LMFDB - Embedded newform 360.2.bs.a.113.12

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [360,2,Mod(113,360)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(360, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([0, 0, 10, 9]))

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

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

chi := DirichletCharacter("360.113");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 360 = 2^{3} \cdot 3^{2} \cdot 5 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	360.bs (of order $12$, degree $4$, 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:	$72$
Relative dimension:	$18$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			113.12
Character	$\chi$	$=$	360.113
Dual form			360.2.bs.a.137.12

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.771894 + 1.55054i) q^{3} +(0.743858 + 2.10871i) q^{5} +(0.110362 + 0.0295714i) q^{7} +(-1.80836 + 2.39371i) q^{9} +O(q^{10})$	\(q+(0.771894 + 1.55054i) q^{3} +(0.743858 + 2.10871i) q^{5} +(0.110362 + 0.0295714i) q^{7} +(-1.80836 + 2.39371i) q^{9} +(-1.32551 + 0.765286i) q^{11} +(0.982882 - 0.263362i) q^{13} +(-2.69547 + 2.78109i) q^{15} +(1.33466 + 1.33466i) q^{17} -3.97876i q^{19} +(0.0393361 + 0.193947i) q^{21} +(-0.815519 - 3.04356i) q^{23} +(-3.89335 + 3.13717i) q^{25} +(-5.10741 - 0.956246i) q^{27} +(4.32262 + 7.48701i) q^{29} +(-1.12574 + 1.94984i) q^{31} +(-2.20977 - 1.46455i) q^{33} +(0.0197360 + 0.254719i) q^{35} +(6.75392 - 6.75392i) q^{37} +(1.16704 + 1.32071i) q^{39} +(7.09348 + 4.09542i) q^{41} +(1.23131 - 4.59533i) q^{43} +(-6.39281 - 2.03273i) q^{45} +(-2.33040 + 8.69716i) q^{47} +(-6.05087 - 3.49347i) q^{49} +(-1.03923 + 3.09967i) q^{51} +(9.31019 - 9.31019i) q^{53} +(-2.59977 - 2.22587i) q^{55} +(6.16924 - 3.07118i) q^{57} +(3.09504 - 5.36076i) q^{59} +(3.06018 + 5.30039i) q^{61} +(-0.270359 + 0.210699i) q^{63} +(1.28648 + 1.87671i) q^{65} +(-2.10549 - 7.85781i) q^{67} +(4.08967 - 3.61380i) q^{69} +3.91728i q^{71} +(-3.45682 - 3.45682i) q^{73} +(-7.86956 - 3.61524i) q^{75} +(-0.168917 + 0.0452612i) q^{77} +(13.0130 - 7.51307i) q^{79} +(-2.45968 - 8.65737i) q^{81} +(-8.98846 - 2.40845i) q^{83} +(-1.82162 + 3.80722i) q^{85} +(-8.27230 + 12.4816i) q^{87} +6.35317 q^{89} +0.116261 q^{91} +(-3.89226 - 0.240437i) q^{93} +(8.39008 - 2.95963i) q^{95} +(-7.85545 - 2.10486i) q^{97} +(0.565134 - 4.55681i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 72 q+O(q^{10}) $ 72 * q	$ 72 q + 12 q^{15} + 16 q^{21} + 24 q^{23} - 12 q^{27} + 12 q^{33} + 12 q^{41} - 16 q^{45} - 36 q^{47} + 24 q^{51} - 40 q^{57} + 12 q^{61} - 44 q^{63} - 72 q^{65} - 36 q^{75} - 48 q^{77} - 20 q^{81} - 60 q^{83} + 24 q^{85} - 40 q^{87} - 84 q^{93} - 60 q^{95} + 24 q^{97}+O(q^{100}) $ 72 * q + 12 * q^15 + 16 * q^21 + 24 * q^23 - 12 * q^27 + 12 * q^33 + 12 * q^41 - 16 * q^45 - 36 * q^47 + 24 * q^51 - 40 * q^57 + 12 * q^61 - 44 * q^63 - 72 * q^65 - 36 * q^75 - 48 * q^77 - 20 * q^81 - 60 * q^83 + 24 * q^85 - 40 * q^87 - 84 * q^93 - 60 * q^95 + 24 * q^97

Display 100 coefficients 10 coefficients

Character values

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

$n$	$181$	$217$	$271$	$281$
$\chi(n)$	$1$	$e\left(\frac{3}{4}\right)$	$1$	$e\left(\frac{5}{6}\right)$

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			0
$2$		0			0
$3$	0.771894	+	1.55054i	0.445653	+	0.895206i
$3$	0.771894	+	1.55054i	0.445653	+	0.895206i
$4$		0			0
$5$	0.743858	+	2.10871i	0.332663	+	0.943046i
$5$	0.743858	+	2.10871i	0.332663	+	0.943046i
$6$		0			0
$7$	0.110362	+	0.0295714i	0.0417129	+	0.0111769i	0.279615	−	0.960112i	$-0.409793\pi$
$7$	0.110362	+	0.0295714i	0.0417129	+	0.0111769i	−0.237902	+	0.971289i	$0.576460\pi$
$8$		0			0
$9$	−1.80836	+	2.39371i	−0.602786	+	0.797903i
$10$		0			0
$11$	−1.32551	+	0.765286i	−0.399658	+	0.230743i	−0.686336	−	0.727284i	$-0.740782\pi$
$11$	−1.32551	+	0.765286i	−0.399658	+	0.230743i	0.286679	+	0.958027i	$0.407449\pi$
$12$		0			0
$13$	0.982882	−	0.263362i	0.272602	−	0.0730436i	−0.119928	−	0.992783i	$-0.538266\pi$
$13$	0.982882	−	0.263362i	0.272602	−	0.0730436i	0.392531	+	0.919739i	$0.371600\pi$
$14$		0			0
$15$	−2.69547	+	2.78109i	−0.695967	+	0.718074i
$16$		0			0
$17$	1.33466	+	1.33466i	0.323703	+	0.323703i	0.850186	−	0.526483i	$-0.176489\pi$
$17$	1.33466	+	1.33466i	0.323703	+	0.323703i	−0.526483	+	0.850186i	$0.676489\pi$
$18$		0			0
$19$		−	3.97876i		−	0.912791i	−0.889777	−	0.456395i	$-0.849140\pi$
$19$		−	3.97876i		−	0.912791i	0.889777	−	0.456395i	$-0.150860\pi$
$20$		0			0
$21$	0.0393361	+	0.193947i	0.00858384	+	0.0423227i
$22$		0			0
$23$	−0.815519	−	3.04356i	−0.170047	−	0.634626i	−0.997342	−	0.0728578i	$-0.976788\pi$
$23$	−0.815519	−	3.04356i	−0.170047	−	0.634626i	0.827295	−	0.561768i	$-0.189879\pi$
$24$		0			0
$25$	−3.89335	+	3.13717i	−0.778670	+	0.627434i
$26$		0			0
$27$	−5.10741	−	0.956246i	−0.982921	−	0.184030i
$28$		0			0
$29$	4.32262	+	7.48701i	0.802691	+	1.39030i	0.917839	+	0.396954i	$0.129933\pi$
$29$	4.32262	+	7.48701i	0.802691	+	1.39030i	−0.115147	+	0.993348i	$0.536734\pi$
$30$		0			0
$31$	−1.12574	+	1.94984i	−0.202189	+	0.350201i	−0.949233	−	0.314573i	$-0.898139\pi$
$31$	−1.12574	+	1.94984i	−0.202189	+	0.350201i	0.747045	+	0.664774i	$0.231472\pi$
$32$		0			0
$33$	−2.20977	−	1.46455i	−0.384671	−	0.254945i
$34$		0			0
$35$	0.0197360	+	0.254719i	0.00333599	+	0.0430553i
$36$		0			0
$37$	6.75392	−	6.75392i	1.11034	−	1.11034i	0.117232	−	0.993105i	$-0.462598\pi$
$37$	6.75392	−	6.75392i	1.11034	−	1.11034i	0.993105	−	0.117232i	$-0.0374022\pi$
$38$		0			0
$39$	1.16704	+	1.32071i	0.186875	+	0.211483i
$40$		0			0
$41$	7.09348	+	4.09542i	1.10782	+	0.639597i	0.938263	−	0.345924i	$-0.112434\pi$
$41$	7.09348	+	4.09542i	1.10782	+	0.639597i	0.169553	+	0.985521i	$0.445768\pi$
$42$		0			0
$43$	1.23131	−	4.59533i	0.187774	−	0.700781i	−0.806246	−	0.591580i	$-0.798504\pi$
$43$	1.23131	−	4.59533i	0.187774	−	0.700781i	0.994020	−	0.109201i	$-0.0348291\pi$
$44$		0			0
$45$	−6.39281	−	2.03273i	−0.952984	−	0.303022i
$46$		0			0
$47$	−2.33040	+	8.69716i	−0.339923	+	1.26861i	0.558509	+	0.829499i	$0.311374\pi$
$47$	−2.33040	+	8.69716i	−0.339923	+	1.26861i	−0.898432	+	0.439113i	$0.855293\pi$
$48$		0			0
$49$	−6.05087	−	3.49347i	−0.864410	−	0.499068i
$50$		0			0
$51$	−1.03923	+	3.09967i	−0.145522	+	0.434040i
$52$		0			0
$53$	9.31019	−	9.31019i	1.27885	−	1.27885i	0.337542	−	0.941310i	$-0.390404\pi$
$53$	9.31019	−	9.31019i	1.27885	−	1.27885i	0.941310	−	0.337542i	$-0.109596\pi$
$54$		0			0
$55$	−2.59977	−	2.22587i	−0.350552	−	0.300136i
$56$		0			0
$57$	6.16924	−	3.07118i	0.817136	−	0.406788i
$58$		0			0
$59$	3.09504	−	5.36076i	0.402940	−	0.697912i	−0.591140	−	0.806569i	$-0.701322\pi$
$59$	3.09504	−	5.36076i	0.402940	−	0.697912i	0.994079	+	0.108657i	$0.0346551\pi$
$60$		0			0
$61$	3.06018	+	5.30039i	0.391816	+	0.678646i	0.992689	−	0.120699i	$-0.0385135\pi$
$61$	3.06018	+	5.30039i	0.391816	+	0.678646i	−0.600873	+	0.799345i	$0.705180\pi$
$62$		0			0
$63$	−0.270359	+	0.210699i	−0.0340621	+	0.0265455i
$64$		0			0
$65$	1.28648	+	1.87671i	0.159568	+	0.232778i
$66$		0			0
$67$	−2.10549	−	7.85781i	−0.257227	−	0.959985i	−0.966838	−	0.255391i	$-0.917796\pi$
$67$	−2.10549	−	7.85781i	−0.257227	−	0.959985i	0.709611	−	0.704594i	$-0.248871\pi$
$68$		0			0
$69$	4.08967	−	3.61380i	0.492338	−	0.435051i
$70$		0			0
$71$			3.91728i			0.464896i	0.972609	+	0.232448i	$0.0746735\pi$
$71$			3.91728i			0.464896i	−0.972609	+	0.232448i	$0.925327\pi$
$72$		0			0
$73$	−3.45682	−	3.45682i	−0.404590	−	0.404590i	0.475257	−	0.879847i	$-0.342355\pi$
$73$	−3.45682	−	3.45682i	−0.404590	−	0.404590i	−0.879847	+	0.475257i	$0.842355\pi$
$74$		0			0
$75$	−7.86956	−	3.61524i	−0.908699	−	0.417452i
$76$		0			0
$77$	−0.168917	+	0.0452612i	−0.0192499	+	0.00515799i
$78$		0			0
$79$	13.0130	−	7.51307i	1.46408	−	0.845286i	0.464882	−	0.885373i	$-0.346097\pi$
$79$	13.0130	−	7.51307i	1.46408	−	0.845286i	0.999196	+	0.0400866i	$0.0127634\pi$
$80$		0			0
$81$	−2.45968	−	8.65737i	−0.273297	−	0.961930i
$82$		0			0
$83$	−8.98846	−	2.40845i	−0.986612	−	0.264362i	−0.270785	−	0.962640i	$-0.587283\pi$
$83$	−8.98846	−	2.40845i	−0.986612	−	0.264362i	−0.715827	+	0.698278i	$0.753950\pi$
$84$		0			0
$85$	−1.82162	+	3.80722i	−0.197583	+	0.412951i
$86$		0			0
$87$	−8.27230	+	12.4816i	−0.886884	+	1.33817i
$88$		0			0
$89$	6.35317			0.673434			0.336717	−	0.941606i	$-0.390683\pi$
$89$	6.35317			0.673434			0.336717	+	0.941606i	$0.390683\pi$
$90$		0			0
$91$	0.116261			0.0121874
$92$		0			0
$93$	−3.89226	−	0.240437i	−0.403608	−	0.0249322i
$94$		0			0
$95$	8.39008	−	2.95963i	0.860804	−	0.303652i
$96$		0			0
$97$	−7.85545	−	2.10486i	−0.797601	−	0.213716i	−0.163070	−	0.986614i	$-0.552140\pi$
$97$	−7.85545	−	2.10486i	−0.797601	−	0.213716i	−0.634530	+	0.772898i	$0.718806\pi$
$98$		0			0
$99$	0.565134	−	4.55681i	0.0567981	−	0.457976i
$100$		0			0
$101$	−6.79549	+	3.92338i	−0.676177	+	0.390391i	−0.798413	−	0.602110i	$-0.794327\pi$
$101$	−6.79549	+	3.92338i	−0.676177	+	0.390391i	0.122236	+	0.992501i	$0.460993\pi$
$102$		0			0
$103$	16.1641	−	4.33115i	1.59269	−	0.426761i	0.649868	−	0.760047i	$-0.274824\pi$
$103$	16.1641	−	4.33115i	1.59269	−	0.426761i	0.942826	+	0.333287i	$0.108158\pi$
$104$		0			0
$105$	−0.379718	+	0.227218i	−0.0370567	+	0.0221742i
$106$		0			0
$107$	−10.5102	−	10.5102i	−1.01606	−	1.01606i	−0.999869	−	0.0161926i	$-0.994846\pi$
$107$	−10.5102	−	10.5102i	−1.01606	−	1.01606i	−0.0161926	−	0.999869i	$-0.505154\pi$
$108$		0			0
$109$		−	7.09853i		−	0.679915i	−0.940441	−	0.339958i	$-0.889587\pi$
$109$		−	7.09853i		−	0.679915i	0.940441	−	0.339958i	$-0.110413\pi$
$110$		0			0
$111$	15.6855	+	5.25892i	1.48881	+	0.499155i
$112$		0			0
$113$	−3.02352	−	11.2839i	−0.284429	−	1.06150i	−0.949255	−	0.314506i	$-0.898161\pi$
$113$	−3.02352	−	11.2839i	−0.284429	−	1.06150i	0.664826	−	0.746998i	$-0.268506\pi$
$114$		0			0
$115$	5.81136	−	3.98367i	0.541912	−	0.371479i
$116$		0			0
$117$	−1.14699	+	2.82899i	−0.106039	+	0.261540i
$118$		0			0
$119$	0.107828	+	0.186764i	0.00988459	+	0.0171206i
$120$		0			0
$121$	−4.32867	+	7.49748i	−0.393516	+	0.681589i
$122$		0			0
$123$	−0.874707	+	14.1600i	−0.0788697	+	1.27676i
$124$		0			0
$125$	−9.51149	−	5.87636i	−0.850733	−	0.525597i
$126$		0			0
$127$	−3.45234	+	3.45234i	−0.306346	+	0.306346i	−0.843490	−	0.537144i	$-0.819503\pi$
$127$	−3.45234	+	3.45234i	−0.306346	+	0.306346i	0.537144	+	0.843490i	$0.319503\pi$
$128$		0			0
$129$	8.07569	−	1.63790i	0.711025	−	0.144209i
$130$		0			0
$131$	14.3530	+	8.28669i	1.25403	+	0.724012i	0.971906	−	0.235368i	$-0.0756295\pi$
$131$	14.3530	+	8.28669i	1.25403	+	0.724012i	0.282119	+	0.959379i	$0.408963\pi$
$132$		0			0
$133$	0.117658	−	0.439104i	0.0102022	−	0.0380752i
$134$		0			0
$135$	−1.78273	−	11.4814i	−0.153433	−	0.988159i
$136$		0			0
$137$	−1.74313	+	6.50545i	−0.148926	+	0.555798i	0.850623	+	0.525775i	$0.176225\pi$
$137$	−1.74313	+	6.50545i	−0.148926	+	0.555798i	−0.999549	+	0.0300231i	$0.990442\pi$
$138$		0			0
$139$	−9.41045	−	5.43313i	−0.798184	−	0.460832i	0.0446517	−	0.999003i	$-0.485782\pi$
$139$	−9.41045	−	5.43313i	−0.798184	−	0.460832i	−0.842836	+	0.538171i	$0.819116\pi$
$140$		0			0
$141$	−15.2841	+	3.09991i	−1.28716	+	0.261059i
$142$		0			0
$143$	−1.10128	+	1.10128i	−0.0920934	+	0.0920934i
$144$		0			0
$145$	−12.5725	+	14.6844i	−1.04409	+	1.21948i
$146$		0			0
$147$	0.746142	−	12.0787i	0.0615408	−	0.996236i
$148$		0			0
$149$	−5.59305	+	9.68745i	−0.458201	+	0.793627i	−0.998866	−	0.0476109i	$-0.984839\pi$
$149$	−5.59305	+	9.68745i	−0.458201	+	0.793627i	0.540665	+	0.841238i	$0.318173\pi$
$150$		0			0
$151$	2.18370	+	3.78228i	0.177707	+	0.307797i	0.941095	−	0.338143i	$-0.109799\pi$
$151$	2.18370	+	3.78228i	0.177707	+	0.307797i	−0.763388	+	0.645940i	$0.776465\pi$
$152$		0			0
$153$	−5.60834	+	0.781244i	−0.453407	+	0.0631598i
$154$		0			0
$155$	−4.94904	−	0.923460i	−0.397516	−	0.0741741i
$156$		0			0
$157$	0.594569	+	2.21896i	0.0474518	+	0.177092i	0.985585	−	0.169183i	$-0.0541129\pi$
$157$	0.594569	+	2.21896i	0.0474518	+	0.177092i	−0.938133	+	0.346276i	$0.887446\pi$
$158$		0			0
$159$	21.6223	+	7.24935i	1.71476	+	0.574911i
$160$		0			0
$161$		−	0.360009i		−	0.0283727i
$162$		0			0
$163$	16.4348	+	16.4348i	1.28727	+	1.28727i	0.936439	+	0.350832i	$0.114101\pi$
$163$	16.4348	+	16.4348i	1.28727	+	1.28727i	0.350832	+	0.936439i	$0.385899\pi$
$164$		0			0
$165$	1.44456	−	5.74918i	0.112459	−	0.447573i
$166$		0			0
$167$	−6.97638	+	1.86932i	−0.539849	+	0.144652i	−0.518432	−	0.855119i	$-0.673484\pi$
$167$	−6.97638	+	1.86932i	−0.539849	+	0.144652i	−0.0214163	+	0.999771i	$0.506818\pi$
$168$		0			0
$169$	−10.3616	+	5.98229i	−0.797049	+	0.460176i
$170$		0			0
$171$	9.52400	+	7.19503i	0.728318	+	0.550218i
$172$		0			0
$173$	1.17220	+	0.314090i	0.0891207	+	0.0238798i	0.303104	−	0.952958i	$-0.401977\pi$
$173$	1.17220	+	0.314090i	0.0891207	+	0.0238798i	−0.213983	+	0.976837i	$0.568644\pi$
$174$		0			0
$175$	−0.522449	+	0.231092i	−0.0394934	+	0.0174689i
$176$		0			0
$177$	10.7011	+	0.661044i	0.804346	+	0.0496871i
$178$		0			0
$179$	−20.5971			−1.53950			−0.769751	−	0.638345i	$-0.779620\pi$
$179$	−20.5971			−1.53950			−0.769751	+	0.638345i	$0.779620\pi$
$180$		0			0
$181$	8.04056			0.597650			0.298825	−	0.954308i	$-0.403405\pi$
$181$	8.04056			0.597650			0.298825	+	0.954308i	$0.403405\pi$
$182$		0			0
$183$	−5.85634	+	8.83628i	−0.432913	+	0.653197i
$184$		0			0
$185$	19.2660	+	9.21812i	1.41647	+	0.677730i
$186$		0			0
$187$	−2.79051	−	0.747716i	−0.204063	−	0.0546784i
$188$		0			0
$189$	−0.535386	−	0.256566i	−0.0389436	−	0.0186625i
$190$		0			0
$191$	13.3940	−	7.73303i	0.969156	−	0.559542i	0.0701772	−	0.997535i	$-0.477644\pi$
$191$	13.3940	−	7.73303i	0.969156	−	0.559542i	0.898979	+	0.437992i	$0.144310\pi$
$192$		0			0
$193$	8.03309	−	2.15246i	0.578234	−	0.154937i	0.0421640	−	0.999111i	$-0.486575\pi$
$193$	8.03309	−	2.15246i	0.578234	−	0.154937i	0.536070	+	0.844173i	$0.319908\pi$
$194$		0			0
$195$	−1.91689	+	3.44337i	−0.137272	+	0.246585i
$196$		0			0
$197$	−13.7578	−	13.7578i	−0.980206	−	0.980206i	0.0196020	−	0.999808i	$-0.493760\pi$
$197$	−13.7578	−	13.7578i	−0.980206	−	0.980206i	−0.999808	+	0.0196020i	$0.993760\pi$
$198$		0			0
$199$			24.9043i			1.76542i	0.469921	+	0.882709i	$0.344283\pi$
$199$			24.9043i			1.76542i	−0.469921	+	0.882709i	$0.655717\pi$
$200$		0			0
$201$	10.5586	−	9.33006i	0.744750	−	0.658091i
$202$		0			0
$203$	0.255652	+	0.954107i	0.0179433	+	0.0669652i
$204$		0			0
$205$	−3.35953	+	18.0045i	−0.234640	+	1.25749i
$206$		0			0
$207$	8.76014	+	3.55173i	0.608872	+	0.246862i
$208$		0			0
$209$	3.04489	+	5.27391i	0.210620	+	0.364804i
$210$		0			0
$211$	−8.84411	+	15.3185i	−0.608854	+	1.05457i	0.382576	+	0.923924i	$0.375037\pi$
$211$	−8.84411	+	15.3185i	−0.608854	+	1.05457i	−0.991430	+	0.130642i	$0.958296\pi$
$212$		0			0
$213$	−6.07391	+	3.02373i	−0.416177	+	0.207182i
$214$		0			0
$215$	10.6062	−	0.821781i	0.723334	−	0.0560450i
$216$		0			0
$217$	−0.181898	+	0.181898i	−0.0123481	+	0.0123481i
$218$		0			0
$219$	2.69164	−	8.02824i	0.181884	−	0.542498i
$220$		0			0
$221$	1.66332	+	0.960316i	0.111887	+	0.0645978i
$222$		0			0
$223$	−3.15413	+	11.7714i	−0.211216	+	0.788270i	0.776248	+	0.630428i	$0.217120\pi$
$223$	−3.15413	+	11.7714i	−0.211216	+	0.788270i	−0.987464	+	0.157842i	$0.949546\pi$
$224$		0			0
$225$	−0.468888	−	14.9927i	−0.0312592	−	0.999511i
$226$		0			0
$227$	−2.24021	+	8.36057i	−0.148688	+	0.554911i	0.850876	+	0.525367i	$0.176072\pi$
$227$	−2.24021	+	8.36057i	−0.148688	+	0.554911i	−0.999563	+	0.0295435i	$0.990595\pi$
$228$		0			0
$229$	−1.02575	−	0.592216i	−0.0677834	−	0.0391347i	0.465725	−	0.884929i	$-0.345793\pi$
$229$	−1.02575	−	0.592216i	−0.0677834	−	0.0391347i	−0.533509	+	0.845795i	$0.679127\pi$
$230$		0			0
$231$	−0.200566	−	0.226976i	−0.0131962	−	0.0149339i
$232$		0			0
$233$	−5.09065	+	5.09065i	−0.333499	+	0.333499i	−0.853914	−	0.520414i	$-0.825777\pi$
$233$	−5.09065	+	5.09065i	−0.333499	+	0.333499i	0.520414	+	0.853914i	$0.325777\pi$
$234$		0			0
$235$	−20.0733	+	1.55531i	−1.30944	+	0.101457i
$236$		0			0
$237$	21.6940	+	14.3779i	1.40918	+	0.933947i
$238$		0			0
$239$	−6.64865	+	11.5158i	−0.430065	+	0.744895i	−0.996878	−	0.0789515i	$-0.974843\pi$
$239$	−6.64865	+	11.5158i	−0.430065	+	0.744895i	0.566813	+	0.823846i	$0.308176\pi$
$240$		0			0
$241$	−11.6768	−	20.2248i	−0.752169	−	1.30280i	−0.946769	−	0.321913i	$-0.895674\pi$
$241$	−11.6768	−	20.2248i	−0.752169	−	1.30280i	0.194600	−	0.980883i	$-0.437659\pi$
$242$		0			0
$243$	11.5250	−	10.4964i	0.739329	−	0.673345i
$244$		0			0
$245$	2.86575	−	15.3582i	0.183086	−	0.981200i
$246$		0			0
$247$	−1.04786	−	3.91065i	−0.0666735	−	0.248829i
$248$		0			0
$249$	−3.20374	−	15.7961i	−0.203029	−	1.00103i
$250$		0			0
$251$		−	22.0413i		−	1.39124i	−0.718412	−	0.695618i	$-0.755131\pi$
$251$		−	22.0413i		−	1.39124i	0.718412	−	0.695618i	$-0.244869\pi$
$252$		0			0
$253$	3.41018	+	3.41018i	0.214396	+	0.214396i
$254$		0			0
$255$	−7.30935	+	0.114270i	−0.457730	+	0.00715588i
$256$		0			0
$257$	4.32253	−	1.15822i	0.269632	−	0.0722477i	−0.121470	−	0.992595i	$-0.538761\pi$
$257$	4.32253	−	1.15822i	0.269632	−	0.0722477i	0.391102	+	0.920347i	$0.372094\pi$
$258$		0			0
$259$	0.945099	−	0.545653i	0.0587256	−	0.0339052i
$260$		0			0
$261$	−25.7386	−	3.19209i	−1.59318	−	0.197585i
$262$		0			0
$263$	−28.8822	−	7.73896i	−1.78095	−	0.477204i	−0.790195	−	0.612856i	$-0.790021\pi$
$263$	−28.8822	−	7.73896i	−1.78095	−	0.477204i	−0.990757	+	0.135651i	$0.956687\pi$
$264$		0			0
$265$	26.5580	+	12.7071i	1.63144	+	0.780589i
$266$		0			0
$267$	4.90397	+	9.85085i	0.300118	+	0.602862i
$268$		0			0
$269$	−17.4857			−1.06612			−0.533061	−	0.846077i	$-0.678958\pi$
$269$	−17.4857			−1.06612			−0.533061	+	0.846077i	$0.678958\pi$
$270$		0			0
$271$	−19.0592			−1.15776			−0.578882	−	0.815411i	$-0.696511\pi$
$271$	−19.0592			−1.15776			−0.578882	+	0.815411i	$0.696511\pi$
$272$		0			0
$273$	0.0897411	+	0.180267i	0.00543138	+	0.0109103i
$274$		0			0
$275$	2.75986	−	7.13789i	0.166426	−	0.430431i
$276$		0			0
$277$	−5.73799	−	1.53749i	−0.344762	−	0.0923788i	0.0822830	−	0.996609i	$-0.473779\pi$
$277$	−5.73799	−	1.53749i	−0.344762	−	0.0923788i	−0.427045	+	0.904230i	$0.640446\pi$
$278$		0			0
$279$	−2.63160	−	6.22070i	−0.157550	−	0.372423i
$280$		0			0
$281$	−12.9185	+	7.45849i	−0.770652	+	0.444936i	−0.833107	−	0.553111i	$-0.813440\pi$
$281$	−12.9185	+	7.45849i	−0.770652	+	0.444936i	0.0624549	+	0.998048i	$0.480107\pi$
$282$		0			0
$283$	12.8077	−	3.43180i	0.761337	−	0.204000i	0.142796	−	0.989752i	$-0.454391\pi$
$283$	12.8077	−	3.43180i	0.761337	−	0.204000i	0.618541	+	0.785753i	$0.287724\pi$
$284$		0			0
$285$	11.0653	+	10.7246i	0.655451	+	0.635273i
$286$		0			0
$287$	0.661743	+	0.661743i	0.0390615	+	0.0390615i
$288$		0			0
$289$		−	13.4374i		−	0.790432i
$290$		0			0
$291$	−2.79990	−	13.8049i	−0.164133	−	0.809260i
$292$		0			0
$293$	−6.31458	−	23.5663i	−0.368902	−	1.37676i	−0.862054	−	0.506816i	$-0.830822\pi$
$293$	−6.31458	−	23.5663i	−0.368902	−	1.37676i	0.493152	−	0.869943i	$-0.335844\pi$
$294$		0			0
$295$	13.6066	+	2.53890i	0.792206	+	0.147821i
$296$		0			0
$297$	7.50174	−	2.64111i	0.435295	−	0.153253i
$298$		0			0
$299$	−1.60312	−	2.77668i	−0.0927107	−	0.160580i
$300$		0			0
$301$	0.271781	−	0.470738i	0.0156652	−	0.0271329i
$302$		0			0
$303$	−11.3288	−	7.50826i	−0.650821	−	0.431338i
$304$		0			0
$305$	−8.90067	+	10.3958i	−0.509651	+	0.595261i
$306$		0			0
$307$	14.4748	−	14.4748i	0.826123	−	0.826123i	−0.160855	−	0.986978i	$-0.551425\pi$
$307$	14.4748	−	14.4748i	0.826123	−	0.826123i	0.986978	+	0.160855i	$0.0514251\pi$
$308$		0			0
$309$	19.1926	+	21.7199i	1.09183	+	1.23560i
$310$		0			0
$311$	−2.90517	−	1.67730i	−0.164737	−	0.0951111i	0.415365	−	0.909655i	$-0.363654\pi$
$311$	−2.90517	−	1.67730i	−0.164737	−	0.0951111i	−0.580102	+	0.814544i	$0.696987\pi$
$312$		0			0
$313$	0.269640	−	1.00631i	0.0152409	−	0.0568800i	−0.957887	−	0.287147i	$-0.907293\pi$
$313$	0.269640	−	1.00631i	0.0152409	−	0.0568800i	0.973128	+	0.230267i	$0.0739599\pi$
$314$		0			0
$315$	−0.645412	−	0.413381i	−0.0363649	−	0.0232914i
$316$		0			0
$317$	3.43336	−	12.8135i	0.192837	−	0.719676i	−0.799980	−	0.600027i	$-0.795156\pi$
$317$	3.43336	−	12.8135i	0.192837	−	0.719676i	0.992816	−	0.119649i	$-0.0381769\pi$
$318$		0			0
$319$	−11.4594	−	6.61609i	−0.641604	−	0.370430i
$320$		0			0
$321$	8.18376	−	24.4093i	0.456773	−	1.36240i
$322$		0			0
$323$	5.31031	−	5.31031i	0.295473	−	0.295473i
$324$		0			0
$325$	−3.00049	+	4.10883i	−0.166437	+	0.227917i
$326$		0			0
$327$	11.0066	−	5.47931i	0.608664	−	0.303007i
$328$		0			0
$329$	−0.514375	+	0.890923i	−0.0283584	+	0.0491182i
$330$		0			0
$331$	−9.12807	−	15.8103i	−0.501724	−	0.869012i	−0.999998	−	0.00199202i	$-0.999366\pi$
$331$	−9.12807	−	15.8103i	−0.501724	−	0.869012i	0.498274	−	0.867020i	$-0.333967\pi$
$332$		0			0
$333$	3.95340	+	28.3804i	0.216645	+	1.55524i
$334$		0			0
$335$	15.0037	−	10.2850i	0.819739	−	0.561929i
$336$		0			0
$337$	7.34401	+	27.4082i	0.400054	+	1.49302i	0.812999	+	0.582264i	$0.197833\pi$
$337$	7.34401	+	27.4082i	0.400054	+	1.49302i	−0.412946	+	0.910756i	$0.635500\pi$
$338$		0			0
$339$	15.1624	−	13.3981i	0.823508	−	0.727686i
$340$		0			0
$341$		−	3.44605i		−	0.186614i
$342$		0			0
$343$	−1.13001	−	1.13001i	−0.0610150	−	0.0610150i
$344$		0			0
$345$	10.6626	+	5.93579i	0.574055	+	0.319572i
$346$		0			0
$347$	6.31078	−	1.69097i	0.338781	−	0.0907760i	−0.0854179	−	0.996345i	$-0.527223\pi$
$347$	6.31078	−	1.69097i	0.338781	−	0.0907760i	0.424199	+	0.905569i	$0.360556\pi$
$348$		0			0
$349$	12.7836	−	7.38060i	0.684289	−	0.395075i	−0.117180	−	0.993111i	$-0.537385\pi$
$349$	12.7836	−	7.38060i	0.684289	−	0.395075i	0.801469	+	0.598036i	$0.204052\pi$
$350$		0			0
$351$	−5.27182	+	0.405222i	−0.281389	+	0.0216291i
$352$		0			0
$353$	3.39401	+	0.909422i	0.180645	+	0.0484036i	0.348007	−	0.937492i	$-0.386858\pi$
$353$	3.39401	+	0.909422i	0.180645	+	0.0484036i	−0.167363	+	0.985895i	$0.553525\pi$
$354$		0			0
$355$	−8.26042	+	2.91390i	−0.438418	+	0.154654i
$356$		0			0
$357$	−0.206353	+	0.311354i	−0.0109214	+	0.0164786i
$358$		0			0
$359$	−4.97487			−0.262564			−0.131282	−	0.991345i	$-0.541909\pi$
$359$	−4.97487			−0.262564			−0.131282	+	0.991345i	$0.541909\pi$
$360$		0			0
$361$	3.16944			0.166813
$362$		0			0
$363$	−14.9664	−	0.924526i	−0.785534	−	0.0485250i
$364$		0			0
$365$	4.71806	−	9.86082i	0.246955	−	0.516139i
$366$		0			0
$367$	−1.60756	−	0.430744i	−0.0839139	−	0.0224847i	0.216618	−	0.976256i	$-0.430497\pi$
$367$	−1.60756	−	0.430744i	−0.0839139	−	0.0224847i	−0.300532	+	0.953772i	$0.597164\pi$
$368$		0			0
$369$	−22.6308	+	9.57372i	−1.17811	+	0.498388i
$370$		0			0
$371$	1.30281	−	0.752176i	0.0676383	−	0.0390510i
$372$		0			0
$373$	20.9089	−	5.60251i	1.08262	−	0.290087i	0.326951	−	0.945041i	$-0.393979\pi$
$373$	20.9089	−	5.60251i	1.08262	−	0.290087i	0.755668	+	0.654954i	$0.227312\pi$
$374$		0			0
$375$	1.76967	−	19.2839i	0.0913855	−	0.995816i
$376$		0			0
$377$	6.22043	+	6.22043i	0.320368	+	0.320368i
$378$		0			0
$379$			19.0015i			0.976040i	0.872832	+	0.488020i	$0.162281\pi$
$379$			19.0015i			0.976040i	−0.872832	+	0.488020i	$0.837719\pi$
$380$		0			0
$381$	−8.01784	−	2.68816i	−0.410767	−	0.137719i
$382$		0			0
$383$	−0.0425467	−	0.158786i	−0.00217403	−	0.00811361i	0.964830	−	0.262874i	$-0.0846702\pi$
$383$	−0.0425467	−	0.158786i	−0.00217403	−	0.00811361i	−0.967004	+	0.254760i	$0.918004\pi$
$384$		0			0
$385$	−0.221093	−	0.322530i	−0.0112680	−	0.0164376i
$386$		0			0
$387$	8.77322	+	11.2574i	0.445968	+	0.572246i
$388$		0			0
$389$	−2.90972	−	5.03979i	−0.147529	−	0.255527i	0.782785	−	0.622293i	$-0.213799\pi$
$389$	−2.90972	−	5.03979i	−0.147529	−	0.255527i	−0.930314	+	0.366765i	$0.880465\pi$
$390$		0			0
$391$	2.97368	−	5.15057i	0.150385	−	0.260475i
$392$		0			0
$393$	−1.76989	+	28.6513i	−0.0892789	+	1.44527i
$394$		0			0
$395$	25.5227	+	21.8521i	1.28419	+	1.09950i
$396$		0			0
$397$	24.9354	−	24.9354i	1.25147	−	1.25147i	0.296410	−	0.955061i	$-0.404210\pi$
$397$	24.9354	−	24.9354i	1.25147	−	1.25147i	0.955061	−	0.296410i	$-0.0957896\pi$
$398$		0			0
$399$	0.771669	−	0.156509i	0.0386318	−	0.00783525i
$400$		0			0
$401$	−2.79653	−	1.61458i	−0.139652	−	0.0806282i	0.428546	−	0.903520i	$-0.359026\pi$
$401$	−2.79653	−	1.61458i	−0.139652	−	0.0806282i	−0.568198	+	0.822892i	$0.692359\pi$
$402$		0			0
$403$	−0.592955	+	2.21294i	−0.0295372	+	0.110234i
$404$		0			0
$405$	16.4263	−	11.6266i	0.816227	−	0.577731i
$406$		0			0
$407$	−3.78374	+	14.1211i	−0.187553	+	0.699957i
$408$		0			0
$409$	−19.5609	−	11.2935i	−0.967223	−	0.558427i	−0.0688347	−	0.997628i	$-0.521928\pi$
$409$	−19.5609	−	11.2935i	−0.967223	−	0.558427i	−0.898389	+	0.439201i	$0.855261\pi$
$410$		0			0
$411$	−11.4325	+	2.31872i	−0.563923	+	0.114374i
$412$		0			0
$413$	0.500100	−	0.500100i	0.0246083	−	0.0246083i
$414$		0			0
$415$	−1.60740	−	20.7456i	−0.0789043	−	1.01836i
$416$		0			0
$417$	1.16042	−	18.7851i	0.0568258	−	0.919910i
$418$		0			0
$419$	−7.58295	+	13.1341i	−0.370451	+	0.641640i	−0.989635	−	0.143606i	$-0.954130\pi$
$419$	−7.58295	+	13.1341i	−0.370451	+	0.641640i	0.619184	+	0.785246i	$0.287464\pi$
$420$		0			0
$421$	−0.877951	−	1.52066i	−0.0427887	−	0.0741122i	0.843838	−	0.536598i	$-0.180291\pi$
$421$	−0.877951	−	1.52066i	−0.0427887	−	0.0741122i	−0.886627	+	0.462486i	$0.846958\pi$
$422$		0			0
$423$	−16.6043	−	21.3059i	−0.807327	−	1.03593i
$424$		0			0
$425$	−9.38337	−	1.00925i	−0.455160	−	0.0489558i
$426$		0			0
$427$	0.180988	+	0.675456i	0.00875862	+	0.0326876i
$428$		0			0
$429$	−2.55765	−	0.857507i	−0.123484	−	0.0414008i
$430$		0			0
$431$		−	12.1379i		−	0.584664i	−0.956317	−	0.292332i	$-0.905569\pi$
$431$		−	12.1379i		−	0.584664i	0.956317	−	0.292332i	$-0.0944311\pi$
$432$		0			0
$433$	−10.0767	−	10.0767i	−0.484257	−	0.484257i	0.422231	−	0.906488i	$-0.361247\pi$
$433$	−10.0767	−	10.0767i	−0.484257	−	0.484257i	−0.906488	+	0.422231i	$0.861247\pi$
$434$		0			0
$435$	−32.4735	−	8.15940i	−1.55699	−	0.391213i
$436$		0			0
$437$	−12.1096	+	3.24476i	−0.579281	+	0.155218i
$438$		0			0
$439$	−11.1267	+	6.42402i	−0.531050	+	0.306602i	−0.741444	−	0.671015i	$-0.765859\pi$
$439$	−11.1267	+	6.42402i	−0.531050	+	0.306602i	0.210394	+	0.977617i	$0.432525\pi$
$440$		0			0
$441$	19.3045	−	8.16657i	0.919262	−	0.388884i
$442$		0			0
$443$	11.7691	+	3.15352i	0.559166	+	0.149828i	0.527323	−	0.849665i	$-0.323196\pi$
$443$	11.7691	+	3.15352i	0.559166	+	0.149828i	0.0318429	+	0.999493i	$0.489862\pi$
$444$		0			0
$445$	4.72585	+	13.3970i	0.224027	+	0.635079i
$446$		0			0
$447$	−19.3380	−	1.19457i	−0.914658	−	0.0565014i
$448$		0			0
$449$	25.5254			1.20462			0.602308	−	0.798264i	$-0.294248\pi$
$449$	25.5254			1.20462			0.602308	+	0.798264i	$0.294248\pi$
$450$		0			0
$451$	−12.5367			−0.590329
$452$		0			0
$453$	−4.17899	+	6.30543i	−0.196346	+	0.296255i
$454$		0			0
$455$	0.0864815	+	0.245161i	0.00405432	+	0.0114933i
$456$		0			0
$457$	−11.0021	−	2.94801i	−0.514657	−	0.137902i	−0.00786315	−	0.999969i	$-0.502503\pi$
$457$	−11.0021	−	2.94801i	−0.514657	−	0.137902i	−0.506794	+	0.862067i	$0.669170\pi$
$458$		0			0
$459$	−5.54040	−	8.09293i	−0.258604	−	0.377746i
$460$		0			0
$461$	5.46431	−	3.15482i	0.254498	−	0.146935i	−0.367324	−	0.930093i	$-0.619726\pi$
$461$	5.46431	−	3.15482i	0.254498	−	0.146935i	0.621822	+	0.783158i	$0.286393\pi$
$462$		0			0
$463$	−23.9219	+	6.40986i	−1.11175	+	0.297891i	−0.767539	−	0.641002i	$-0.778519\pi$
$463$	−23.9219	+	6.40986i	−1.11175	+	0.297891i	−0.344207	+	0.938894i	$0.611852\pi$
$464$		0			0
$465$	−2.38827	−	8.38651i	−0.110753	−	0.388915i
$466$		0			0
$467$	15.3279	+	15.3279i	0.709292	+	0.709292i	0.966386	−	0.257094i	$-0.0827651\pi$
$467$	15.3279	+	15.3279i	0.709292	+	0.709292i	−0.257094	+	0.966386i	$0.582765\pi$
$468$		0			0
$469$		−	0.929466i		−	0.0429188i
$470$		0			0
$471$	−2.98165	+	2.63471i	−0.137387	+	0.121401i
$472$		0			0
$473$	1.88462	+	7.03348i	0.0866548	+	0.323400i
$474$		0			0
$475$	12.4820	+	15.4907i	0.572716	+	0.710763i
$476$		0			0
$477$	5.44971	+	39.1220i	0.249525	+	1.79127i
$478$		0			0
$479$	12.2729	+	21.2573i	0.560764	+	0.971272i	0.997430	+	0.0716481i	$0.0228259\pi$
$479$	12.2729	+	21.2573i	0.560764	+	0.971272i	−0.436666	+	0.899624i	$0.643841\pi$
$480$		0			0
$481$	4.85957	−	8.41703i	0.221578	−	0.383784i
$482$		0			0
$483$	0.558209	−	0.277889i	0.0253994	−	0.0126444i
$484$		0			0
$485$	−1.40479	−	18.1306i	−0.0637882	−	0.823269i
$486$		0			0
$487$	2.61300	−	2.61300i	0.118406	−	0.118406i	−0.645421	−	0.763827i	$-0.723318\pi$
$487$	2.61300	−	2.61300i	0.118406	−	0.118406i	0.763827	+	0.645421i	$0.223318\pi$
$488$		0			0
$489$	−12.7969	+	38.1687i	−0.578695	+	1.72605i
$490$		0			0
$491$	−21.2606	−	12.2748i	−0.959478	−	0.553955i	−0.0634657	−	0.997984i	$-0.520215\pi$
$491$	−21.2606	−	12.2748i	−0.959478	−	0.553955i	−0.896012	+	0.444029i	$0.853549\pi$
$492$		0			0
$493$	−4.22338	+	15.7619i	−0.190211	+	0.709879i
$494$		0			0
$495$	10.0294	−	2.19791i	0.450787	−	0.0987888i
$496$		0			0
$497$	−0.115840	+	0.432319i	−0.00519611	+	0.0193922i
$498$		0			0
$499$	−37.3223	−	21.5480i	−1.67077	−	0.964622i	−0.967206	−	0.253994i	$-0.918256\pi$
$499$	−37.3223	−	21.5480i	−1.67077	−	0.964622i	−0.703568	−	0.710628i	$-0.748411\pi$
$500$		0			0
$501$	−8.28348	−	9.37426i	−0.370079	−	0.418811i
$502$		0			0
$503$	−4.96402	+	4.96402i	−0.221335	+	0.221335i	−0.809060	−	0.587726i	$-0.800023\pi$
$503$	−4.96402	+	4.96402i	−0.221335	+	0.221335i	0.587726	+	0.809060i	$0.300023\pi$
$504$		0			0
$505$	−13.3282	−	11.4113i	−0.593096	−	0.507797i
$506$		0			0
$507$	−17.2739	−	11.4484i	−0.767160	−	0.508443i
$508$		0			0
$509$	−8.96626	+	15.5300i	−0.397423	+	0.688356i	−0.993407	−	0.114640i	$-0.963429\pi$
$509$	−8.96626	+	15.5300i	−0.397423	+	0.688356i	0.595984	+	0.802996i	$0.296762\pi$
$510$		0			0
$511$	−0.279278	−	0.483724i	−0.0123546	−	0.0213987i
$512$		0			0
$513$	−3.80468	+	20.3212i	−0.167981	+	0.897201i
$514$		0			0
$515$	21.1569	+	30.8636i	0.932286	+	1.36001i
$516$		0			0
$517$	−3.56684	−	13.3116i	−0.156870	−	0.585445i
$518$		0			0
$519$	0.417805	+	2.05999i	0.0183396	+	0.0904235i
$520$		0			0
$521$			44.5999i			1.95396i	0.213339	+	0.976978i	$0.431566\pi$
$521$			44.5999i			1.95396i	−0.213339	+	0.976978i	$0.568434\pi$
$522$		0			0
$523$	27.1479	+	27.1479i	1.18710	+	1.18710i	0.977866	+	0.209230i	$0.0670958\pi$
$523$	27.1479	+	27.1479i	1.18710	+	1.18710i	0.209230	+	0.977866i	$0.432904\pi$
$524$		0			0
$525$	−0.761593	−	0.631699i	−0.0332386	−	0.0275696i
$526$		0			0
$527$	−4.10486	+	1.09989i	−0.178810	+	0.0479121i
$528$		0			0
$529$	11.3204	−	6.53584i	0.492192	−	0.284167i
$530$		0			0
$531$	7.23516	+	17.1028i	0.313979	+	0.742198i
$532$		0			0
$533$	8.05063	+	2.15716i	0.348712	+	0.0934370i
$534$		0			0
$535$	14.3449	−	29.9812i	0.620186	−	1.29620i
$536$		0			0
$537$	−15.8988	−	31.9367i	−0.686084	−	1.37817i
$538$		0			0
$539$	10.6940			0.460624
$540$		0			0
$541$	43.8226			1.88408			0.942040	−	0.335500i	$-0.108905\pi$
$541$	43.8226			1.88408			0.942040	+	0.335500i	$0.108905\pi$
$542$		0			0
$543$	6.20646	+	12.4672i	0.266345	+	0.535020i
$544$		0			0
$545$	14.9688	−	5.28029i	0.641191	−	0.226183i
$546$		0			0
$547$	−0.0856777	−	0.0229573i	−0.00366331	−	0.000981582i	0.256987	−	0.966415i	$-0.417270\pi$
$547$	−0.0856777	−	0.0229573i	−0.00366331	−	0.000981582i	−0.260650	+	0.965433i	$0.583937\pi$
$548$		0			0
$549$	−18.2215	−	2.25983i	−0.777675	−	0.0964471i
$550$		0			0
$551$	29.7890	−	17.1987i	1.26906	−	0.732689i
$552$		0			0
$553$	1.65831	−	0.444344i	0.0705187	−	0.0188954i
$554$		0			0
$555$	0.578253	+	36.9882i	0.0245455	+	1.57006i
$556$		0			0
$557$	9.78830	+	9.78830i	0.414744	+	0.414744i	0.883387	−	0.468644i	$-0.155257\pi$
$557$	9.78830	+	9.78830i	0.414744	+	0.414744i	−0.468644	+	0.883387i	$0.655257\pi$
$558$		0			0
$559$		−	4.84095i		−	0.204750i
$560$		0			0
$561$	−0.994617	−	4.90397i	−0.0419928	−	0.207046i
$562$		0			0
$563$	7.61191	+	28.4080i	0.320804	+	1.19726i	0.918464	+	0.395506i	$0.129431\pi$
$563$	7.61191	+	28.4080i	0.320804	+	1.19726i	−0.597660	+	0.801750i	$0.703903\pi$
$564$		0			0
$565$	21.5455	−	14.7694i	0.906428	−	0.621353i
$566$		0			0
$567$	−0.0154444	−	1.02818i	−0.000648602	−	0.0431795i
$568$		0			0
$569$	−6.57609	−	11.3901i	−0.275684	−	0.477499i	0.694624	−	0.719373i	$-0.255571\pi$
$569$	−6.57609	−	11.3901i	−0.275684	−	0.477499i	−0.970307	+	0.241875i	$0.922238\pi$
$570$		0			0
$571$	−19.8231	+	34.3346i	−0.829570	+	1.43686i	0.0688055	+	0.997630i	$0.478081\pi$
$571$	−19.8231	+	34.3346i	−0.829570	+	1.43686i	−0.898376	+	0.439228i	$0.855252\pi$
$572$		0			0
$573$	22.3291	+	14.7989i	0.932813	+	0.618232i
$574$		0			0
$575$	12.7233	+	9.29122i	0.530596	+	0.387471i
$576$		0			0
$577$	−13.2442	+	13.2442i	−0.551362	+	0.551362i	−0.926834	−	0.375472i	$-0.877481\pi$
$577$	−13.2442	+	13.2442i	−0.551362	+	0.551362i	0.375472	+	0.926834i	$0.377481\pi$
$578$		0			0
$579$	9.53817	+	10.7942i	0.396393	+	0.448590i
$580$		0			0
$581$	−0.920763	−	0.531603i	−0.0381997	−	0.0220546i
$582$		0			0
$583$	−5.21583	+	19.4658i	−0.216018	+	0.806189i
$584$		0			0
$585$	−6.81872	−	0.314311i	−0.281919	−	0.0129952i
$586$		0			0
$587$	0.944150	−	3.52362i	0.0389693	−	0.145435i	−0.943700	−	0.330802i	$-0.892681\pi$
$587$	0.944150	−	3.52362i	0.0389693	−	0.145435i	0.982669	+	0.185367i	$0.0593474\pi$
$588$		0			0
$589$	7.75794	+	4.47905i	0.319660	+	0.184556i
$590$		0			0
$591$	10.7125	−	31.9517i	0.440654	−	1.31432i
$592$		0			0
$593$	−7.97207	+	7.97207i	−0.327374	+	0.327374i	−0.851587	−	0.524213i	$-0.824359\pi$
$593$	−7.97207	+	7.97207i	−0.327374	+	0.327374i	0.524213	+	0.851587i	$0.324359\pi$
$594$		0			0
$595$	−0.313623	+	0.366305i	−0.0128573	+	0.0150170i
$596$		0			0
$597$	−38.6151	+	19.2235i	−1.58041	+	0.786764i
$598$		0			0
$599$	6.96513	−	12.0640i	0.284588	−	0.492920i	−0.687921	−	0.725785i	$-0.741477\pi$
$599$	6.96513	−	12.0640i	0.284588	−	0.492920i	0.972509	+	0.232865i	$0.0748100\pi$
$600$		0			0
$601$	6.60510	+	11.4404i	0.269427	+	0.466662i	0.968714	−	0.248179i	$-0.0798322\pi$
$601$	6.60510	+	11.4404i	0.269427	+	0.466662i	−0.699287	+	0.714841i	$0.746499\pi$
$602$		0			0
$603$	22.6168	+	9.16981i	0.921027	+	0.373423i
$604$		0			0
$605$	−19.0300	−	3.55087i	−0.773678	−	0.144364i
$606$		0			0
$607$	−5.17251	−	19.3041i	−0.209946	−	0.783528i	−0.987885	−	0.155188i	$-0.950402\pi$
$607$	−5.17251	−	19.3041i	−0.209946	−	0.783528i	0.777939	−	0.628340i	$-0.216265\pi$
$608$		0			0
$609$	−1.28205	+	1.13287i	−0.0519511	+	0.0459062i
$610$		0			0
$611$			9.16202i			0.370656i
$612$		0			0
$613$	−26.9613	−	26.9613i	−1.08896	−	1.08896i	−0.995636	−	0.0933206i	$-0.970252\pi$
$613$	−26.9613	−	26.9613i	−1.08896	−	1.08896i	−0.0933206	−	0.995636i	$-0.529748\pi$
$614$		0			0
$615$	−30.5100	+	8.68850i	−1.23028	+	0.350354i
$616$		0			0
$617$	−32.8675	+	8.80683i	−1.32320	+	0.354549i	−0.850174	−	0.526501i	$-0.823504\pi$
$617$	−32.8675	+	8.80683i	−1.32320	+	0.354549i	−0.473022	+	0.881051i	$0.656837\pi$
$618$		0			0
$619$	35.3205	−	20.3923i	1.41965	−	0.819636i	0.423383	−	0.905951i	$-0.360842\pi$
$619$	35.3205	−	20.3923i	1.41965	−	0.819636i	0.996268	+	0.0863145i	$0.0275090\pi$
$620$		0			0
$621$	1.25480	+	16.3245i	0.0503532	+	0.655081i
$622$		0			0
$623$	0.701148	+	0.187872i	0.0280909	+	0.00752694i
$624$		0			0
$625$	5.31636	−	24.4282i	0.212654	−	0.977127i
$626$		0			0
$627$	−5.82708	+	8.79214i	−0.232711	+	0.351124i
$628$		0			0
$629$	18.0284			0.718839
$630$		0			0
$631$	4.31220			0.171666			0.0858330	−	0.996310i	$-0.472645\pi$
$631$	4.31220			0.171666			0.0858330	+	0.996310i	$0.472645\pi$
$632$		0			0
$633$	−30.5786	−	1.88894i	−1.21539	−	0.0750787i
$634$		0			0
$635$	−9.84806	−	4.71195i	−0.390808	−	0.186988i
$636$		0			0
$637$	−6.86734	−	1.84010i	−0.272094	−	0.0729074i
$638$		0			0
$639$	−9.37683	−	7.08385i	−0.370941	−	0.280233i
$640$		0			0
$641$	−9.77848	+	5.64561i	−0.386227	+	0.222988i	−0.680524	−	0.732726i	$-0.738248\pi$
$641$	−9.77848	+	5.64561i	−0.386227	+	0.222988i	0.294297	+	0.955714i	$0.404914\pi$
$642$		0			0
$643$	9.20088	−	2.46537i	0.362847	−	0.0972246i	−0.0727891	−	0.997347i	$-0.523190\pi$
$643$	9.20088	−	2.46537i	0.362847	−	0.0972246i	0.435636	+	0.900123i	$0.356523\pi$
$644$		0			0
$645$	9.46104	+	15.8110i	0.372528	+	0.622556i
$646$		0			0
$647$	12.4066	+	12.4066i	0.487753	+	0.487753i	0.907596	−	0.419844i	$-0.137915\pi$
$647$	12.4066	+	12.4066i	0.487753	+	0.487753i	−0.419844	+	0.907596i	$0.637915\pi$
$648$		0			0
$649$			9.47436i			0.371901i
$650$		0			0
$651$	−0.422447	−	0.141635i	−0.0165570	−	0.00555110i
$652$		0			0
$653$	−2.13499	−	7.96788i	−0.0835485	−	0.311807i	0.911487	−	0.411329i	$-0.134935\pi$
$653$	−2.13499	−	7.96788i	−0.0835485	−	0.311807i	−0.995035	+	0.0995219i	$0.968269\pi$
$654$		0			0
$655$	−6.79769	+	36.4304i	−0.265608	+	1.42346i
$656$		0			0
$657$	14.5258	−	2.02345i	0.566705	−	0.0789422i
$658$		0			0
$659$	2.07491	+	3.59385i	0.0808270	+	0.139996i	0.903605	−	0.428366i	$-0.140911\pi$
$659$	2.07491	+	3.59385i	0.0808270	+	0.139996i	−0.822778	+	0.568362i	$0.807577\pi$
$660$		0			0
$661$	8.97252	−	15.5409i	0.348991	−	0.604470i	−0.637080	−	0.770798i	$-0.719858\pi$
$661$	8.97252	−	15.5409i	0.348991	−	0.604470i	0.986070	+	0.166328i	$0.0531911\pi$
$662$		0			0
$663$	−0.205106	+	3.32030i	−0.00796565	+	0.128950i
$664$		0			0
$665$	1.01347	−	0.0785249i	0.0393005	−	0.00304507i
$666$		0			0
$667$	19.2620	−	19.2620i	0.745826	−	0.745826i
$668$		0			0
$669$	−20.6867	+	4.19565i	−0.799793	+	0.162213i
$670$		0			0
$671$	−8.11264	−	4.68383i	−0.313185	−	0.180817i
$672$		0			0
$673$	8.27970	−	30.9003i	0.319159	−	1.19112i	−0.600896	−	0.799328i	$-0.705189\pi$
$673$	8.27970	−	30.9003i	0.319159	−	1.19112i	0.920055	−	0.391790i	$-0.128144\pi$
$674$		0			0
$675$	22.8848	−	12.2998i	0.880837	−	0.473419i
$676$		0			0
$677$	4.46747	−	16.6728i	0.171699	−	0.640788i	−0.825392	−	0.564561i	$-0.809046\pi$
$677$	4.46747	−	16.6728i	0.171699	−	0.640788i	0.997090	−	0.0762279i	$-0.0242877\pi$
$678$		0			0
$679$	−0.804700	−	0.464594i	−0.0308816	−	0.0178295i
$680$		0			0
$681$	−14.6926	+	2.97994i	−0.563022	+	0.114192i
$682$		0			0
$683$	14.2046	−	14.2046i	0.543525	−	0.543525i	−0.381036	−	0.924560i	$-0.624432\pi$
$683$	14.2046	−	14.2046i	0.543525	−	0.543525i	0.924560	+	0.381036i	$0.124432\pi$
$684$		0			0
$685$	−15.0148	+	1.16337i	−0.573685	+	0.0444500i
$686$		0			0
$687$	0.126487	−	2.04759i	0.00482576	−	0.0781206i
$688$		0			0
$689$	6.69886	−	11.6028i	0.255206	−	0.442030i
$690$		0			0
$691$	−11.8875	−	20.5898i	−0.452223	−	0.783274i	0.546300	−	0.837589i	$-0.316036\pi$
$691$	−11.8875	−	20.5898i	−0.452223	−	0.783274i	−0.998524	+	0.0543155i	$0.982702\pi$
$692$		0			0
$693$	0.197121	−	0.486187i	0.00748799	−	0.0184687i
$694$		0			0
$695$	4.45687	−	23.8854i	0.169059	−	0.906026i
$696$		0			0
$697$	4.00139	+	14.9334i	0.151564	+	0.565643i
$698$		0			0
$699$	−11.8227	−	3.96382i	−0.447176	−	0.149925i
$700$		0			0
$701$			22.6750i			0.856421i	0.903679	+	0.428211i	$0.140856\pi$
$701$			22.6750i			0.856421i	−0.903679	+	0.428211i	$0.859144\pi$
$702$		0			0
$703$	−26.8722	−	26.8722i	−1.01351	−	1.01351i
$704$		0			0
$705$	−17.9060	−	29.9240i	−0.674381	−	1.12700i
$706$		0			0
$707$	−0.865984	+	0.232040i	−0.0325687	+	0.00872675i
$708$		0			0
$709$	36.6443	−	21.1566i	1.37620	−	0.794552i	0.384504	−	0.923123i	$-0.374373\pi$
$709$	36.6443	−	21.1566i	1.37620	−	0.794552i	0.991700	+	0.128572i	$0.0410392\pi$
$710$		0			0
$711$	−5.54811	+	44.7357i	−0.208070	+	1.67772i
$712$		0			0
$713$	6.85251	+	1.83612i	0.256628	+	0.0687634i
$714$		0			0
$715$	−3.14147	−	1.50308i	−0.117484	−	0.0562122i
$716$		0			0
$717$	−22.9878	−	1.42003i	−0.858494	−	0.0530320i
$718$		0			0
$719$	−17.5127			−0.653115			−0.326558	−	0.945177i	$-0.605889\pi$
$719$	−17.5127			−0.653115			−0.326558	+	0.945177i	$0.605889\pi$
$720$		0			0
$721$	1.91198			0.0712058
$722$		0			0
$723$	22.3462	−	33.7168i	0.831063	−	1.25394i
$724$		0			0
$725$	−40.3175	−	15.5887i	−1.49735	−	0.578951i
$726$		0			0
$727$	24.3910	+	6.53554i	0.904611	+	0.242390i	0.680995	−	0.732288i	$-0.261547\pi$
$727$	24.3910	+	6.53554i	0.904611	+	0.242390i	0.223615	+	0.974677i	$0.428214\pi$
$728$		0			0
$729$	25.1712	+	9.76788i	0.932266	+	0.361773i
$730$		0			0
$731$	7.77660	−	4.48982i	0.287628	−	0.166062i
$732$		0			0
$733$	−29.4396	+	7.88831i	−1.08738	+	0.291361i	−0.757614	−	0.652703i	$-0.773635\pi$
$733$	−29.4396	+	7.88831i	−1.08738	+	0.291361i	−0.329761	+	0.944064i	$0.606968\pi$
$734$		0			0
$735$	26.0256	−	7.41145i	0.959968	−	0.273376i
$736$		0			0
$737$	8.80434	+	8.80434i	0.324312	+	0.324312i
$738$		0			0
$739$			26.8829i			0.988902i	0.869206	+	0.494451i	$0.164631\pi$
$739$			26.8829i			0.988902i	−0.869206	+	0.494451i	$0.835369\pi$
$740$		0			0
$741$	5.25480	−	4.64336i	0.193040	−	0.170578i
$742$		0			0
$743$	−6.34950	−	23.6967i	−0.232941	−	0.869347i	−0.979066	−	0.203541i	$-0.934755\pi$
$743$	−6.34950	−	23.6967i	−0.232941	−	0.869347i	0.746126	−	0.665805i	$-0.231912\pi$
$744$		0			0
$745$	−24.5885	−	4.58806i	−0.900853	−	0.168094i
$746$		0			0
$747$	22.0195	−	17.1604i	0.805651	−	0.627867i
$748$		0			0
$749$	−0.849127	−	1.47073i	−0.0310264	−	0.0537394i
$750$		0			0
$751$	6.85220	−	11.8684i	0.250040	−	0.433082i	−0.713496	−	0.700659i	$-0.752890\pi$
$751$	6.85220	−	11.8684i	0.250040	−	0.433082i	0.963537	+	0.267577i	$0.0862228\pi$
$752$		0			0
$753$	34.1760	−	17.0136i	1.24544	−	0.620009i
$754$		0			0
$755$	−6.35138	+	7.41827i	−0.231150	+	0.269979i
$756$		0			0
$757$	−4.31103	+	4.31103i	−0.156687	+	0.156687i	−0.781097	−	0.624410i	$-0.785340\pi$
$757$	−4.31103	+	4.31103i	−0.156687	+	0.156687i	0.624410	+	0.781097i	$0.285340\pi$
$758$		0			0
$759$	−2.65533	+	7.91992i	−0.0963822	+	0.287475i
$760$		0			0
$761$	8.78180	+	5.07017i	0.318340	+	0.183794i	0.650652	−	0.759376i	$-0.274496\pi$
$761$	8.78180	+	5.07017i	0.318340	+	0.183794i	−0.332312	+	0.943169i	$0.607829\pi$
$762$		0			0
$763$	0.209913	−	0.783408i	0.00759938	−	0.0283613i
$764$		0			0
$765$	−5.81923	−	11.2453i	−0.210395	−	0.406573i
$766$		0			0
$767$	1.63023	−	6.08411i	0.0588643	−	0.219685i
$768$		0			0
$769$	−26.5641	−	15.3368i	−0.957927	−	0.553060i	−0.0623927	−	0.998052i	$-0.519873\pi$
$769$	−26.5641	−	15.3368i	−0.957927	−	0.553060i	−0.895534	+	0.444992i	$0.853206\pi$
$770$		0			0
$771$	5.13240	+	5.80824i	0.184839	+	0.209179i
$772$		0			0
$773$	2.71452	−	2.71452i	0.0976346	−	0.0976346i	−0.656602	−	0.754237i	$-0.728007\pi$
$773$	2.71452	−	2.71452i	0.0976346	−	0.0976346i	0.754237	+	0.656602i	$0.228007\pi$
$774$		0			0
$775$	−1.73407	−	11.1230i	−0.0622896	−	0.399551i
$776$		0			0
$777$	1.57557	+	1.04423i	0.0565234	+	0.0374615i
$778$		0			0
$779$	16.2947	−	28.2233i	0.583819	−	1.01120i
$780$		0			0
$781$	−2.99784	−	5.19241i	−0.107271	−	0.185799i
$782$		0			0
$783$	−14.9180	−	42.3727i	−0.533125	−	1.51428i
$784$		0			0
$785$	−4.23688	+	2.90437i	−0.151221	+	0.103661i
$786$		0			0
$787$	5.79552	+	21.6292i	0.206588	+	0.770997i	0.988960	+	0.148185i	$0.0473432\pi$
$787$	5.79552	+	21.6292i	0.206588	+	0.770997i	−0.782371	+	0.622812i	$0.785990\pi$
$788$		0			0
$789$	−10.2944	−	50.7567i	−0.366491	−	1.80699i
$790$		0			0
$791$		−	1.33473i		−	0.0474575i
$792$		0			0
$793$	4.40372	+	4.40372i	0.156381	+	0.156381i
$794$		0			0
$795$	0.797114	+	50.9878i	0.0282707	+	1.80835i
$796$		0			0
$797$	−3.07052	+	0.822742i	−0.108763	+	0.0291430i	−0.312790	−	0.949822i	$-0.601264\pi$
$797$	−3.07052	+	0.822742i	−0.108763	+	0.0291430i	0.204027	+	0.978965i	$0.434597\pi$
$798$		0			0
$799$	−14.7181	+	8.49748i	−0.520688	+	0.300619i
$800$		0			0
$801$	−11.4888	+	15.2076i	−0.405937	+	0.537335i
$802$		0			0
$803$	7.22752	+	1.93661i	0.255054	+	0.0683414i
$804$		0			0
$805$	0.759157	−	0.267796i	0.0267568	−	0.00943856i
$806$		0			0
$807$	−13.4971	−	27.1123i	−0.475121	−	0.954399i
$808$		0			0
$809$	47.2988			1.66294			0.831469	−	0.555572i	$-0.187501\pi$
$809$	47.2988			1.66294			0.831469	+	0.555572i	$0.187501\pi$
$810$		0			0
$811$	22.9109			0.804509			0.402255	−	0.915528i	$-0.368227\pi$
$811$	22.9109			0.804509			0.402255	+	0.915528i	$0.368227\pi$
$812$		0			0
$813$	−14.7117	−	29.5521i	−0.515961	−	1.03644i
$814$		0			0
$815$	−22.4311	+	46.8814i	−0.785727	+	1.64218i
$816$		0			0
$817$	−18.2837	−	4.89911i	−0.639667	−	0.171398i
$818$		0			0
$819$	−0.210241	+	0.278294i	−0.00734643	+	0.00972440i
$820$		0			0
$821$	−7.41305	+	4.27993i	−0.258717	+	0.149370i	−0.623749	−	0.781625i	$-0.714391\pi$
$821$	−7.41305	+	4.27993i	−0.258717	+	0.149370i	0.365032	+	0.930995i	$0.381058\pi$
$822$		0			0
$823$	24.1727	−	6.47705i	0.842607	−	0.225776i	0.188401	−	0.982092i	$-0.439670\pi$
$823$	24.1727	−	6.47705i	0.842607	−	0.225776i	0.654206	+	0.756316i	$0.273003\pi$
$824$		0			0
$825$	13.1979	−	1.23041i	0.459493	−	0.0428375i
$826$		0			0
$827$	11.9174	+	11.9174i	0.414409	+	0.414409i	0.883271	−	0.468862i	$-0.155336\pi$
$827$	11.9174	+	11.9174i	0.414409	+	0.414409i	−0.468862	+	0.883271i	$0.655336\pi$
$828$		0			0
$829$		−	1.80574i		−	0.0627161i	−0.999508	−	0.0313580i	$-0.990017\pi$
$829$		−	1.80574i		−	0.0627161i	0.999508	−	0.0313580i	$-0.00998321\pi$
$830$		0			0
$831$	−2.04518	−	10.0838i	−0.0709465	−	0.349802i
$832$		0			0
$833$	−3.41327	−	12.7385i	−0.118263	−	0.441362i
$834$		0			0
$835$	−9.13129	−	13.3207i	−0.316001	−	0.460982i
$836$		0			0
$837$	7.61413	−	8.88213i	0.263183	−	0.307011i
$838$		0			0
$839$	−8.93623	−	15.4780i	−0.308513	−	0.534360i	0.669524	−	0.742790i	$-0.266498\pi$
$839$	−8.93623	−	15.4780i	−0.308513	−	0.534360i	−0.978037	+	0.208430i	$0.933165\pi$
$840$		0			0
$841$	−22.8702	+	39.6123i	−0.788626	+	1.36594i
$842$		0			0
$843$	−21.5364	−	14.2735i	−0.741753	−	0.491605i
$844$		0			0
$845$	−20.3225	−	17.3997i	−0.699116	−	0.598570i
$846$		0			0
$847$	−0.699432	+	0.699432i	−0.0240328	+	0.0240328i
$848$		0			0
$849$	15.2073	+	17.2098i	0.521914	+	0.590640i
$850$		0			0
$851$	−26.0639	−	15.0480i	−0.893458	−	0.515838i
$852$		0			0
$853$	−7.97105	+	29.7484i	−0.272924	+	1.01856i	0.684297	+	0.729204i	$0.260109\pi$
$853$	−7.97105	+	29.7484i	−0.272924	+	1.01856i	−0.957220	+	0.289361i	$0.906557\pi$
$854$		0			0
$855$	−8.08776	+	25.4355i	−0.276596	+	0.869875i
$856$		0			0
$857$	13.2035	−	49.2761i	0.451023	−	1.68324i	−0.248503	−	0.968631i	$-0.579938\pi$
$857$	13.2035	−	49.2761i	0.451023	−	1.68324i	0.699525	−	0.714608i	$-0.253395\pi$
$858$		0			0
$859$	47.8279	+	27.6135i	1.63187	+	0.942160i	0.983516	+	0.180819i	$0.0578748\pi$
$859$	47.8279	+	27.6135i	1.63187	+	0.942160i	0.648352	+	0.761341i	$0.275459\pi$
$860$		0			0
$861$	−0.515265	+	1.53686i	−0.0175602	+	0.0523759i
$862$		0			0
$863$	−18.1635	+	18.1635i	−0.618292	+	0.618292i	−0.945093	−	0.326801i	$-0.894029\pi$
$863$	−18.1635	+	18.1635i	−0.618292	+	0.618292i	0.326801	+	0.945093i	$0.394029\pi$
$864$		0			0
$865$	0.209624	+	2.70547i	0.00712743	+	0.0919888i
$866$		0			0
$867$	20.8352	−	10.3722i	0.707600	−	0.352259i
$868$		0			0
$869$	−11.4993	+	19.9174i	−0.390087	+	0.675650i
$870$		0			0
$871$	−4.13891	−	7.16879i	−0.140241	−	0.242905i
$872$		0			0
$873$	19.2439	−	14.9973i	0.651308	−	0.507582i
$874$		0			0
$875$	−0.875935	−	0.929795i	−0.0296120	−	0.0314328i
$876$		0			0
$877$	7.72869	+	28.8439i	0.260979	+	0.973988i	0.964666	+	0.263477i	$0.0848694\pi$
$877$	7.72869	+	28.8439i	0.260979	+	0.973988i	−0.703686	+	0.710511i	$0.748464\pi$
$878$		0			0
$879$	31.6664	−	27.9817i	1.06808	−	0.943800i
$880$		0			0
$881$		−	40.4534i		−	1.36291i	−0.731860	−	0.681455i	$-0.761348\pi$
$881$		−	40.4534i		−	1.36291i	0.731860	−	0.681455i	$-0.238652\pi$
$882$		0			0
$883$	−29.4193	−	29.4193i	−0.990038	−	0.990038i	0.00991332	−	0.999951i	$-0.496844\pi$
$883$	−29.4193	−	29.4193i	−0.990038	−	0.990038i	−0.999951	+	0.00991332i	$0.996844\pi$
$884$		0			0
$885$	6.56617	+	23.0573i	0.220719	+	0.775064i
$886$		0			0
$887$	37.7248	−	10.1083i	1.26667	−	0.339405i	0.437919	−	0.899014i	$-0.355716\pi$
$887$	37.7248	−	10.1083i	1.26667	−	0.339405i	0.828756	+	0.559610i	$0.189049\pi$
$888$		0			0
$889$	−0.483098	+	0.278917i	−0.0162026	+	0.00935457i
$890$		0			0
$891$	9.88570	+	9.59311i	0.331184	+	0.321381i
$892$		0			0
$893$	34.6039	+	9.27210i	1.15798	+	0.310279i
$894$		0			0
$895$	−15.3213	−	43.4335i	−0.512136	−	1.45182i
$896$		0			0
$897$	3.06792	−	4.62900i	0.102435	−	0.154558i
$898$		0			0
$899$	−19.4646			−0.649180
$900$		0			0
$901$	24.8519			0.827937
$902$		0			0
$903$	0.939685	+	0.0580474i	0.0312708	+	0.00193170i
$904$		0			0
$905$	5.98104	+	16.9552i	0.198816	+	0.563612i
$906$		0			0
$907$	−30.8631	−	8.26974i	−1.02479	−	0.274592i	−0.292995	−	0.956114i	$-0.594652\pi$
$907$	−30.8631	−	8.26974i	−1.02479	−	0.274592i	−0.731798	+	0.681522i	$0.761318\pi$
$908$		0			0
$909$	2.89726	−	23.3613i	0.0960962	−	0.774846i
$910$		0			0
$911$	−3.70467	+	2.13889i	−0.122741	+	0.0708646i	−0.560114	−	0.828416i	$-0.689242\pi$
$911$	−3.70467	+	2.13889i	−0.122741	+	0.0708646i	0.437372	+	0.899280i	$0.355909\pi$
$912$		0			0
$913$	13.7575	−	3.68631i	0.455307	−	0.121999i
$914$		0			0
$915$	−22.9895	−	5.77641i	−0.760009	−	0.190962i
$916$		0			0
$917$	1.33897	+	1.33897i	0.0442168	+	0.0442168i
$918$		0			0
$919$			31.2478i			1.03077i	0.856959	+	0.515384i	$0.172351\pi$
$919$			31.2478i			1.03077i	−0.856959	+	0.515384i	$0.827649\pi$
$920$		0			0
$921$	33.6169	+	11.2708i	1.10771	+	0.371386i
$922$		0			0
$923$	1.03166	+	3.85022i	0.0339576	+	0.126732i
$924$		0			0
$925$	−5.10720	+	47.4835i	−0.167924	+	1.56125i
$926$		0			0
$927$	−18.8629	+	46.5243i	−0.619540	+	1.52806i
$928$		0			0
$929$	−9.02026	−	15.6235i	−0.295945	−	0.512592i	0.679259	−	0.733898i	$-0.262301\pi$
$929$	−9.02026	−	15.6235i	−0.295945	−	0.512592i	−0.975204	+	0.221307i	$0.928968\pi$
$930$		0			0
$931$	−13.8997	+	24.0750i	−0.455544	+	0.789026i
$932$		0			0
$933$	0.358241	−	5.79929i	0.0117283	−	0.189860i
$934$		0			0
$935$	−0.499027	−	6.44059i	−0.0163199	−	0.210630i
$936$		0			0
$937$	−20.1646	+	20.1646i	−0.658747	+	0.658747i	−0.955084	−	0.296336i	$-0.904235\pi$
$937$	−20.1646	+	20.1646i	−0.658747	+	0.658747i	0.296336	+	0.955084i	$0.404235\pi$
$938$		0			0
$939$	1.76846	−	0.358677i	0.0577114	−	0.0117050i
$940$		0			0
$941$	15.2020	+	8.77687i	0.495571	+	0.286118i	0.726883	−	0.686762i	$-0.240968\pi$
$941$	15.2020	+	8.77687i	0.495571	+	0.286118i	−0.231312	+	0.972880i	$0.574302\pi$
$942$		0			0
$943$	6.67979	−	24.9293i	0.217524	−	0.811810i
$944$		0			0
$945$	0.142774	−	1.31983i	0.00464444	−	0.0429339i
$946$		0			0
$947$	8.17408	−	30.5061i	0.265622	−	0.991315i	−0.696247	−	0.717803i	$-0.745148\pi$
$947$	8.17408	−	30.5061i	0.265622	−	0.991315i	0.961869	−	0.273512i	$-0.0881854\pi$
$948$		0			0
$949$	−4.30804	−	2.48725i	−0.139845	−	0.0807395i
$950$		0			0
$951$	22.5180	−	4.56708i	0.730197	−	0.148098i
$952$		0			0
$953$	−7.09439	+	7.09439i	−0.229810	+	0.229810i	−0.812613	−	0.582803i	$-0.801956\pi$
$953$	−7.09439	+	7.09439i	−0.229810	+	0.229810i	0.582803	+	0.812613i	$0.301956\pi$
$954$		0			0
$955$	26.2700	+	22.4918i	0.850077	+	0.727819i
$956$		0			0
$957$	1.41308	−	22.8752i	0.0456783	−	0.739451i
$958$		0			0
$959$	−0.384751	+	0.666408i	−0.0124243	+	0.0215194i
$960$		0			0
$961$	12.9654	+	22.4568i	0.418239	+	0.724412i
$962$		0			0
$963$	44.1647	−	6.15215i	1.42319	−	0.198250i
$964$		0			0
$965$	10.5144	+	15.3384i	0.338470	+	0.493759i
$966$		0			0
$967$	14.8641	+	55.4735i	0.477997	+	1.78391i	0.609715	+	0.792621i	$0.291284\pi$
$967$	14.8641	+	55.4735i	0.477997	+	1.78391i	−0.131719	+	0.991287i	$0.542050\pi$
$968$		0			0
$969$	12.3328	+	4.13486i	0.396188	+	0.132831i
$970$		0			0
$971$			40.2580i			1.29194i	0.763362	+	0.645970i	$0.223547\pi$
$971$			40.2580i			1.29194i	−0.763362	+	0.645970i	$0.776453\pi$
$972$		0			0
$973$	−0.877891	−	0.877891i	−0.0281439	−	0.0281439i
$974$		0			0
$975$	−8.68697	−	1.48081i	−0.278206	−	0.0474238i
$976$		0			0
$977$	−20.7215	+	5.55232i	−0.662941	+	0.177634i	−0.574573	−	0.818453i	$-0.694832\pi$
$977$	−20.7215	+	5.55232i	−0.662941	+	0.177634i	−0.0883680	+	0.996088i	$0.528165\pi$
$978$		0			0
$979$	−8.42122	+	4.86199i	−0.269143	+	0.155390i
$980$		0			0
$981$	16.9918	+	12.8367i	0.542506	+	0.409844i
$982$		0			0
$983$	−39.7890	−	10.6614i	−1.26907	−	0.340047i	−0.439396	−	0.898293i	$-0.644808\pi$
$983$	−39.7890	−	10.6614i	−1.26907	−	0.340047i	−0.829675	+	0.558247i	$0.811474\pi$
$984$		0			0
$985$	18.7775	−	39.2452i	0.598300	−	1.25046i
$986$		0			0
$987$	−1.77846	−	0.109861i	−0.0566089	−	0.00349691i
$988$		0			0
$989$	−14.9903			−0.476664
$990$		0			0
$991$	−23.6495			−0.751251			−0.375626	−	0.926771i	$-0.622572\pi$
$991$	−23.6495			−0.751251			−0.375626	+	0.926771i	$0.622572\pi$
$992$		0			0
$993$	17.4686	−	26.3573i	0.554349	−	0.836424i
$994$		0			0
$995$	−52.5160	+	18.5252i	−1.66487	+	0.587290i
$996$		0			0
$997$	−26.2993	−	7.04689i	−0.832908	−	0.223177i	−0.182926	−	0.983127i	$-0.558557\pi$
$997$	−26.2993	−	7.04689i	−0.832908	−	0.223177i	−0.649982	+	0.759950i	$0.725224\pi$
$998$		0			0
$999$	−40.9534	+	28.0366i	−1.29571	+	0.887038i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	360.2.bs.a.113.12	✓	72
3.2	odd	2		1080.2.bt.a.233.7		72
4.3	odd	2		720.2.cu.e.113.7		72
5.2	odd	4	inner	360.2.bs.a.257.16	yes	72
9.2	odd	6	inner	360.2.bs.a.353.16	yes	72
9.7	even	3		1080.2.bt.a.953.2		72
15.2	even	4		1080.2.bt.a.17.2		72
20.7	even	4		720.2.cu.e.257.3		72
36.11	even	6		720.2.cu.e.353.3		72
45.2	even	12	inner	360.2.bs.a.137.12	yes	72
45.7	odd	12		1080.2.bt.a.737.7		72
180.47	odd	12		720.2.cu.e.497.7		72

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
360.2.bs.a.113.12	✓	72	1.1	even	1	trivial
360.2.bs.a.137.12	yes	72	45.2	even	12	inner
360.2.bs.a.257.16	yes	72	5.2	odd	4	inner
360.2.bs.a.353.16	yes	72	9.2	odd	6	inner
720.2.cu.e.113.7		72	4.3	odd	2
720.2.cu.e.257.3		72	20.7	even	4
720.2.cu.e.353.3		72	36.11	even	6
720.2.cu.e.497.7		72	180.47	odd	12
1080.2.bt.a.17.2		72	15.2	even	4
1080.2.bt.a.233.7		72	3.2	odd	2
1080.2.bt.a.737.7		72	45.7	odd	12
1080.2.bt.a.953.2		72	9.7	even	3

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.bs (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.771894 + 1.55054i) q^{3} +(0.743858 + 2.10871i) q^{5} +(0.110362 + 0.0295714i) q^{7} +(-1.80836 + 2.39371i) q^{9} +O(q^{10})\)	\(q+(0.771894 + 1.55054i) q^{3} +(0.743858 + 2.10871i) q^{5} +(0.110362 + 0.0295714i) q^{7} +(-1.80836 + 2.39371i) q^{9} +(-1.32551 + 0.765286i) q^{11} +(0.982882 - 0.263362i) q^{13} +(-2.69547 + 2.78109i) q^{15} +(1.33466 + 1.33466i) q^{17} -3.97876i q^{19} +(0.0393361 + 0.193947i) q^{21} +(-0.815519 - 3.04356i) q^{23} +(-3.89335 + 3.13717i) q^{25} +(-5.10741 - 0.956246i) q^{27} +(4.32262 + 7.48701i) q^{29} +(-1.12574 + 1.94984i) q^{31} +(-2.20977 - 1.46455i) q^{33} +(0.0197360 + 0.254719i) q^{35} +(6.75392 - 6.75392i) q^{37} +(1.16704 + 1.32071i) q^{39} +(7.09348 + 4.09542i) q^{41} +(1.23131 - 4.59533i) q^{43} +(-6.39281 - 2.03273i) q^{45} +(-2.33040 + 8.69716i) q^{47} +(-6.05087 - 3.49347i) q^{49} +(-1.03923 + 3.09967i) q^{51} +(9.31019 - 9.31019i) q^{53} +(-2.59977 - 2.22587i) q^{55} +(6.16924 - 3.07118i) q^{57} +(3.09504 - 5.36076i) q^{59} +(3.06018 + 5.30039i) q^{61} +(-0.270359 + 0.210699i) q^{63} +(1.28648 + 1.87671i) q^{65} +(-2.10549 - 7.85781i) q^{67} +(4.08967 - 3.61380i) q^{69} +3.91728i q^{71} +(-3.45682 - 3.45682i) q^{73} +(-7.86956 - 3.61524i) q^{75} +(-0.168917 + 0.0452612i) q^{77} +(13.0130 - 7.51307i) q^{79} +(-2.45968 - 8.65737i) q^{81} +(-8.98846 - 2.40845i) q^{83} +(-1.82162 + 3.80722i) q^{85} +(-8.27230 + 12.4816i) q^{87} +6.35317 q^{89} +0.116261 q^{91} +(-3.89226 - 0.240437i) q^{93} +(8.39008 - 2.95963i) q^{95} +(-7.85545 - 2.10486i) q^{97} +(0.565134 - 4.55681i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 72 q+O(q^{10}) \) 72 * q	\( 72 q + 12 q^{15} + 16 q^{21} + 24 q^{23} - 12 q^{27} + 12 q^{33} + 12 q^{41} - 16 q^{45} - 36 q^{47} + 24 q^{51} - 40 q^{57} + 12 q^{61} - 44 q^{63} - 72 q^{65} - 36 q^{75} - 48 q^{77} - 20 q^{81} - 60 q^{83} + 24 q^{85} - 40 q^{87} - 84 q^{93} - 60 q^{95} + 24 q^{97}+O(q^{100}) \) 72 * q + 12 * q^15 + 16 * q^21 + 24 * q^23 - 12 * q^27 + 12 * q^33 + 12 * q^41 - 16 * q^45 - 36 * q^47 + 24 * q^51 - 40 * q^57 + 12 * q^61 - 44 * q^63 - 72 * q^65 - 36 * q^75 - 48 * q^77 - 20 * q^81 - 60 * q^83 + 24 * q^85 - 40 * q^87 - 84 * q^93 - 60 * q^95 + 24 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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