LMFDB - Embedded newform 370.2.h.a.253.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [370,2,Mod(117,370)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("370.117"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(370, base_ring=CyclotomicField(4)) chi = DirichletCharacter(H, H._module([1, 3])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 370 = 2 \cdot 5 \cdot 37 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	370.h (of order $4$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [2,2,0] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(3)] == traces)

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

Self dual:	no
Analytic conductor:	$2.95446487479$
Analytic rank:	$0$
Dimension:	$2$
Coefficient field:	$\Q(i)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} + 1 $ x^2 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{9}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			253.1
Root			$1.00000i$ of defining polynomial
Character	$\chi$	$=$	370.253
Dual form			370.2.h.a.117.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+1.00000 q^{2} +1.00000 q^{4} +(-1.00000 + 2.00000i) q^{5} +(-2.00000 + 2.00000i) q^{7} +1.00000 q^{8} +3.00000i q^{9} +(-1.00000 + 2.00000i) q^{10} +4.00000 q^{13} +(-2.00000 + 2.00000i) q^{14} +1.00000 q^{16} +2.00000i q^{17} +3.00000i q^{18} +(-2.00000 - 2.00000i) q^{19} +(-1.00000 + 2.00000i) q^{20} +4.00000 q^{23} +(-3.00000 - 4.00000i) q^{25} +4.00000 q^{26} +(-2.00000 + 2.00000i) q^{28} +(7.00000 - 7.00000i) q^{29} +(-4.00000 - 4.00000i) q^{31} +1.00000 q^{32} +2.00000i q^{34} +(-2.00000 - 6.00000i) q^{35} +3.00000i q^{36} +(-1.00000 + 6.00000i) q^{37} +(-2.00000 - 2.00000i) q^{38} +(-1.00000 + 2.00000i) q^{40} +4.00000 q^{43} +(-6.00000 - 3.00000i) q^{45} +4.00000 q^{46} +(-2.00000 + 2.00000i) q^{47} -1.00000i q^{49} +(-3.00000 - 4.00000i) q^{50} +4.00000 q^{52} +(-1.00000 - 1.00000i) q^{53} +(-2.00000 + 2.00000i) q^{56} +(7.00000 - 7.00000i) q^{58} +(-2.00000 - 2.00000i) q^{59} +(1.00000 + 1.00000i) q^{61} +(-4.00000 - 4.00000i) q^{62} +(-6.00000 - 6.00000i) q^{63} +1.00000 q^{64} +(-4.00000 + 8.00000i) q^{65} +2.00000i q^{68} +(-2.00000 - 6.00000i) q^{70} +12.0000 q^{71} +3.00000i q^{72} +(5.00000 - 5.00000i) q^{73} +(-1.00000 + 6.00000i) q^{74} +(-2.00000 - 2.00000i) q^{76} +(-12.0000 - 12.0000i) q^{79} +(-1.00000 + 2.00000i) q^{80} -9.00000 q^{81} +(4.00000 + 4.00000i) q^{83} +(-4.00000 - 2.00000i) q^{85} +4.00000 q^{86} +(7.00000 - 7.00000i) q^{89} +(-6.00000 - 3.00000i) q^{90} +(-8.00000 + 8.00000i) q^{91} +4.00000 q^{92} +(-2.00000 + 2.00000i) q^{94} +(6.00000 - 2.00000i) q^{95} +12.0000i q^{97} -1.00000i q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q + 2 q^{2} + 2 q^{4} - 2 q^{5} - 4 q^{7} + 2 q^{8} - 2 q^{10} + 8 q^{13} - 4 q^{14} + 2 q^{16} - 4 q^{19} - 2 q^{20} + 8 q^{23} - 6 q^{25} + 8 q^{26} - 4 q^{28} + 14 q^{29} - 8 q^{31} + 2 q^{32} - 4 q^{35}+ \cdots + 12 q^{95}+O(q^{100}) $ 2 * q + 2 * q^2 + 2 * q^4 - 2 * q^5 - 4 * q^7 + 2 * q^8 - 2 * q^10 + 8 * q^13 - 4 * q^14 + 2 * q^16 - 4 * q^19 - 2 * q^20 + 8 * q^23 - 6 * q^25 + 8 * q^26 - 4 * q^28 + 14 * q^29 - 8 * q^31 + 2 * q^32 - 4 * q^35 - 2 * q^37 - 4 * q^38 - 2 * q^40 + 8 * q^43 - 12 * q^45 + 8 * q^46 - 4 * q^47 - 6 * q^50 + 8 * q^52 - 2 * q^53 - 4 * q^56 + 14 * q^58 - 4 * q^59 + 2 * q^61 - 8 * q^62 - 12 * q^63 + 2 * q^64 - 8 * q^65 - 4 * q^70 + 24 * q^71 + 10 * q^73 - 2 * q^74 - 4 * q^76 - 24 * q^79 - 2 * q^80 - 18 * q^81 + 8 * q^83 - 8 * q^85 + 8 * q^86 + 14 * q^89 - 12 * q^90 - 16 * q^91 + 8 * q^92 - 4 * q^94 + 12 * q^95

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/370\mathbb{Z}\right)^\times$.

$n$	$261$	$297$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$e\left(\frac{3}{4}\right)$

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 $

$2$	1.00000			0.707107
$2$	1.00000			0.707107
$3$		0			0		−0.707107	−	0.707107i	$-0.750000\pi$
$3$		0			0		0.707107	+	0.707107i	$0.250000\pi$
$4$	1.00000			0.500000
$5$	−1.00000	+	2.00000i	−0.447214	+	0.894427i
$5$	−1.00000	+	2.00000i	−0.447214	+	0.894427i
$6$		0			0
$7$	−2.00000	+	2.00000i	−0.755929	+	0.755929i	−0.975579	−	0.219650i	$-0.929509\pi$
$7$	−2.00000	+	2.00000i	−0.755929	+	0.755929i	0.219650	+	0.975579i	$0.429509\pi$
$8$	1.00000			0.353553
$9$			3.00000i			1.00000i
$10$	−1.00000	+	2.00000i	−0.316228	+	0.632456i
$11$		0			0		1.00000			$0$
$11$		0			0		−1.00000			$\pi$
$12$		0			0
$13$	4.00000			1.10940			0.554700	−	0.832050i	$-0.312833\pi$
$13$	4.00000			1.10940			0.554700	+	0.832050i	$0.312833\pi$
$14$	−2.00000	+	2.00000i	−0.534522	+	0.534522i
$15$		0			0
$16$	1.00000			0.250000
$17$			2.00000i			0.485071i	0.970143	+	0.242536i	$0.0779791\pi$
$17$			2.00000i			0.485071i	−0.970143	+	0.242536i	$0.922021\pi$
$18$			3.00000i			0.707107i
$19$	−2.00000	−	2.00000i	−0.458831	−	0.458831i	0.439440	−	0.898272i	$-0.355177\pi$
$19$	−2.00000	−	2.00000i	−0.458831	−	0.458831i	−0.898272	+	0.439440i	$0.855177\pi$
$20$	−1.00000	+	2.00000i	−0.223607	+	0.447214i
$21$		0			0
$22$		0			0
$23$	4.00000			0.834058			0.417029	−	0.908893i	$-0.363071\pi$
$23$	4.00000			0.834058			0.417029	+	0.908893i	$0.363071\pi$
$24$		0			0
$25$	−3.00000	−	4.00000i	−0.600000	−	0.800000i
$26$	4.00000			0.784465
$27$		0			0
$28$	−2.00000	+	2.00000i	−0.377964	+	0.377964i
$29$	7.00000	−	7.00000i	1.29987	−	1.29987i	0.371391	−	0.928477i	$-0.378881\pi$
$29$	7.00000	−	7.00000i	1.29987	−	1.29987i	0.928477	−	0.371391i	$-0.121119\pi$
$30$		0			0
$31$	−4.00000	−	4.00000i	−0.718421	−	0.718421i	0.249861	−	0.968282i	$-0.419615\pi$
$31$	−4.00000	−	4.00000i	−0.718421	−	0.718421i	−0.968282	+	0.249861i	$0.919615\pi$
$32$	1.00000			0.176777
$33$		0			0
$34$			2.00000i			0.342997i
$35$	−2.00000	−	6.00000i	−0.338062	−	1.01419i
$36$			3.00000i			0.500000i
$37$	−1.00000	+	6.00000i	−0.164399	+	0.986394i
$37$	−1.00000	+	6.00000i	−0.164399	+	0.986394i
$38$	−2.00000	−	2.00000i	−0.324443	−	0.324443i
$39$		0			0
$40$	−1.00000	+	2.00000i	−0.158114	+	0.316228i
$41$		0			0		1.00000			$0$
$41$		0			0		−1.00000			$\pi$
$42$		0			0
$43$	4.00000			0.609994			0.304997	−	0.952353i	$-0.401344\pi$
$43$	4.00000			0.609994			0.304997	+	0.952353i	$0.401344\pi$
$44$		0			0
$45$	−6.00000	−	3.00000i	−0.894427	−	0.447214i
$46$	4.00000			0.589768
$47$	−2.00000	+	2.00000i	−0.291730	+	0.291730i	−0.837763	−	0.546033i	$-0.816137\pi$
$47$	−2.00000	+	2.00000i	−0.291730	+	0.291730i	0.546033	+	0.837763i	$0.316137\pi$
$48$		0			0
$49$		−	1.00000i		−	0.142857i
$50$	−3.00000	−	4.00000i	−0.424264	−	0.565685i
$51$		0			0
$52$	4.00000			0.554700
$53$	−1.00000	−	1.00000i	−0.137361	−	0.137361i	0.635083	−	0.772444i	$-0.280966\pi$
$53$	−1.00000	−	1.00000i	−0.137361	−	0.137361i	−0.772444	+	0.635083i	$0.780966\pi$
$54$		0			0
$55$		0			0
$56$	−2.00000	+	2.00000i	−0.267261	+	0.267261i
$57$		0			0
$58$	7.00000	−	7.00000i	0.919145	−	0.919145i
$59$	−2.00000	−	2.00000i	−0.260378	−	0.260378i	0.564830	−	0.825208i	$-0.308942\pi$
$59$	−2.00000	−	2.00000i	−0.260378	−	0.260378i	−0.825208	+	0.564830i	$0.808942\pi$
$60$		0			0
$61$	1.00000	+	1.00000i	0.128037	+	0.128037i	0.768221	−	0.640184i	$-0.221142\pi$
$61$	1.00000	+	1.00000i	0.128037	+	0.128037i	−0.640184	+	0.768221i	$0.721142\pi$
$62$	−4.00000	−	4.00000i	−0.508001	−	0.508001i
$63$	−6.00000	−	6.00000i	−0.755929	−	0.755929i
$64$	1.00000			0.125000
$65$	−4.00000	+	8.00000i	−0.496139	+	0.992278i
$66$		0			0
$67$		0			0		0.707107	−	0.707107i	$-0.250000\pi$
$67$		0			0		−0.707107	+	0.707107i	$0.750000\pi$
$68$			2.00000i			0.242536i
$69$		0			0
$70$	−2.00000	−	6.00000i	−0.239046	−	0.717137i
$71$	12.0000			1.42414			0.712069	−	0.702109i	$-0.247758\pi$
$71$	12.0000			1.42414			0.712069	+	0.702109i	$0.247758\pi$
$72$			3.00000i			0.353553i
$73$	5.00000	−	5.00000i	0.585206	−	0.585206i	−0.351123	−	0.936329i	$-0.614200\pi$
$73$	5.00000	−	5.00000i	0.585206	−	0.585206i	0.936329	+	0.351123i	$0.114200\pi$
$74$	−1.00000	+	6.00000i	−0.116248	+	0.697486i
$75$		0			0
$76$	−2.00000	−	2.00000i	−0.229416	−	0.229416i
$77$		0			0
$78$		0			0
$79$	−12.0000	−	12.0000i	−1.35011	−	1.35011i	−0.885537	−	0.464568i	$-0.846210\pi$
$79$	−12.0000	−	12.0000i	−1.35011	−	1.35011i	−0.464568	−	0.885537i	$-0.653790\pi$
$80$	−1.00000	+	2.00000i	−0.111803	+	0.223607i
$81$	−9.00000			−1.00000
$82$		0			0
$83$	4.00000	+	4.00000i	0.439057	+	0.439057i	0.891695	−	0.452638i	$-0.149517\pi$
$83$	4.00000	+	4.00000i	0.439057	+	0.439057i	−0.452638	+	0.891695i	$0.649517\pi$
$84$		0			0
$85$	−4.00000	−	2.00000i	−0.433861	−	0.216930i
$86$	4.00000			0.431331
$87$		0			0
$88$		0			0
$89$	7.00000	−	7.00000i	0.741999	−	0.741999i	−0.230964	−	0.972962i	$-0.574188\pi$
$89$	7.00000	−	7.00000i	0.741999	−	0.741999i	0.972962	+	0.230964i	$0.0741879\pi$
$90$	−6.00000	−	3.00000i	−0.632456	−	0.316228i
$91$	−8.00000	+	8.00000i	−0.838628	+	0.838628i
$92$	4.00000			0.417029
$93$		0			0
$94$	−2.00000	+	2.00000i	−0.206284	+	0.206284i
$95$	6.00000	−	2.00000i	0.615587	−	0.205196i
$96$		0			0
$97$			12.0000i			1.21842i	0.793011	+	0.609208i	$0.208512\pi$
$97$			12.0000i			1.21842i	−0.793011	+	0.609208i	$0.791488\pi$
$98$		−	1.00000i		−	0.101015i
$99$		0			0
$100$	−3.00000	−	4.00000i	−0.300000	−	0.400000i
$101$		−	10.0000i		−	0.995037i	−0.867453	−	0.497519i	$-0.834245\pi$
$101$		−	10.0000i		−	0.995037i	0.867453	−	0.497519i	$-0.165755\pi$
$102$		0			0
$103$		−	16.0000i		−	1.57653i	−0.615338	−	0.788263i	$-0.710980\pi$
$103$		−	16.0000i		−	1.57653i	0.615338	−	0.788263i	$-0.289020\pi$
$104$	4.00000			0.392232
$105$		0			0
$106$	−1.00000	−	1.00000i	−0.0971286	−	0.0971286i
$107$	8.00000	−	8.00000i	0.773389	−	0.773389i	−0.205308	−	0.978697i	$-0.565820\pi$
$107$	8.00000	−	8.00000i	0.773389	−	0.773389i	0.978697	+	0.205308i	$0.0658197\pi$
$108$		0			0
$109$	3.00000	+	3.00000i	0.287348	+	0.287348i	0.836031	−	0.548683i	$-0.184871\pi$
$109$	3.00000	+	3.00000i	0.287348	+	0.287348i	−0.548683	+	0.836031i	$0.684871\pi$
$110$		0			0
$111$		0			0
$112$	−2.00000	+	2.00000i	−0.188982	+	0.188982i
$113$			14.0000i			1.31701i	0.752577	+	0.658505i	$0.228811\pi$
$113$			14.0000i			1.31701i	−0.752577	+	0.658505i	$0.771189\pi$
$114$		0			0
$115$	−4.00000	+	8.00000i	−0.373002	+	0.746004i
$116$	7.00000	−	7.00000i	0.649934	−	0.649934i
$117$			12.0000i			1.10940i
$118$	−2.00000	−	2.00000i	−0.184115	−	0.184115i
$119$	−4.00000	−	4.00000i	−0.366679	−	0.366679i
$120$		0			0
$121$	11.0000			1.00000
$122$	1.00000	+	1.00000i	0.0905357	+	0.0905357i
$123$		0			0
$124$	−4.00000	−	4.00000i	−0.359211	−	0.359211i
$125$	11.0000	−	2.00000i	0.983870	−	0.178885i
$126$	−6.00000	−	6.00000i	−0.534522	−	0.534522i
$127$	−2.00000	+	2.00000i	−0.177471	+	0.177471i	−0.790253	−	0.612781i	$-0.790051\pi$
$127$	−2.00000	+	2.00000i	−0.177471	+	0.177471i	0.612781	+	0.790253i	$0.290051\pi$
$128$	1.00000			0.0883883
$129$		0			0
$130$	−4.00000	+	8.00000i	−0.350823	+	0.701646i
$131$	6.00000	+	6.00000i	0.524222	+	0.524222i	0.918844	−	0.394621i	$-0.129124\pi$
$131$	6.00000	+	6.00000i	0.524222	+	0.524222i	−0.394621	+	0.918844i	$0.629124\pi$
$132$		0			0
$133$	8.00000			0.693688
$134$		0			0
$135$		0			0
$136$			2.00000i			0.171499i
$137$	−7.00000	+	7.00000i	−0.598050	+	0.598050i	−0.939793	−	0.341743i	$-0.888983\pi$
$137$	−7.00000	+	7.00000i	−0.598050	+	0.598050i	0.341743	+	0.939793i	$0.388983\pi$
$138$		0			0
$139$	−20.0000			−1.69638			−0.848189	−	0.529694i	$-0.822307\pi$
$139$	−20.0000			−1.69638			−0.848189	+	0.529694i	$0.822307\pi$
$140$	−2.00000	−	6.00000i	−0.169031	−	0.507093i
$141$		0			0
$142$	12.0000			1.00702
$143$		0			0
$144$			3.00000i			0.250000i
$145$	7.00000	+	21.0000i	0.581318	+	1.74396i
$146$	5.00000	−	5.00000i	0.413803	−	0.413803i
$147$		0			0
$148$	−1.00000	+	6.00000i	−0.0821995	+	0.493197i
$149$			6.00000i			0.491539i	0.969328	+	0.245770i	$0.0790407\pi$
$149$			6.00000i			0.491539i	−0.969328	+	0.245770i	$0.920959\pi$
$150$		0			0
$151$		−	20.0000i		−	1.62758i	−0.581161	−	0.813788i	$-0.697401\pi$
$151$		−	20.0000i		−	1.62758i	0.581161	−	0.813788i	$-0.302599\pi$
$152$	−2.00000	−	2.00000i	−0.162221	−	0.162221i
$153$	−6.00000			−0.485071
$154$		0			0
$155$	12.0000	−	4.00000i	0.963863	−	0.321288i
$156$		0			0
$157$	−7.00000	+	7.00000i	−0.558661	+	0.558661i	−0.928926	−	0.370265i	$-0.879267\pi$
$157$	−7.00000	+	7.00000i	−0.558661	+	0.558661i	0.370265	+	0.928926i	$0.379267\pi$
$158$	−12.0000	−	12.0000i	−0.954669	−	0.954669i
$159$		0			0
$160$	−1.00000	+	2.00000i	−0.0790569	+	0.158114i
$161$	−8.00000	+	8.00000i	−0.630488	+	0.630488i
$162$	−9.00000			−0.707107
$163$			24.0000i			1.87983i	0.341415	+	0.939913i	$0.389094\pi$
$163$			24.0000i			1.87983i	−0.341415	+	0.939913i	$0.610906\pi$
$164$		0			0
$165$		0			0
$166$	4.00000	+	4.00000i	0.310460	+	0.310460i
$167$		−	8.00000i		−	0.619059i	−0.950890	−	0.309529i	$-0.899829\pi$
$167$		−	8.00000i		−	0.619059i	0.950890	−	0.309529i	$-0.100171\pi$
$168$		0			0
$169$	3.00000			0.230769
$170$	−4.00000	−	2.00000i	−0.306786	−	0.153393i
$171$	6.00000	−	6.00000i	0.458831	−	0.458831i
$172$	4.00000			0.304997
$173$	−5.00000	+	5.00000i	−0.380143	+	0.380143i	−0.871154	−	0.491011i	$-0.836628\pi$
$173$	−5.00000	+	5.00000i	−0.380143	+	0.380143i	0.491011	+	0.871154i	$0.336628\pi$
$174$		0			0
$175$	14.0000	+	2.00000i	1.05830	+	0.151186i
$176$		0			0
$177$		0			0
$178$	7.00000	−	7.00000i	0.524672	−	0.524672i
$179$	2.00000	−	2.00000i	0.149487	−	0.149487i	−0.628402	−	0.777889i	$-0.716291\pi$
$179$	2.00000	−	2.00000i	0.149487	−	0.149487i	0.777889	+	0.628402i	$0.216291\pi$
$180$	−6.00000	−	3.00000i	−0.447214	−	0.223607i
$181$	−8.00000			−0.594635			−0.297318	−	0.954779i	$-0.596092\pi$
$181$	−8.00000			−0.594635			−0.297318	+	0.954779i	$0.596092\pi$
$182$	−8.00000	+	8.00000i	−0.592999	+	0.592999i
$183$		0			0
$184$	4.00000			0.294884
$185$	−11.0000	−	8.00000i	−0.808736	−	0.588172i
$186$		0			0
$187$		0			0
$188$	−2.00000	+	2.00000i	−0.145865	+	0.145865i
$189$		0			0
$190$	6.00000	−	2.00000i	0.435286	−	0.145095i
$191$	16.0000	−	16.0000i	1.15772	−	1.15772i	0.172754	−	0.984965i	$-0.444733\pi$
$191$	16.0000	−	16.0000i	1.15772	−	1.15772i	0.984965	−	0.172754i	$-0.0552667\pi$
$192$		0			0
$193$	14.0000			1.00774			0.503871	−	0.863779i	$-0.331909\pi$
$193$	14.0000			1.00774			0.503871	+	0.863779i	$0.331909\pi$
$194$			12.0000i			0.861550i
$195$		0			0
$196$		−	1.00000i		−	0.0714286i
$197$	3.00000	−	3.00000i	0.213741	−	0.213741i	−0.592113	−	0.805855i	$-0.701706\pi$
$197$	3.00000	−	3.00000i	0.213741	−	0.213741i	0.805855	+	0.592113i	$0.201706\pi$
$198$		0			0
$199$	−8.00000	+	8.00000i	−0.567105	+	0.567105i	−0.931316	−	0.364211i	$-0.881339\pi$
$199$	−8.00000	+	8.00000i	−0.567105	+	0.567105i	0.364211	+	0.931316i	$0.381339\pi$
$200$	−3.00000	−	4.00000i	−0.212132	−	0.282843i
$201$		0			0
$202$		−	10.0000i		−	0.703598i
$203$			28.0000i			1.96521i
$204$		0			0
$205$		0			0
$206$		−	16.0000i		−	1.11477i
$207$			12.0000i			0.834058i
$208$	4.00000			0.277350
$209$		0			0
$210$		0			0
$211$	−8.00000			−0.550743			−0.275371	−	0.961338i	$-0.588801\pi$
$211$	−8.00000			−0.550743			−0.275371	+	0.961338i	$0.588801\pi$
$212$	−1.00000	−	1.00000i	−0.0686803	−	0.0686803i
$213$		0			0
$214$	8.00000	−	8.00000i	0.546869	−	0.546869i
$215$	−4.00000	+	8.00000i	−0.272798	+	0.545595i
$216$		0			0
$217$	16.0000			1.08615
$218$	3.00000	+	3.00000i	0.203186	+	0.203186i
$219$		0			0
$220$		0			0
$221$			8.00000i			0.538138i
$222$		0			0
$223$	−6.00000	−	6.00000i	−0.401790	−	0.401790i	0.477074	−	0.878863i	$-0.341698\pi$
$223$	−6.00000	−	6.00000i	−0.401790	−	0.401790i	−0.878863	+	0.477074i	$0.841698\pi$
$224$	−2.00000	+	2.00000i	−0.133631	+	0.133631i
$225$	12.0000	−	9.00000i	0.800000	−	0.600000i
$226$			14.0000i			0.931266i
$227$			12.0000i			0.796468i	0.917284	+	0.398234i	$0.130377\pi$
$227$			12.0000i			0.796468i	−0.917284	+	0.398234i	$0.869623\pi$
$228$		0			0
$229$			16.0000i			1.05731i	0.848837	+	0.528655i	$0.177303\pi$
$229$			16.0000i			1.05731i	−0.848837	+	0.528655i	$0.822697\pi$
$230$	−4.00000	+	8.00000i	−0.263752	+	0.527504i
$231$		0			0
$232$	7.00000	−	7.00000i	0.459573	−	0.459573i
$233$	5.00000	−	5.00000i	0.327561	−	0.327561i	−0.524097	−	0.851658i	$-0.675597\pi$
$233$	5.00000	−	5.00000i	0.327561	−	0.327561i	0.851658	+	0.524097i	$0.175597\pi$
$234$			12.0000i			0.784465i
$235$	−2.00000	−	6.00000i	−0.130466	−	0.391397i
$236$	−2.00000	−	2.00000i	−0.130189	−	0.130189i
$237$		0			0
$238$	−4.00000	−	4.00000i	−0.259281	−	0.259281i
$239$	8.00000	+	8.00000i	0.517477	+	0.517477i	0.916807	−	0.399330i	$-0.130757\pi$
$239$	8.00000	+	8.00000i	0.517477	+	0.517477i	−0.399330	+	0.916807i	$0.630757\pi$
$240$		0			0
$241$	−19.0000	+	19.0000i	−1.22390	+	1.22390i	−0.257663	+	0.966235i	$0.582952\pi$
$241$	−19.0000	+	19.0000i	−1.22390	+	1.22390i	−0.966235	+	0.257663i	$0.917048\pi$
$242$	11.0000			0.707107
$243$		0			0
$244$	1.00000	+	1.00000i	0.0640184	+	0.0640184i
$245$	2.00000	+	1.00000i	0.127775	+	0.0638877i
$246$		0			0
$247$	−8.00000	−	8.00000i	−0.509028	−	0.509028i
$248$	−4.00000	−	4.00000i	−0.254000	−	0.254000i
$249$		0			0
$250$	11.0000	−	2.00000i	0.695701	−	0.126491i
$251$	−14.0000	−	14.0000i	−0.883672	−	0.883672i	0.110234	−	0.993906i	$-0.464840\pi$
$251$	−14.0000	−	14.0000i	−0.883672	−	0.883672i	−0.993906	+	0.110234i	$0.964840\pi$
$252$	−6.00000	−	6.00000i	−0.377964	−	0.377964i
$253$		0			0
$254$	−2.00000	+	2.00000i	−0.125491	+	0.125491i
$255$		0			0
$256$	1.00000			0.0625000
$257$		−	18.0000i		−	1.12281i	−0.827541	−	0.561405i	$-0.810261\pi$
$257$		−	18.0000i		−	1.12281i	0.827541	−	0.561405i	$-0.189739\pi$
$258$		0			0
$259$	−10.0000	−	14.0000i	−0.621370	−	0.869918i
$260$	−4.00000	+	8.00000i	−0.248069	+	0.496139i
$261$	21.0000	+	21.0000i	1.29987	+	1.29987i
$262$	6.00000	+	6.00000i	0.370681	+	0.370681i
$263$	10.0000	−	10.0000i	0.616626	−	0.616626i	−0.328038	−	0.944664i	$-0.606387\pi$
$263$	10.0000	−	10.0000i	0.616626	−	0.616626i	0.944664	+	0.328038i	$0.106387\pi$
$264$		0			0
$265$	3.00000	−	1.00000i	0.184289	−	0.0614295i
$266$	8.00000			0.490511
$267$		0			0
$268$		0			0
$269$		−	14.0000i		−	0.853595i	−0.904347	−	0.426798i	$-0.859642\pi$
$269$		−	14.0000i		−	0.853595i	0.904347	−	0.426798i	$-0.140358\pi$
$270$		0			0
$271$	−28.0000			−1.70088			−0.850439	−	0.526073i	$-0.823664\pi$
$271$	−28.0000			−1.70088			−0.850439	+	0.526073i	$0.823664\pi$
$272$			2.00000i			0.121268i
$273$		0			0
$274$	−7.00000	+	7.00000i	−0.422885	+	0.422885i
$275$		0			0
$276$		0			0
$277$	−12.0000			−0.721010			−0.360505	−	0.932757i	$-0.617396\pi$
$277$	−12.0000			−0.721010			−0.360505	+	0.932757i	$0.617396\pi$
$278$	−20.0000			−1.19952
$279$	12.0000	−	12.0000i	0.718421	−	0.718421i
$280$	−2.00000	−	6.00000i	−0.119523	−	0.358569i
$281$	1.00000	−	1.00000i	0.0596550	−	0.0596550i	−0.676650	−	0.736305i	$-0.736569\pi$
$281$	1.00000	−	1.00000i	0.0596550	−	0.0596550i	0.736305	+	0.676650i	$0.236569\pi$
$282$		0			0
$283$			24.0000i			1.42665i	0.700832	+	0.713326i	$0.252812\pi$
$283$			24.0000i			1.42665i	−0.700832	+	0.713326i	$0.747188\pi$
$284$	12.0000			0.712069
$285$		0			0
$286$		0			0
$287$		0			0
$288$			3.00000i			0.176777i
$289$	13.0000			0.764706
$290$	7.00000	+	21.0000i	0.411054	+	1.23316i
$291$		0			0
$292$	5.00000	−	5.00000i	0.292603	−	0.292603i
$293$	9.00000	+	9.00000i	0.525786	+	0.525786i	0.919313	−	0.393527i	$-0.128745\pi$
$293$	9.00000	+	9.00000i	0.525786	+	0.525786i	−0.393527	+	0.919313i	$0.628745\pi$
$294$		0			0
$295$	6.00000	−	2.00000i	0.349334	−	0.116445i
$296$	−1.00000	+	6.00000i	−0.0581238	+	0.348743i
$297$		0			0
$298$			6.00000i			0.347571i
$299$	16.0000			0.925304
$300$		0			0
$301$	−8.00000	+	8.00000i	−0.461112	+	0.461112i
$302$		−	20.0000i		−	1.15087i
$303$		0			0
$304$	−2.00000	−	2.00000i	−0.114708	−	0.114708i
$305$	−3.00000	+	1.00000i	−0.171780	+	0.0572598i
$306$	−6.00000			−0.342997
$307$		0			0		0.707107	−	0.707107i	$-0.250000\pi$
$307$		0			0		−0.707107	+	0.707107i	$0.750000\pi$
$308$		0			0
$309$		0			0
$310$	12.0000	−	4.00000i	0.681554	−	0.227185i
$311$	−4.00000	−	4.00000i	−0.226819	−	0.226819i	0.584543	−	0.811363i	$-0.301274\pi$
$311$	−4.00000	−	4.00000i	−0.226819	−	0.226819i	−0.811363	+	0.584543i	$0.801274\pi$
$312$		0			0
$313$	−26.0000			−1.46961			−0.734803	−	0.678280i	$-0.762726\pi$
$313$	−26.0000			−1.46961			−0.734803	+	0.678280i	$0.762726\pi$
$314$	−7.00000	+	7.00000i	−0.395033	+	0.395033i
$315$	18.0000	−	6.00000i	1.01419	−	0.338062i
$316$	−12.0000	−	12.0000i	−0.675053	−	0.675053i
$317$	5.00000	+	5.00000i	0.280828	+	0.280828i	0.833439	−	0.552611i	$-0.186369\pi$
$317$	5.00000	+	5.00000i	0.280828	+	0.280828i	−0.552611	+	0.833439i	$0.686369\pi$
$318$		0			0
$319$		0			0
$320$	−1.00000	+	2.00000i	−0.0559017	+	0.111803i
$321$		0			0
$322$	−8.00000	+	8.00000i	−0.445823	+	0.445823i
$323$	4.00000	−	4.00000i	0.222566	−	0.222566i
$324$	−9.00000			−0.500000
$325$	−12.0000	−	16.0000i	−0.665640	−	0.887520i
$326$			24.0000i			1.32924i
$327$		0			0
$328$		0			0
$329$		−	8.00000i		−	0.441054i
$330$		0			0
$331$	6.00000	−	6.00000i	0.329790	−	0.329790i	−0.522717	−	0.852506i	$-0.675081\pi$
$331$	6.00000	−	6.00000i	0.329790	−	0.329790i	0.852506	+	0.522717i	$0.175081\pi$
$332$	4.00000	+	4.00000i	0.219529	+	0.219529i
$333$	−18.0000	−	3.00000i	−0.986394	−	0.164399i
$334$		−	8.00000i		−	0.437741i
$335$		0			0
$336$		0			0
$337$	−15.0000	−	15.0000i	−0.817102	−	0.817102i	0.168585	−	0.985687i	$-0.446080\pi$
$337$	−15.0000	−	15.0000i	−0.817102	−	0.817102i	−0.985687	+	0.168585i	$0.946080\pi$
$338$	3.00000			0.163178
$339$		0			0
$340$	−4.00000	−	2.00000i	−0.216930	−	0.108465i
$341$		0			0
$342$	6.00000	−	6.00000i	0.324443	−	0.324443i
$343$	−12.0000	−	12.0000i	−0.647939	−	0.647939i
$344$	4.00000			0.215666
$345$		0			0
$346$	−5.00000	+	5.00000i	−0.268802	+	0.268802i
$347$	−12.0000			−0.644194			−0.322097	−	0.946707i	$-0.604388\pi$
$347$	−12.0000			−0.644194			−0.322097	+	0.946707i	$0.604388\pi$
$348$		0			0
$349$		−	14.0000i		−	0.749403i	−0.927146	−	0.374701i	$-0.877745\pi$
$349$		−	14.0000i		−	0.749403i	0.927146	−	0.374701i	$-0.122255\pi$
$350$	14.0000	+	2.00000i	0.748331	+	0.106904i
$351$		0			0
$352$		0			0
$353$		−	36.0000i		−	1.91609i	−0.286623	−	0.958043i	$-0.592533\pi$
$353$		−	36.0000i		−	1.91609i	0.286623	−	0.958043i	$-0.407467\pi$
$354$		0			0
$355$	−12.0000	+	24.0000i	−0.636894	+	1.27379i
$356$	7.00000	−	7.00000i	0.370999	−	0.370999i
$357$		0			0
$358$	2.00000	−	2.00000i	0.105703	−	0.105703i
$359$		−	24.0000i		−	1.26667i	−0.773877	−	0.633336i	$-0.781685\pi$
$359$		−	24.0000i		−	1.26667i	0.773877	−	0.633336i	$-0.218315\pi$
$360$	−6.00000	−	3.00000i	−0.316228	−	0.158114i
$361$		−	11.0000i		−	0.578947i
$362$	−8.00000			−0.420471
$363$		0			0
$364$	−8.00000	+	8.00000i	−0.419314	+	0.419314i
$365$	5.00000	+	15.0000i	0.261712	+	0.785136i
$366$		0			0
$367$	18.0000	−	18.0000i	0.939592	−	0.939592i	−0.0586842	−	0.998277i	$-0.518691\pi$
$367$	18.0000	−	18.0000i	0.939592	−	0.939592i	0.998277	+	0.0586842i	$0.0186905\pi$
$368$	4.00000			0.208514
$369$		0			0
$370$	−11.0000	−	8.00000i	−0.571863	−	0.415900i
$371$	4.00000			0.207670
$372$		0			0
$373$	25.0000	−	25.0000i	1.29445	−	1.29445i	0.362446	−	0.932005i	$-0.381942\pi$
$373$	25.0000	−	25.0000i	1.29445	−	1.29445i	0.932005	−	0.362446i	$-0.118058\pi$
$374$		0			0
$375$		0			0
$376$	−2.00000	+	2.00000i	−0.103142	+	0.103142i
$377$	28.0000	−	28.0000i	1.44207	−	1.44207i
$378$		0			0
$379$		−	4.00000i		−	0.205466i	−0.994709	−	0.102733i	$-0.967241\pi$
$379$		−	4.00000i		−	0.205466i	0.994709	−	0.102733i	$-0.0327588\pi$
$380$	6.00000	−	2.00000i	0.307794	−	0.102598i
$381$		0			0
$382$	16.0000	−	16.0000i	0.818631	−	0.818631i
$383$	−36.0000			−1.83951			−0.919757	−	0.392488i	$-0.871614\pi$
$383$	−36.0000			−1.83951			−0.919757	+	0.392488i	$0.871614\pi$
$384$		0			0
$385$		0			0
$386$	14.0000			0.712581
$387$			12.0000i			0.609994i
$388$			12.0000i			0.609208i
$389$	−17.0000	−	17.0000i	−0.861934	−	0.861934i	0.129628	−	0.991563i	$-0.458622\pi$
$389$	−17.0000	−	17.0000i	−0.861934	−	0.861934i	−0.991563	+	0.129628i	$0.958622\pi$
$390$		0			0
$391$			8.00000i			0.404577i
$392$		−	1.00000i		−	0.0505076i
$393$		0			0
$394$	3.00000	−	3.00000i	0.151138	−	0.151138i
$395$	36.0000	−	12.0000i	1.81136	−	0.603786i
$396$		0			0
$397$	−25.0000	−	25.0000i	−1.25471	−	1.25471i	−0.953583	−	0.301131i	$-0.902636\pi$
$397$	−25.0000	−	25.0000i	−1.25471	−	1.25471i	−0.301131	−	0.953583i	$-0.597364\pi$
$398$	−8.00000	+	8.00000i	−0.401004	+	0.401004i
$399$		0			0
$400$	−3.00000	−	4.00000i	−0.150000	−	0.200000i
$401$	1.00000	+	1.00000i	0.0499376	+	0.0499376i	0.731635	−	0.681697i	$-0.238758\pi$
$401$	1.00000	+	1.00000i	0.0499376	+	0.0499376i	−0.681697	+	0.731635i	$0.738758\pi$
$402$		0			0
$403$	−16.0000	−	16.0000i	−0.797017	−	0.797017i
$404$		−	10.0000i		−	0.497519i
$405$	9.00000	−	18.0000i	0.447214	−	0.894427i
$406$			28.0000i			1.38962i
$407$		0			0
$408$		0			0
$409$	−13.0000	+	13.0000i	−0.642809	+	0.642809i	−0.951245	−	0.308436i	$-0.900194\pi$
$409$	−13.0000	+	13.0000i	−0.642809	+	0.642809i	0.308436	+	0.951245i	$0.400194\pi$
$410$		0			0
$411$		0			0
$412$		−	16.0000i		−	0.788263i
$413$	8.00000			0.393654
$414$			12.0000i			0.589768i
$415$	−12.0000	+	4.00000i	−0.589057	+	0.196352i
$416$	4.00000			0.196116
$417$		0			0
$418$		0			0
$419$			36.0000i			1.75872i	0.476162	+	0.879358i	$0.342028\pi$
$419$			36.0000i			1.75872i	−0.476162	+	0.879358i	$0.657972\pi$
$420$		0			0
$421$	11.0000	+	11.0000i	0.536107	+	0.536107i	0.922383	−	0.386276i	$-0.126239\pi$
$421$	11.0000	+	11.0000i	0.536107	+	0.536107i	−0.386276	+	0.922383i	$0.626239\pi$
$422$	−8.00000			−0.389434
$423$	−6.00000	−	6.00000i	−0.291730	−	0.291730i
$424$	−1.00000	−	1.00000i	−0.0485643	−	0.0485643i
$425$	8.00000	−	6.00000i	0.388057	−	0.291043i
$426$		0			0
$427$	−4.00000			−0.193574
$428$	8.00000	−	8.00000i	0.386695	−	0.386695i
$429$		0			0
$430$	−4.00000	+	8.00000i	−0.192897	+	0.385794i
$431$	−4.00000	−	4.00000i	−0.192673	−	0.192673i	0.604177	−	0.796850i	$-0.293502\pi$
$431$	−4.00000	−	4.00000i	−0.192673	−	0.192673i	−0.796850	+	0.604177i	$0.793502\pi$
$432$		0			0
$433$	−21.0000	−	21.0000i	−1.00920	−	1.00920i	−0.999957	−	0.00923827i	$-0.997059\pi$
$433$	−21.0000	−	21.0000i	−1.00920	−	1.00920i	−0.00923827	−	0.999957i	$-0.502941\pi$
$434$	16.0000			0.768025
$435$		0			0
$436$	3.00000	+	3.00000i	0.143674	+	0.143674i
$437$	−8.00000	−	8.00000i	−0.382692	−	0.382692i
$438$		0			0
$439$	−8.00000	+	8.00000i	−0.381819	+	0.381819i	−0.871757	−	0.489938i	$-0.837019\pi$
$439$	−8.00000	+	8.00000i	−0.381819	+	0.381819i	0.489938	+	0.871757i	$0.337019\pi$
$440$		0			0
$441$	3.00000			0.142857
$442$			8.00000i			0.380521i
$443$	−20.0000	+	20.0000i	−0.950229	+	0.950229i	−0.998819	−	0.0485901i	$-0.984527\pi$
$443$	−20.0000	+	20.0000i	−0.950229	+	0.950229i	0.0485901	+	0.998819i	$0.484527\pi$
$444$		0			0
$445$	7.00000	+	21.0000i	0.331832	+	0.995495i
$446$	−6.00000	−	6.00000i	−0.284108	−	0.284108i
$447$		0			0
$448$	−2.00000	+	2.00000i	−0.0944911	+	0.0944911i
$449$	23.0000	+	23.0000i	1.08544	+	1.08544i	0.995992	+	0.0894454i	$0.0285095\pi$
$449$	23.0000	+	23.0000i	1.08544	+	1.08544i	0.0894454	+	0.995992i	$0.471491\pi$
$450$	12.0000	−	9.00000i	0.565685	−	0.424264i
$451$		0			0
$452$			14.0000i			0.658505i
$453$		0			0
$454$			12.0000i			0.563188i
$455$	−8.00000	−	24.0000i	−0.375046	−	1.12514i
$456$		0			0
$457$		−	28.0000i		−	1.30978i	−0.755722	−	0.654892i	$-0.772714\pi$
$457$		−	28.0000i		−	1.30978i	0.755722	−	0.654892i	$-0.227286\pi$
$458$			16.0000i			0.747631i
$459$		0			0
$460$	−4.00000	+	8.00000i	−0.186501	+	0.373002i
$461$	−19.0000	+	19.0000i	−0.884918	+	0.884918i	−0.994030	−	0.109111i	$-0.965200\pi$
$461$	−19.0000	+	19.0000i	−0.884918	+	0.884918i	0.109111	+	0.994030i	$0.465200\pi$
$462$		0			0
$463$	4.00000			0.185896			0.0929479	−	0.995671i	$-0.470371\pi$
$463$	4.00000			0.185896			0.0929479	+	0.995671i	$0.470371\pi$
$464$	7.00000	−	7.00000i	0.324967	−	0.324967i
$465$		0			0
$466$	5.00000	−	5.00000i	0.231621	−	0.231621i
$467$		−	8.00000i		−	0.370196i	−0.982720	−	0.185098i	$-0.940740\pi$
$467$		−	8.00000i		−	0.370196i	0.982720	−	0.185098i	$-0.0592602\pi$
$468$			12.0000i			0.554700i
$469$		0			0
$470$	−2.00000	−	6.00000i	−0.0922531	−	0.276759i
$471$		0			0
$472$	−2.00000	−	2.00000i	−0.0920575	−	0.0920575i
$473$		0			0
$474$		0			0
$475$	−2.00000	+	14.0000i	−0.0917663	+	0.642364i
$476$	−4.00000	−	4.00000i	−0.183340	−	0.183340i
$477$	3.00000	−	3.00000i	0.137361	−	0.137361i
$478$	8.00000	+	8.00000i	0.365911	+	0.365911i
$479$	28.0000	+	28.0000i	1.27935	+	1.27935i	0.941030	+	0.338322i	$0.109859\pi$
$479$	28.0000	+	28.0000i	1.27935	+	1.27935i	0.338322	+	0.941030i	$0.390141\pi$
$480$		0			0
$481$	−4.00000	+	24.0000i	−0.182384	+	1.09431i
$482$	−19.0000	+	19.0000i	−0.865426	+	0.865426i
$483$		0			0
$484$	11.0000			0.500000
$485$	−24.0000	−	12.0000i	−1.08978	−	0.544892i
$486$		0			0
$487$			32.0000i			1.45006i	0.688718	+	0.725029i	$0.258174\pi$
$487$			32.0000i			1.45006i	−0.688718	+	0.725029i	$0.741826\pi$
$488$	1.00000	+	1.00000i	0.0452679	+	0.0452679i
$489$		0			0
$490$	2.00000	+	1.00000i	0.0903508	+	0.0451754i
$491$	−8.00000			−0.361035			−0.180517	−	0.983572i	$-0.557777\pi$
$491$	−8.00000			−0.361035			−0.180517	+	0.983572i	$0.557777\pi$
$492$		0			0
$493$	14.0000	+	14.0000i	0.630528	+	0.630528i
$494$	−8.00000	−	8.00000i	−0.359937	−	0.359937i
$495$		0			0
$496$	−4.00000	−	4.00000i	−0.179605	−	0.179605i
$497$	−24.0000	+	24.0000i	−1.07655	+	1.07655i
$498$		0			0
$499$	2.00000	−	2.00000i	0.0895323	−	0.0895323i	−0.660922	−	0.750454i	$-0.729835\pi$
$499$	2.00000	−	2.00000i	0.0895323	−	0.0895323i	0.750454	+	0.660922i	$0.229835\pi$
$500$	11.0000	−	2.00000i	0.491935	−	0.0894427i
$501$		0			0
$502$	−14.0000	−	14.0000i	−0.624851	−	0.624851i
$503$	−16.0000			−0.713405			−0.356702	−	0.934218i	$-0.616099\pi$
$503$	−16.0000			−0.713405			−0.356702	+	0.934218i	$0.616099\pi$
$504$	−6.00000	−	6.00000i	−0.267261	−	0.267261i
$505$	20.0000	+	10.0000i	0.889988	+	0.444994i
$506$		0			0
$507$		0			0
$508$	−2.00000	+	2.00000i	−0.0887357	+	0.0887357i
$509$	30.0000			1.32973			0.664863	−	0.746965i	$-0.268490\pi$
$509$	30.0000			1.32973			0.664863	+	0.746965i	$0.268490\pi$
$510$		0			0
$511$			20.0000i			0.884748i
$512$	1.00000			0.0441942
$513$		0			0
$514$		−	18.0000i		−	0.793946i
$515$	32.0000	+	16.0000i	1.41009	+	0.705044i
$516$		0			0
$517$		0			0
$518$	−10.0000	−	14.0000i	−0.439375	−	0.615125i
$519$		0			0
$520$	−4.00000	+	8.00000i	−0.175412	+	0.350823i
$521$			10.0000i			0.438108i	0.975713	+	0.219054i	$0.0702971\pi$
$521$			10.0000i			0.438108i	−0.975713	+	0.219054i	$0.929703\pi$
$522$	21.0000	+	21.0000i	0.919145	+	0.919145i
$523$	24.0000			1.04945			0.524723	−	0.851273i	$-0.324169\pi$
$523$	24.0000			1.04945			0.524723	+	0.851273i	$0.324169\pi$
$524$	6.00000	+	6.00000i	0.262111	+	0.262111i
$525$		0			0
$526$	10.0000	−	10.0000i	0.436021	−	0.436021i
$527$	8.00000	−	8.00000i	0.348485	−	0.348485i
$528$		0			0
$529$	−7.00000			−0.304348
$530$	3.00000	−	1.00000i	0.130312	−	0.0434372i
$531$	6.00000	−	6.00000i	0.260378	−	0.260378i
$532$	8.00000			0.346844
$533$		0			0
$534$		0			0
$535$	8.00000	+	24.0000i	0.345870	+	1.03761i
$536$		0			0
$537$		0			0
$538$		−	14.0000i		−	0.603583i
$539$		0			0
$540$		0			0
$541$	11.0000	−	11.0000i	0.472927	−	0.472927i	−0.429934	−	0.902861i	$-0.641463\pi$
$541$	11.0000	−	11.0000i	0.472927	−	0.472927i	0.902861	+	0.429934i	$0.141463\pi$
$542$	−28.0000			−1.20270
$543$		0			0
$544$			2.00000i			0.0857493i
$545$	−9.00000	+	3.00000i	−0.385518	+	0.128506i
$546$		0			0
$547$	8.00000			0.342055			0.171028	−	0.985266i	$-0.445291\pi$
$547$	8.00000			0.342055			0.171028	+	0.985266i	$0.445291\pi$
$548$	−7.00000	+	7.00000i	−0.299025	+	0.299025i
$549$	−3.00000	+	3.00000i	−0.128037	+	0.128037i
$550$		0			0
$551$	−28.0000			−1.19284
$552$		0			0
$553$	48.0000			2.04117
$554$	−12.0000			−0.509831
$555$		0			0
$556$	−20.0000			−0.848189
$557$	−12.0000			−0.508456			−0.254228	−	0.967144i	$-0.581821\pi$
$557$	−12.0000			−0.508456			−0.254228	+	0.967144i	$0.581821\pi$
$558$	12.0000	−	12.0000i	0.508001	−	0.508001i
$559$	16.0000			0.676728
$560$	−2.00000	−	6.00000i	−0.0845154	−	0.253546i
$561$		0			0
$562$	1.00000	−	1.00000i	0.0421825	−	0.0421825i
$563$	24.0000			1.01148			0.505740	−	0.862686i	$-0.331220\pi$
$563$	24.0000			1.01148			0.505740	+	0.862686i	$0.331220\pi$
$564$		0			0
$565$	−28.0000	−	14.0000i	−1.17797	−	0.588984i
$566$			24.0000i			1.00880i
$567$	18.0000	−	18.0000i	0.755929	−	0.755929i
$568$	12.0000			0.503509
$569$	−3.00000	+	3.00000i	−0.125767	+	0.125767i	−0.767188	−	0.641422i	$-0.778345\pi$
$569$	−3.00000	+	3.00000i	−0.125767	+	0.125767i	0.641422	+	0.767188i	$0.278345\pi$
$570$		0			0
$571$	12.0000			0.502184			0.251092	−	0.967963i	$-0.419210\pi$
$571$	12.0000			0.502184			0.251092	+	0.967963i	$0.419210\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$	−12.0000	−	16.0000i	−0.500435	−	0.667246i
$576$			3.00000i			0.125000i
$577$		−	18.0000i		−	0.749350i	−0.927156	−	0.374675i	$-0.877754\pi$
$577$		−	18.0000i		−	0.749350i	0.927156	−	0.374675i	$-0.122246\pi$
$578$	13.0000			0.540729
$579$		0			0
$580$	7.00000	+	21.0000i	0.290659	+	0.871978i
$581$	−16.0000			−0.663792
$582$		0			0
$583$		0			0
$584$	5.00000	−	5.00000i	0.206901	−	0.206901i
$585$	−24.0000	−	12.0000i	−0.992278	−	0.496139i
$586$	9.00000	+	9.00000i	0.371787	+	0.371787i
$587$	28.0000			1.15568			0.577842	−	0.816149i	$-0.303895\pi$
$587$	28.0000			1.15568			0.577842	+	0.816149i	$0.303895\pi$
$588$		0			0
$589$			16.0000i			0.659269i
$590$	6.00000	−	2.00000i	0.247016	−	0.0823387i
$591$		0			0
$592$	−1.00000	+	6.00000i	−0.0410997	+	0.246598i
$593$	−1.00000	−	1.00000i	−0.0410651	−	0.0410651i	0.686276	−	0.727341i	$-0.259244\pi$
$593$	−1.00000	−	1.00000i	−0.0410651	−	0.0410651i	−0.727341	+	0.686276i	$0.759244\pi$
$594$		0			0
$595$	12.0000	−	4.00000i	0.491952	−	0.163984i
$596$			6.00000i			0.245770i
$597$		0			0
$598$	16.0000			0.654289
$599$			36.0000i			1.47092i	0.677568	+	0.735460i	$0.263034\pi$
$599$			36.0000i			1.47092i	−0.677568	+	0.735460i	$0.736966\pi$
$600$		0			0
$601$	32.0000			1.30531			0.652654	−	0.757656i	$-0.273656\pi$
$601$	32.0000			1.30531			0.652654	+	0.757656i	$0.273656\pi$
$602$	−8.00000	+	8.00000i	−0.326056	+	0.326056i
$603$		0			0
$604$		−	20.0000i		−	0.813788i
$605$	−11.0000	+	22.0000i	−0.447214	+	0.894427i
$606$		0			0
$607$	−12.0000			−0.487065			−0.243532	−	0.969893i	$-0.578306\pi$
$607$	−12.0000			−0.487065			−0.243532	+	0.969893i	$0.578306\pi$
$608$	−2.00000	−	2.00000i	−0.0811107	−	0.0811107i
$609$		0			0
$610$	−3.00000	+	1.00000i	−0.121466	+	0.0404888i
$611$	−8.00000	+	8.00000i	−0.323645	+	0.323645i
$612$	−6.00000			−0.242536
$613$	5.00000	−	5.00000i	0.201948	−	0.201948i	−0.598886	−	0.800834i	$-0.704390\pi$
$613$	5.00000	−	5.00000i	0.201948	−	0.201948i	0.800834	+	0.598886i	$0.204390\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	−15.0000	−	15.0000i	−0.603877	−	0.603877i	0.337462	−	0.941339i	$-0.390432\pi$
$617$	−15.0000	−	15.0000i	−0.603877	−	0.603877i	−0.941339	+	0.337462i	$0.890432\pi$
$618$		0			0
$619$		0			0			−	1.00000i	$-0.5\pi$
$619$		0			0				1.00000i	$0.5\pi$
$620$	12.0000	−	4.00000i	0.481932	−	0.160644i
$621$		0			0
$622$	−4.00000	−	4.00000i	−0.160385	−	0.160385i
$623$			28.0000i			1.12180i
$624$		0			0
$625$	−7.00000	+	24.0000i	−0.280000	+	0.960000i
$626$	−26.0000			−1.03917
$627$		0			0
$628$	−7.00000	+	7.00000i	−0.279330	+	0.279330i
$629$	−12.0000	−	2.00000i	−0.478471	−	0.0797452i
$630$	18.0000	−	6.00000i	0.717137	−	0.239046i
$631$	16.0000	+	16.0000i	0.636950	+	0.636950i	0.949802	−	0.312852i	$-0.101284\pi$
$631$	16.0000	+	16.0000i	0.636950	+	0.636950i	−0.312852	+	0.949802i	$0.601284\pi$
$632$	−12.0000	−	12.0000i	−0.477334	−	0.477334i
$633$		0			0
$634$	5.00000	+	5.00000i	0.198575	+	0.198575i
$635$	−2.00000	−	6.00000i	−0.0793676	−	0.238103i
$636$		0			0
$637$		−	4.00000i		−	0.158486i
$638$		0			0
$639$			36.0000i			1.42414i
$640$	−1.00000	+	2.00000i	−0.0395285	+	0.0790569i
$641$	−48.0000			−1.89589			−0.947943	−	0.318440i	$-0.896841\pi$
$641$	−48.0000			−1.89589			−0.947943	+	0.318440i	$0.896841\pi$
$642$		0			0
$643$			44.0000i			1.73519i	0.497271	+	0.867595i	$0.334335\pi$
$643$			44.0000i			1.73519i	−0.497271	+	0.867595i	$0.665665\pi$
$644$	−8.00000	+	8.00000i	−0.315244	+	0.315244i
$645$		0			0
$646$	4.00000	−	4.00000i	0.157378	−	0.157378i
$647$	−32.0000			−1.25805			−0.629025	−	0.777385i	$-0.716546\pi$
$647$	−32.0000			−1.25805			−0.629025	+	0.777385i	$0.716546\pi$
$648$	−9.00000			−0.353553
$649$		0			0
$650$	−12.0000	−	16.0000i	−0.470679	−	0.627572i
$651$		0			0
$652$			24.0000i			0.939913i
$653$			4.00000i			0.156532i	0.996933	+	0.0782660i	$0.0249384\pi$
$653$			4.00000i			0.156532i	−0.996933	+	0.0782660i	$0.975062\pi$
$654$		0			0
$655$	−18.0000	+	6.00000i	−0.703318	+	0.234439i
$656$		0			0
$657$	15.0000	+	15.0000i	0.585206	+	0.585206i
$658$		−	8.00000i		−	0.311872i
$659$	20.0000			0.779089			0.389545	−	0.921008i	$-0.372632\pi$
$659$	20.0000			0.779089			0.389545	+	0.921008i	$0.372632\pi$
$660$		0			0
$661$	21.0000	+	21.0000i	0.816805	+	0.816805i	0.985644	−	0.168838i	$-0.0540016\pi$
$661$	21.0000	+	21.0000i	0.816805	+	0.816805i	−0.168838	+	0.985644i	$0.554002\pi$
$662$	6.00000	−	6.00000i	0.233197	−	0.233197i
$663$		0			0
$664$	4.00000	+	4.00000i	0.155230	+	0.155230i
$665$	−8.00000	+	16.0000i	−0.310227	+	0.620453i
$666$	−18.0000	−	3.00000i	−0.697486	−	0.116248i
$667$	28.0000	−	28.0000i	1.08416	−	1.08416i
$668$		−	8.00000i		−	0.309529i
$669$		0			0
$670$		0			0
$671$		0			0
$672$		0			0
$673$	9.00000	+	9.00000i	0.346925	+	0.346925i	0.858963	−	0.512038i	$-0.171109\pi$
$673$	9.00000	+	9.00000i	0.346925	+	0.346925i	−0.512038	+	0.858963i	$0.671109\pi$
$674$	−15.0000	−	15.0000i	−0.577778	−	0.577778i
$675$		0			0
$676$	3.00000			0.115385
$677$	25.0000	+	25.0000i	0.960828	+	0.960828i	0.999261	−	0.0384331i	$-0.0122367\pi$
$677$	25.0000	+	25.0000i	0.960828	+	0.960828i	−0.0384331	+	0.999261i	$0.512237\pi$
$678$		0			0
$679$	−24.0000	−	24.0000i	−0.921035	−	0.921035i
$680$	−4.00000	−	2.00000i	−0.153393	−	0.0766965i
$681$		0			0
$682$		0			0
$683$	−36.0000			−1.37750			−0.688751	−	0.724998i	$-0.741841\pi$
$683$	−36.0000			−1.37750			−0.688751	+	0.724998i	$0.741841\pi$
$684$	6.00000	−	6.00000i	0.229416	−	0.229416i
$685$	−7.00000	−	21.0000i	−0.267456	−	0.802369i
$686$	−12.0000	−	12.0000i	−0.458162	−	0.458162i
$687$		0			0
$688$	4.00000			0.152499
$689$	−4.00000	−	4.00000i	−0.152388	−	0.152388i
$690$		0			0
$691$		−	20.0000i		−	0.760836i	−0.924815	−	0.380418i	$-0.875780\pi$
$691$		−	20.0000i		−	0.760836i	0.924815	−	0.380418i	$-0.124220\pi$
$692$	−5.00000	+	5.00000i	−0.190071	+	0.190071i
$693$		0			0
$694$	−12.0000			−0.455514
$695$	20.0000	−	40.0000i	0.758643	−	1.51729i
$696$		0			0
$697$		0			0
$698$		−	14.0000i		−	0.529908i
$699$		0			0
$700$	14.0000	+	2.00000i	0.529150	+	0.0755929i
$701$	31.0000	−	31.0000i	1.17085	−	1.17085i	0.188847	−	0.982006i	$-0.439525\pi$
$701$	31.0000	−	31.0000i	1.17085	−	1.17085i	0.982006	−	0.188847i	$-0.0604752\pi$
$702$		0			0
$703$	14.0000	−	10.0000i	0.528020	−	0.377157i
$704$		0			0
$705$		0			0
$706$		−	36.0000i		−	1.35488i
$707$	20.0000	+	20.0000i	0.752177	+	0.752177i
$708$		0			0
$709$	−27.0000	−	27.0000i	−1.01401	−	1.01401i	−0.999901	−	0.0141058i	$-0.995510\pi$
$709$	−27.0000	−	27.0000i	−1.01401	−	1.01401i	−0.0141058	−	0.999901i	$-0.504490\pi$
$710$	−12.0000	+	24.0000i	−0.450352	+	0.900704i
$711$	36.0000	−	36.0000i	1.35011	−	1.35011i
$712$	7.00000	−	7.00000i	0.262336	−	0.262336i
$713$	−16.0000	−	16.0000i	−0.599205	−	0.599205i
$714$		0			0
$715$		0			0
$716$	2.00000	−	2.00000i	0.0747435	−	0.0747435i
$717$		0			0
$718$		−	24.0000i		−	0.895672i
$719$		−	4.00000i		−	0.149175i	−0.997214	−	0.0745874i	$-0.976236\pi$
$719$		−	4.00000i		−	0.149175i	0.997214	−	0.0745874i	$-0.0237640\pi$
$720$	−6.00000	−	3.00000i	−0.223607	−	0.111803i
$721$	32.0000	+	32.0000i	1.19174	+	1.19174i
$722$		−	11.0000i		−	0.409378i
$723$		0			0
$724$	−8.00000			−0.297318
$725$	−49.0000	−	7.00000i	−1.81981	−	0.259973i
$726$		0			0
$727$	28.0000			1.03846			0.519231	−	0.854634i	$-0.326218\pi$
$727$	28.0000			1.03846			0.519231	+	0.854634i	$0.326218\pi$
$728$	−8.00000	+	8.00000i	−0.296500	+	0.296500i
$729$		−	27.0000i		−	1.00000i
$730$	5.00000	+	15.0000i	0.185058	+	0.555175i
$731$			8.00000i			0.295891i
$732$		0			0
$733$	−15.0000	+	15.0000i	−0.554038	+	0.554038i	−0.927604	−	0.373566i	$-0.878135\pi$
$733$	−15.0000	+	15.0000i	−0.554038	+	0.554038i	0.373566	+	0.927604i	$0.378135\pi$
$734$	18.0000	−	18.0000i	0.664392	−	0.664392i
$735$		0			0
$736$	4.00000			0.147442
$737$		0			0
$738$		0			0
$739$	−20.0000			−0.735712			−0.367856	−	0.929883i	$-0.619908\pi$
$739$	−20.0000			−0.735712			−0.367856	+	0.929883i	$0.619908\pi$
$740$	−11.0000	−	8.00000i	−0.404368	−	0.294086i
$741$		0			0
$742$	4.00000			0.146845
$743$	−10.0000	+	10.0000i	−0.366864	+	0.366864i	−0.866332	−	0.499468i	$-0.833529\pi$
$743$	−10.0000	+	10.0000i	−0.366864	+	0.366864i	0.499468	+	0.866332i	$0.333529\pi$
$744$		0			0
$745$	−12.0000	−	6.00000i	−0.439646	−	0.219823i
$746$	25.0000	−	25.0000i	0.915315	−	0.915315i
$747$	−12.0000	+	12.0000i	−0.439057	+	0.439057i
$748$		0			0
$749$			32.0000i			1.16925i
$750$		0			0
$751$		−	40.0000i		−	1.45962i	−0.683650	−	0.729810i	$-0.739608\pi$
$751$		−	40.0000i		−	1.45962i	0.683650	−	0.729810i	$-0.260392\pi$
$752$	−2.00000	+	2.00000i	−0.0729325	+	0.0729325i
$753$		0			0
$754$	28.0000	−	28.0000i	1.01970	−	1.01970i
$755$	40.0000	+	20.0000i	1.45575	+	0.727875i
$756$		0			0
$757$		−	28.0000i		−	1.01768i	−0.860862	−	0.508839i	$-0.830075\pi$
$757$		−	28.0000i		−	1.01768i	0.860862	−	0.508839i	$-0.169925\pi$
$758$		−	4.00000i		−	0.145287i
$759$		0			0
$760$	6.00000	−	2.00000i	0.217643	−	0.0725476i
$761$		0			0		1.00000			$0$
$761$		0			0		−1.00000			$\pi$
$762$		0			0
$763$	−12.0000			−0.434429
$764$	16.0000	−	16.0000i	0.578860	−	0.578860i
$765$	6.00000	−	12.0000i	0.216930	−	0.433861i
$766$	−36.0000			−1.30073
$767$	−8.00000	−	8.00000i	−0.288863	−	0.288863i
$768$		0			0
$769$	−3.00000	+	3.00000i	−0.108183	+	0.108183i	−0.759126	−	0.650943i	$-0.774373\pi$
$769$	−3.00000	+	3.00000i	−0.108183	+	0.108183i	0.650943	+	0.759126i	$0.274373\pi$
$770$		0			0
$771$		0			0
$772$	14.0000			0.503871
$773$	−21.0000	−	21.0000i	−0.755318	−	0.755318i	0.220149	−	0.975466i	$-0.429346\pi$
$773$	−21.0000	−	21.0000i	−0.755318	−	0.755318i	−0.975466	+	0.220149i	$0.929346\pi$
$774$			12.0000i			0.431331i
$775$	−4.00000	+	28.0000i	−0.143684	+	1.00579i
$776$			12.0000i			0.430775i
$777$		0			0
$778$	−17.0000	−	17.0000i	−0.609480	−	0.609480i
$779$		0			0
$780$		0			0
$781$		0			0
$782$			8.00000i			0.286079i
$783$		0			0
$784$		−	1.00000i		−	0.0357143i
$785$	−7.00000	−	21.0000i	−0.249841	−	0.749522i
$786$		0			0
$787$	−12.0000	+	12.0000i	−0.427754	+	0.427754i	−0.887863	−	0.460109i	$-0.847810\pi$
$787$	−12.0000	+	12.0000i	−0.427754	+	0.427754i	0.460109	+	0.887863i	$0.347810\pi$
$788$	3.00000	−	3.00000i	0.106871	−	0.106871i
$789$		0			0
$790$	36.0000	−	12.0000i	1.28082	−	0.426941i
$791$	−28.0000	−	28.0000i	−0.995565	−	0.995565i
$792$		0			0
$793$	4.00000	+	4.00000i	0.142044	+	0.142044i
$794$	−25.0000	−	25.0000i	−0.887217	−	0.887217i
$795$		0			0
$796$	−8.00000	+	8.00000i	−0.283552	+	0.283552i
$797$	28.0000			0.991811			0.495905	−	0.868377i	$-0.334836\pi$
$797$	28.0000			0.991811			0.495905	+	0.868377i	$0.334836\pi$
$798$		0			0
$799$	−4.00000	−	4.00000i	−0.141510	−	0.141510i
$800$	−3.00000	−	4.00000i	−0.106066	−	0.141421i
$801$	21.0000	+	21.0000i	0.741999	+	0.741999i
$802$	1.00000	+	1.00000i	0.0353112	+	0.0353112i
$803$		0			0
$804$		0			0
$805$	−8.00000	−	24.0000i	−0.281963	−	0.845889i
$806$	−16.0000	−	16.0000i	−0.563576	−	0.563576i
$807$		0			0
$808$		−	10.0000i		−	0.351799i
$809$	−23.0000	+	23.0000i	−0.808637	+	0.808637i	−0.984428	−	0.175791i	$-0.943752\pi$
$809$	−23.0000	+	23.0000i	−0.808637	+	0.808637i	0.175791	+	0.984428i	$0.443752\pi$
$810$	9.00000	−	18.0000i	0.316228	−	0.632456i
$811$	12.0000			0.421377			0.210688	−	0.977553i	$-0.432429\pi$
$811$	12.0000			0.421377			0.210688	+	0.977553i	$0.432429\pi$
$812$			28.0000i			0.982607i
$813$		0			0
$814$		0			0
$815$	−48.0000	−	24.0000i	−1.68137	−	0.840683i
$816$		0			0
$817$	−8.00000	−	8.00000i	−0.279885	−	0.279885i
$818$	−13.0000	+	13.0000i	−0.454534	+	0.454534i
$819$	−24.0000	−	24.0000i	−0.838628	−	0.838628i
$820$		0			0
$821$	42.0000			1.46581			0.732905	−	0.680331i	$-0.238164\pi$
$821$	42.0000			1.46581			0.732905	+	0.680331i	$0.238164\pi$
$822$		0			0
$823$	14.0000	+	14.0000i	0.488009	+	0.488009i	0.907678	−	0.419668i	$-0.137854\pi$
$823$	14.0000	+	14.0000i	0.488009	+	0.488009i	−0.419668	+	0.907678i	$0.637854\pi$
$824$		−	16.0000i		−	0.557386i
$825$		0			0
$826$	8.00000			0.278356
$827$			52.0000i			1.80822i	0.427303	+	0.904109i	$0.359464\pi$
$827$			52.0000i			1.80822i	−0.427303	+	0.904109i	$0.640536\pi$
$828$			12.0000i			0.417029i
$829$	37.0000	−	37.0000i	1.28506	−	1.28506i	0.347314	−	0.937749i	$-0.387094\pi$
$829$	37.0000	−	37.0000i	1.28506	−	1.28506i	0.937749	−	0.347314i	$-0.112906\pi$
$830$	−12.0000	+	4.00000i	−0.416526	+	0.138842i
$831$		0			0
$832$	4.00000			0.138675
$833$	2.00000			0.0692959
$834$		0			0
$835$	16.0000	+	8.00000i	0.553703	+	0.276851i
$836$		0			0
$837$		0			0
$838$			36.0000i			1.24360i
$839$		0			0			−	1.00000i	$-0.5\pi$
$839$		0			0				1.00000i	$0.5\pi$
$840$		0			0
$841$		−	69.0000i		−	2.37931i
$842$	11.0000	+	11.0000i	0.379085	+	0.379085i
$843$		0			0
$844$	−8.00000			−0.275371
$845$	−3.00000	+	6.00000i	−0.103203	+	0.206406i
$846$	−6.00000	−	6.00000i	−0.206284	−	0.206284i
$847$	−22.0000	+	22.0000i	−0.755929	+	0.755929i
$848$	−1.00000	−	1.00000i	−0.0343401	−	0.0343401i
$849$		0			0
$850$	8.00000	−	6.00000i	0.274398	−	0.205798i
$851$	−4.00000	+	24.0000i	−0.137118	+	0.822709i
$852$		0			0
$853$			4.00000i			0.136957i	0.997653	+	0.0684787i	$0.0218145\pi$
$853$			4.00000i			0.136957i	−0.997653	+	0.0684787i	$0.978185\pi$
$854$	−4.00000			−0.136877
$855$	6.00000	+	18.0000i	0.205196	+	0.615587i
$856$	8.00000	−	8.00000i	0.273434	−	0.273434i
$857$			12.0000i			0.409912i	0.978771	+	0.204956i	$0.0657052\pi$
$857$			12.0000i			0.409912i	−0.978771	+	0.204956i	$0.934295\pi$
$858$		0			0
$859$	18.0000	+	18.0000i	0.614152	+	0.614152i	0.944025	−	0.329873i	$-0.107006\pi$
$859$	18.0000	+	18.0000i	0.614152	+	0.614152i	−0.329873	+	0.944025i	$0.607006\pi$
$860$	−4.00000	+	8.00000i	−0.136399	+	0.272798i
$861$		0			0
$862$	−4.00000	−	4.00000i	−0.136241	−	0.136241i
$863$	−26.0000	−	26.0000i	−0.885050	−	0.885050i	0.108992	−	0.994043i	$-0.465238\pi$
$863$	−26.0000	−	26.0000i	−0.885050	−	0.885050i	−0.994043	+	0.108992i	$0.965238\pi$
$864$		0			0
$865$	−5.00000	−	15.0000i	−0.170005	−	0.510015i
$866$	−21.0000	−	21.0000i	−0.713609	−	0.713609i
$867$		0			0
$868$	16.0000			0.543075
$869$		0			0
$870$		0			0
$871$		0			0
$872$	3.00000	+	3.00000i	0.101593	+	0.101593i
$873$	−36.0000			−1.21842
$874$	−8.00000	−	8.00000i	−0.270604	−	0.270604i
$875$	−18.0000	+	26.0000i	−0.608511	+	0.878960i
$876$		0			0
$877$	−7.00000	+	7.00000i	−0.236373	+	0.236373i	−0.815347	−	0.578973i	$-0.803454\pi$
$877$	−7.00000	+	7.00000i	−0.236373	+	0.236373i	0.578973	+	0.815347i	$0.303454\pi$
$878$	−8.00000	+	8.00000i	−0.269987	+	0.269987i
$879$		0			0
$880$		0			0
$881$		−	30.0000i		−	1.01073i	−0.862907	−	0.505363i	$-0.831359\pi$
$881$		−	30.0000i		−	1.01073i	0.862907	−	0.505363i	$-0.168641\pi$
$882$	3.00000			0.101015
$883$		−	36.0000i		−	1.21150i	−0.795656	−	0.605748i	$-0.792874\pi$
$883$		−	36.0000i		−	1.21150i	0.795656	−	0.605748i	$-0.207126\pi$
$884$			8.00000i			0.269069i
$885$		0			0
$886$	−20.0000	+	20.0000i	−0.671913	+	0.671913i
$887$	10.0000	+	10.0000i	0.335767	+	0.335767i	0.854772	−	0.519004i	$-0.173697\pi$
$887$	10.0000	+	10.0000i	0.335767	+	0.335767i	−0.519004	+	0.854772i	$0.673697\pi$
$888$		0			0
$889$		−	8.00000i		−	0.268311i
$890$	7.00000	+	21.0000i	0.234641	+	0.703922i
$891$		0			0
$892$	−6.00000	−	6.00000i	−0.200895	−	0.200895i
$893$	8.00000			0.267710
$894$		0			0
$895$	2.00000	+	6.00000i	0.0668526	+	0.200558i
$896$	−2.00000	+	2.00000i	−0.0668153	+	0.0668153i
$897$		0			0
$898$	23.0000	+	23.0000i	0.767520	+	0.767520i
$899$	−56.0000			−1.86770
$900$	12.0000	−	9.00000i	0.400000	−	0.300000i
$901$	2.00000	−	2.00000i	0.0666297	−	0.0666297i
$902$		0			0
$903$		0			0
$904$			14.0000i			0.465633i
$905$	8.00000	−	16.0000i	0.265929	−	0.531858i
$906$		0			0
$907$			52.0000i			1.72663i	0.504664	+	0.863316i	$0.331616\pi$
$907$			52.0000i			1.72663i	−0.504664	+	0.863316i	$0.668384\pi$
$908$			12.0000i			0.398234i
$909$	30.0000			0.995037
$910$	−8.00000	−	24.0000i	−0.265197	−	0.795592i
$911$	16.0000	−	16.0000i	0.530104	−	0.530104i	−0.390499	−	0.920603i	$-0.627698\pi$
$911$	16.0000	−	16.0000i	0.530104	−	0.530104i	0.920603	+	0.390499i	$0.127698\pi$
$912$		0			0
$913$		0			0
$914$		−	28.0000i		−	0.926158i
$915$		0			0
$916$			16.0000i			0.528655i
$917$	−24.0000			−0.792550
$918$		0			0
$919$	−28.0000	+	28.0000i	−0.923635	+	0.923635i	−0.997284	−	0.0736494i	$-0.976535\pi$
$919$	−28.0000	+	28.0000i	−0.923635	+	0.923635i	0.0736494	+	0.997284i	$0.476535\pi$
$920$	−4.00000	+	8.00000i	−0.131876	+	0.263752i
$921$		0			0
$922$	−19.0000	+	19.0000i	−0.625732	+	0.625732i
$923$	48.0000			1.57994
$924$		0			0
$925$	27.0000	−	14.0000i	0.887755	−	0.460317i
$926$	4.00000			0.131448
$927$	48.0000			1.57653
$928$	7.00000	−	7.00000i	0.229786	−	0.229786i
$929$	−10.0000			−0.328089			−0.164045	−	0.986453i	$-0.552454\pi$
$929$	−10.0000			−0.328089			−0.164045	+	0.986453i	$0.552454\pi$
$930$		0			0
$931$	−2.00000	+	2.00000i	−0.0655474	+	0.0655474i
$932$	5.00000	−	5.00000i	0.163780	−	0.163780i
$933$		0			0
$934$		−	8.00000i		−	0.261768i
$935$		0			0
$936$			12.0000i			0.392232i
$937$	23.0000	−	23.0000i	0.751377	−	0.751377i	−0.223359	−	0.974736i	$-0.571702\pi$
$937$	23.0000	−	23.0000i	0.751377	−	0.751377i	0.974736	+	0.223359i	$0.0717022\pi$
$938$		0			0
$939$		0			0
$940$	−2.00000	−	6.00000i	−0.0652328	−	0.195698i
$941$	−8.00000			−0.260793			−0.130396	−	0.991462i	$-0.541625\pi$
$941$	−8.00000			−0.260793			−0.130396	+	0.991462i	$0.541625\pi$
$942$		0			0
$943$		0			0
$944$	−2.00000	−	2.00000i	−0.0650945	−	0.0650945i
$945$		0			0
$946$		0			0
$947$			32.0000i			1.03986i	0.854209	+	0.519930i	$0.174042\pi$
$947$			32.0000i			1.03986i	−0.854209	+	0.519930i	$0.825958\pi$
$948$		0			0
$949$	20.0000	−	20.0000i	0.649227	−	0.649227i
$950$	−2.00000	+	14.0000i	−0.0648886	+	0.454220i
$951$		0			0
$952$	−4.00000	−	4.00000i	−0.129641	−	0.129641i
$953$	−15.0000	+	15.0000i	−0.485898	+	0.485898i	−0.907009	−	0.421111i	$-0.861640\pi$
$953$	−15.0000	+	15.0000i	−0.485898	+	0.485898i	0.421111	+	0.907009i	$0.361640\pi$
$954$	3.00000	−	3.00000i	0.0971286	−	0.0971286i
$955$	16.0000	+	48.0000i	0.517748	+	1.55324i
$956$	8.00000	+	8.00000i	0.258738	+	0.258738i
$957$		0			0
$958$	28.0000	+	28.0000i	0.904639	+	0.904639i
$959$		−	28.0000i		−	0.904167i
$960$		0			0
$961$			1.00000i			0.0322581i
$962$	−4.00000	+	24.0000i	−0.128965	+	0.773791i
$963$	24.0000	+	24.0000i	0.773389	+	0.773389i
$964$	−19.0000	+	19.0000i	−0.611949	+	0.611949i
$965$	−14.0000	+	28.0000i	−0.450676	+	0.901352i
$966$		0			0
$967$			12.0000i			0.385894i	0.981209	+	0.192947i	$0.0618045\pi$
$967$			12.0000i			0.385894i	−0.981209	+	0.192947i	$0.938195\pi$
$968$	11.0000			0.353553
$969$		0			0
$970$	−24.0000	−	12.0000i	−0.770594	−	0.385297i
$971$	−8.00000			−0.256732			−0.128366	−	0.991727i	$-0.540973\pi$
$971$	−8.00000			−0.256732			−0.128366	+	0.991727i	$0.540973\pi$
$972$		0			0
$973$	40.0000	−	40.0000i	1.28234	−	1.28234i
$974$			32.0000i			1.02535i
$975$		0			0
$976$	1.00000	+	1.00000i	0.0320092	+	0.0320092i
$977$	18.0000			0.575871			0.287936	−	0.957650i	$-0.407031\pi$
$977$	18.0000			0.575871			0.287936	+	0.957650i	$0.407031\pi$
$978$		0			0
$979$		0			0
$980$	2.00000	+	1.00000i	0.0638877	+	0.0319438i
$981$	−9.00000	+	9.00000i	−0.287348	+	0.287348i
$982$	−8.00000			−0.255290
$983$	30.0000	−	30.0000i	0.956851	−	0.956851i	−0.0422554	−	0.999107i	$-0.513454\pi$
$983$	30.0000	−	30.0000i	0.956851	−	0.956851i	0.999107	+	0.0422554i	$0.0134543\pi$
$984$		0			0
$985$	3.00000	+	9.00000i	0.0955879	+	0.286764i
$986$	14.0000	+	14.0000i	0.445851	+	0.445851i
$987$		0			0
$988$	−8.00000	−	8.00000i	−0.254514	−	0.254514i
$989$	16.0000			0.508770
$990$		0			0
$991$	−4.00000	−	4.00000i	−0.127064	−	0.127064i	0.640715	−	0.767779i	$-0.278638\pi$
$991$	−4.00000	−	4.00000i	−0.127064	−	0.127064i	−0.767779	+	0.640715i	$0.778638\pi$
$992$	−4.00000	−	4.00000i	−0.127000	−	0.127000i
$993$		0			0
$994$	−24.0000	+	24.0000i	−0.761234	+	0.761234i
$995$	−8.00000	−	24.0000i	−0.253617	−	0.760851i
$996$		0			0
$997$		−	28.0000i		−	0.886769i	−0.896332	−	0.443384i	$-0.853778\pi$
$997$		−	28.0000i		−	0.886769i	0.896332	−	0.443384i	$-0.146222\pi$
$998$	2.00000	−	2.00000i	0.0633089	−	0.0633089i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	370.2.h.a.253.1	yes	2
5.2	odd	4		370.2.g.b.327.1	yes	2
37.6	odd	4		370.2.g.b.43.1	✓	2
185.117	even	4	inner	370.2.h.a.117.1	yes	2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
370.2.g.b.43.1	✓	2	37.6	odd	4
370.2.g.b.327.1	yes	2	5.2	odd	4
370.2.h.a.117.1	yes	2	185.117	even	4	inner
370.2.h.a.253.1	yes	2	1.1	even	1	trivial

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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 370 = 2 \cdot 5 \cdot 37 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	370.h (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} +1.00000 q^{4} +(-1.00000 + 2.00000i) q^{5} +(-2.00000 + 2.00000i) q^{7} +1.00000 q^{8} +3.00000i q^{9} +(-1.00000 + 2.00000i) q^{10} +4.00000 q^{13} +(-2.00000 + 2.00000i) q^{14} +1.00000 q^{16} +2.00000i q^{17} +3.00000i q^{18} +(-2.00000 - 2.00000i) q^{19} +(-1.00000 + 2.00000i) q^{20} +4.00000 q^{23} +(-3.00000 - 4.00000i) q^{25} +4.00000 q^{26} +(-2.00000 + 2.00000i) q^{28} +(7.00000 - 7.00000i) q^{29} +(-4.00000 - 4.00000i) q^{31} +1.00000 q^{32} +2.00000i q^{34} +(-2.00000 - 6.00000i) q^{35} +3.00000i q^{36} +(-1.00000 + 6.00000i) q^{37} +(-2.00000 - 2.00000i) q^{38} +(-1.00000 + 2.00000i) q^{40} +4.00000 q^{43} +(-6.00000 - 3.00000i) q^{45} +4.00000 q^{46} +(-2.00000 + 2.00000i) q^{47} -1.00000i q^{49} +(-3.00000 - 4.00000i) q^{50} +4.00000 q^{52} +(-1.00000 - 1.00000i) q^{53} +(-2.00000 + 2.00000i) q^{56} +(7.00000 - 7.00000i) q^{58} +(-2.00000 - 2.00000i) q^{59} +(1.00000 + 1.00000i) q^{61} +(-4.00000 - 4.00000i) q^{62} +(-6.00000 - 6.00000i) q^{63} +1.00000 q^{64} +(-4.00000 + 8.00000i) q^{65} +2.00000i q^{68} +(-2.00000 - 6.00000i) q^{70} +12.0000 q^{71} +3.00000i q^{72} +(5.00000 - 5.00000i) q^{73} +(-1.00000 + 6.00000i) q^{74} +(-2.00000 - 2.00000i) q^{76} +(-12.0000 - 12.0000i) q^{79} +(-1.00000 + 2.00000i) q^{80} -9.00000 q^{81} +(4.00000 + 4.00000i) q^{83} +(-4.00000 - 2.00000i) q^{85} +4.00000 q^{86} +(7.00000 - 7.00000i) q^{89} +(-6.00000 - 3.00000i) q^{90} +(-8.00000 + 8.00000i) q^{91} +4.00000 q^{92} +(-2.00000 + 2.00000i) q^{94} +(6.00000 - 2.00000i) q^{95} +12.0000i q^{97} -1.00000i q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q + 2 q^{2} + 2 q^{4} - 2 q^{5} - 4 q^{7} + 2 q^{8} - 2 q^{10} + 8 q^{13} - 4 q^{14} + 2 q^{16} - 4 q^{19} - 2 q^{20} + 8 q^{23} - 6 q^{25} + 8 q^{26} - 4 q^{28} + 14 q^{29} - 8 q^{31} + 2 q^{32} - 4 q^{35}+ \cdots + 12 q^{95}+O(q^{100}) \) 2 * q + 2 * q^2 + 2 * q^4 - 2 * q^5 - 4 * q^7 + 2 * q^8 - 2 * q^10 + 8 * q^13 - 4 * q^14 + 2 * q^16 - 4 * q^19 - 2 * q^20 + 8 * q^23 - 6 * q^25 + 8 * q^26 - 4 * q^28 + 14 * q^29 - 8 * q^31 + 2 * q^32 - 4 * q^35 - 2 * q^37 - 4 * q^38 - 2 * q^40 + 8 * q^43 - 12 * q^45 + 8 * q^46 - 4 * q^47 - 6 * q^50 + 8 * q^52 - 2 * q^53 - 4 * q^56 + 14 * q^58 - 4 * q^59 + 2 * q^61 - 8 * q^62 - 12 * q^63 + 2 * q^64 - 8 * q^65 - 4 * q^70 + 24 * q^71 + 10 * q^73 - 2 * q^74 - 4 * q^76 - 24 * q^79 - 2 * q^80 - 18 * q^81 + 8 * q^83 - 8 * q^85 + 8 * q^86 + 14 * q^89 - 12 * q^90 - 16 * q^91 + 8 * q^92 - 4 * q^94 + 12 * q^95

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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