0797753	+	0.344420i
$899$			0.448102i			0.0149450i
$900$		0			0
$901$			15.3115i			0.510100i
$902$	5.18813	−	1.20169i	0.172746	−	0.0400119i
$903$		0			0
$904$	−34.7952	−	3.58157i	−1.15727	−	0.119121i
$905$	−7.66214	−	6.34353i	−0.254698	−	0.210866i
$906$		0			0
$907$	36.0510	+	36.0510i	1.19706	+	1.19706i	0.975044	+	0.222011i	$0.0712621\pi$
$907$	36.0510	+	36.0510i	1.19706	+	1.19706i	0.222011	+	0.975044i	$0.428738\pi$
$908$	4.46963	−	13.0414i	0.148330	−	0.432793i
$909$		0			0
$910$	18.9904	−	37.9552i	0.629527	−	1.25820i
$911$		−	24.0944i		−	0.798282i	−0.916890	−	0.399141i	$-0.869308\pi$
$911$		−	24.0944i		−	0.798282i	0.916890	−	0.399141i	$-0.130692\pi$
$912$		0			0
$913$	0.689236	+	0.689236i	0.0228104	+	0.0228104i
$914$	24.1289	+	15.0534i	0.798113	+	0.497922i
$915$		0			0
$916$	30.8501	−	15.1013i	1.01932	−	0.498963i
$917$	−5.79377	+	5.79377i	−0.191327	+	0.191327i
$918$		0			0
$919$		−	47.1031i		−	1.55379i	−0.629632	−	0.776893i	$-0.716794\pi$
$919$		−	47.1031i		−	1.55379i	0.629632	−	0.776893i	$-0.283206\pi$
$920$	−30.0688	+	29.5501i	−0.991339	+	0.974238i
$921$		0			0
$922$	6.20253	+	26.7786i	0.204269	+	0.881906i
$923$	−8.99592	−	8.99592i	−0.296104	−	0.296104i
$924$		0			0
$925$	30.2772	−	44.4795i	0.995508	−	1.46248i
$926$	−2.31616	+	3.71254i	−0.0761137	+	0.122002i
$927$		0			0
$928$	−15.7295	+	34.0498i	−0.516347	+	1.11774i
$929$	34.0301			1.11649			0.558246	−	0.829675i	$-0.311474\pi$
$929$	34.0301			1.11649			0.558246	+	0.829675i	$0.311474\pi$
$930$		0			0
$931$		−	4.01936i		−	0.131729i
$932$	−15.7448	+	45.9398i	−0.515738	+	1.50481i
$933$		0			0
$934$	3.51235	+	2.19127i	0.114928	+	0.0717004i
$935$	4.95123	−	0.466149i	0.161923	−	0.0152447i
$936$		0			0
$937$	26.9441	−	26.9441i	0.880227	−	0.880227i	−0.113330	−	0.993557i	$-0.536152\pi$
$937$	26.9441	−	26.9441i	0.880227	−	0.880227i	0.993557	+	0.113330i	$0.0361519\pi$
$938$	−3.73808	−	16.1387i	−0.122053	−	0.526947i
$939$		0			0
$940$	39.6132	−	24.2375i	1.29204	−	0.790539i
$941$	19.1115			0.623018			0.311509	−	0.950243i	$-0.399166\pi$
$941$	19.1115			0.623018			0.311509	+	0.950243i	$0.399166\pi$
$942$		0			0
$943$	15.0682	+	15.0682i	0.490687	+	0.490687i
$944$	27.4350	+	21.3083i	0.892934	+	0.693527i
$945$		0			0
$946$	13.4020	+	8.36118i	0.435738	+	0.271846i
$947$	−26.6896	+	26.6896i	−0.867294	+	0.867294i	−0.992172	−	0.124878i	$-0.960146\pi$
$947$	−26.6896	+	26.6896i	−0.867294	+	0.867294i	0.124878	+	0.992172i	$0.460146\pi$
$948$		0			0
$949$	17.1173			0.555652
$950$	−2.08616	+	0.920016i	−0.0676841	+	0.0298493i
$951$		0			0
$952$	−14.8668	−	18.2785i	−0.481835	−	0.592411i
$953$	−18.0251	+	18.0251i	−0.583890	+	0.583890i	−0.935970	−	0.352080i	$-0.885475\pi$
$953$	−18.0251	+	18.0251i	−0.583890	+	0.583890i	0.352080	+	0.935970i	$0.385475\pi$
$954$		0			0
$955$	−5.45486	−	4.51611i	−0.176515	−	0.146138i
$956$	35.6297	−	17.4410i	1.15235	−	0.564082i
$957$		0			0
$958$	8.79103	+	37.9541i	0.284025	+	1.22624i
$959$	−11.8075			−0.381284
$960$		0			0
$961$	−30.9954			−0.999853
$962$	−10.4464	−	45.1010i	−0.336805	−	1.45411i
$963$		0			0
$964$	5.20244	−	2.54663i	0.167559	−	0.0820214i
$965$	−3.39159	+	0.319311i	−0.109179	+	0.0102790i
$966$		0			0
$967$	20.9523	−	20.9523i	0.673779	−	0.673779i	−0.284806	−	0.958585i	$-0.591929\pi$
$967$	20.9523	−	20.9523i	0.673779	−	0.673779i	0.958585	+	0.284806i	$0.0919291\pi$
$968$	−17.1554	−	21.0923i	−0.551395	−	0.677933i
$969$		0			0
$970$	−44.8793	+	14.9463i	−1.44099	+	0.479896i
$971$	6.93592			0.222584			0.111292	−	0.993788i	$-0.464501\pi$
$971$	6.93592			0.222584			0.111292	+	0.993788i	$0.464501\pi$
$972$		0			0
$973$	−57.5182	+	57.5182i	−1.84395	+	1.84395i
$974$	−47.0599	−	29.3594i	−1.50789	−	0.940737i
$975$		0			0
$976$	−39.6844	−	30.8222i	−1.27027	−	0.986595i
$977$	6.98111	+	6.98111i	0.223346	+	0.223346i	0.809906	−	0.586560i	$-0.199518\pi$
$977$	6.98111	+	6.98111i	0.223346	+	0.223346i	−0.586560	+	0.809906i	$0.699518\pi$
$978$		0			0
$979$	0.656493			0.0209816
$980$	−54.1971	−	13.0511i	−1.73126	−	0.416903i
$981$		0			0
$982$	−0.825484	−	3.56392i	−0.0263422	−	0.113729i
$983$	−21.0079	+	21.0079i	−0.670047	+	0.670047i	−0.957727	−	0.287680i	$-0.907116\pi$
$983$	−21.0079	+	21.0079i	−0.670047	+	0.670047i	0.287680	+	0.957727i	$0.407116\pi$
$984$		0			0
$985$	1.65712	+	17.6013i	0.0528004	+	0.560823i
$986$	15.0208	+	9.37107i	0.478359	+	0.298436i
$987$		0			0
$988$	−0.636020	+	1.85576i	−0.0202345	+	0.0590397i
$989$			63.2081i			2.00990i
$990$		0			0
$991$	6.65846			0.211513			0.105756	−	0.994392i	$-0.466274\pi$
$991$	6.65846			0.211513			0.105756	+	0.994392i	$0.466274\pi$
$992$	0.347062	+	0.160328i	0.0110192	+	0.00509040i
$993$		0			0
$994$	−13.8122	+	22.1394i	−0.438096	+	0.702219i
$995$	−27.1632	−	22.4886i	−0.861132	−	0.712936i
$996$		0			0
$997$	9.19447	+	9.19447i	0.291192	+	0.291192i	0.837551	−	0.546359i	$-0.183987\pi$
$997$	9.19447	+	9.19447i	0.291192	+	0.291192i	−0.546359	+	0.837551i	$0.683987\pi$
$998$	−8.16779	−	35.2634i	−0.258547	−	1.11624i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	360.2.x.a.53.11	yes	48
3.2	odd	2	inner	360.2.x.a.53.14	yes	48
4.3	odd	2		1440.2.bj.a.593.7		48
5.2	odd	4	inner	360.2.x.a.197.23	yes	48
8.3	odd	2		1440.2.bj.a.593.17		48
8.5	even	2	inner	360.2.x.a.53.2	✓	48
12.11	even	2		1440.2.bj.a.593.18		48
15.2	even	4	inner	360.2.x.a.197.2	yes	48
20.7	even	4		1440.2.bj.a.17.8		48
24.5	odd	2	inner	360.2.x.a.53.23	yes	48
24.11	even	2		1440.2.bj.a.593.8		48
40.27	even	4		1440.2.bj.a.17.18		48
40.37	odd	4	inner	360.2.x.a.197.14	yes	48
60.47	odd	4		1440.2.bj.a.17.17		48
120.77	even	4	inner	360.2.x.a.197.11	yes	48
120.107	odd	4		1440.2.bj.a.17.7		48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
360.2.x.a.53.2	✓	48	8.5	even	2	inner
360.2.x.a.53.11	yes	48	1.1	even	1	trivial
360.2.x.a.53.14	yes	48	3.2	odd	2	inner
360.2.x.a.53.23	yes	48	24.5	odd	2	inner
360.2.x.a.197.2	yes	48	15.2	even	4	inner
360.2.x.a.197.11	yes	48	120.77	even	4	inner
360.2.x.a.197.14	yes	48	40.37	odd	4	inner
360.2.x.a.197.23	yes	48	5.2	odd	4	inner
1440.2.bj.a.17.7		48	120.107	odd	4
1440.2.bj.a.17.8		48	20.7	even	4
1440.2.bj.a.17.17		48	60.47	odd	4
1440.2.bj.a.17.18		48	40.27	even	4
1440.2.bj.a.593.7		48	4.3	odd	2
1440.2.bj.a.593.8		48	24.11	even	2
1440.2.bj.a.593.17		48	8.3	odd	2
1440.2.bj.a.593.18		48	12.11	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:	\( N \)	\(=\)	\( 360 = 2^{3} \cdot 3^{2} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	360.x (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.319115 - 1.37774i) q^{2} +(-1.79633 + 0.879316i) q^{4} +(-1.42597 + 1.72238i) q^{5} +(3.11972 - 3.11972i) q^{7} +(1.78470 + 2.19427i) q^{8} +O(q^{10})\)	\(q+(-0.319115 - 1.37774i) q^{2} +(-1.79633 + 0.879316i) q^{4} +(-1.42597 + 1.72238i) q^{5} +(3.11972 - 3.11972i) q^{7} +(1.78470 + 2.19427i) q^{8} +(2.82804 + 1.41498i) q^{10} +1.17794 q^{11} +(2.15100 - 2.15100i) q^{13} +(-5.29371 - 3.30261i) q^{14} +(2.45361 - 3.15908i) q^{16} +(-1.33507 - 1.33507i) q^{17} +0.322444 q^{19} +(1.04700 - 4.34785i) q^{20} +(-0.375899 - 1.62290i) q^{22} +(4.71347 - 4.71347i) q^{23} +(-0.933209 - 4.91214i) q^{25} +(-3.64993 - 2.27710i) q^{26} +(-2.86083 + 8.34726i) q^{28} -6.63043i q^{29} -0.0675826 q^{31} +(-5.13538 - 2.37232i) q^{32} +(-1.41334 + 2.26543i) q^{34} +(0.924721 + 9.82198i) q^{35} +(7.60938 + 7.60938i) q^{37} +(-0.102897 - 0.444244i) q^{38} +(-6.32432 - 0.0550251i) q^{40} +3.19684i q^{41} +(-6.70505 + 6.70505i) q^{43} +(-2.11597 + 1.03578i) q^{44} +(-7.99807 - 4.98979i) q^{46} +(7.34279 + 7.34279i) q^{47} -12.4653i q^{49} +(-6.46985 + 2.85326i) q^{50} +(-1.97250 + 5.75531i) q^{52} +(-5.73432 - 5.73432i) q^{53} +(-1.67971 + 2.02887i) q^{55} +(12.4133 + 1.27774i) q^{56} +(-9.13501 + 2.11587i) q^{58} +8.68448i q^{59} -12.5620i q^{61} +(0.0215666 + 0.0931112i) q^{62} +(-1.62966 + 7.83225i) q^{64} +(0.637580 + 6.77210i) q^{65} +(1.87740 + 1.87740i) q^{67} +(3.57219 + 1.22428i) q^{68} +(13.2370 - 4.40837i) q^{70} -4.18221i q^{71} +(3.97893 + 3.97893i) q^{73} +(8.05547 - 12.9120i) q^{74} +(-0.579216 + 0.283530i) q^{76} +(3.67485 - 3.67485i) q^{77} +9.66644i q^{79} +(1.94238 + 8.73082i) q^{80} +(4.40441 - 1.02016i) q^{82} +(0.585119 + 0.585119i) q^{83} +(4.20329 - 0.395732i) q^{85} +(11.3775 + 7.09813i) q^{86} +(2.10228 + 2.58473i) q^{88} +0.557322 q^{89} -13.4210i q^{91} +(-4.32232 + 12.6116i) q^{92} +(7.77325 - 12.4596i) q^{94} +(-0.459796 + 0.555372i) q^{95} +(-10.5772 + 10.5772i) q^{97} +(-17.1739 + 3.97786i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q+O(q^{10}) \) 48 * q	\( 48 q + 16 q^{10} - 8 q^{16} + 16 q^{22} - 32 q^{28} + 32 q^{31} - 56 q^{40} - 16 q^{46} - 56 q^{52} - 80 q^{58} - 64 q^{70} + 48 q^{76} - 48 q^{82} + 64 q^{88} - 32 q^{97}+O(q^{100}) \) 48 * q + 16 * q^10 - 8 * q^16 + 16 * q^22 - 32 * q^28 + 32 * q^31 - 56 * q^40 - 16 * q^46 - 56 * q^52 - 80 * q^58 - 64 * q^70 + 48 * q^76 - 48 * q^82 + 64 * q^88 - 32 * q^97

Introduction

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