LMFDB - Embedded newform 390.2.p.g.161.2

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [390,2,Mod(161,390)] 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("390.161"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(390, base_ring=CyclotomicField(4)) chi = DirichletCharacter(H, H._module([2, 0, 3])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 390 = 2 \cdot 3 \cdot 5 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	390.p (of order $4$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [8,0,0,0,0,4,0] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(7)] == traces)

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

Self dual:	no
Analytic conductor:	$3.11416567883$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(i)$
Coefficient field:	8.0.40960000.1
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} + 7x^{4} + 1 $ x^8 + 7*x^4 + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			161.2
Root			$-1.14412 + 1.14412i$ of defining polynomial
Character	$\chi$	$=$	390.161
Dual form			390.2.p.g.281.2

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.707107 - 0.707107i) q^{2} +(1.58114 + 0.707107i) q^{3} +1.00000i q^{4} +(-0.707107 - 0.707107i) q^{5} +(-0.618034 - 1.61803i) q^{6} +(0.707107 - 0.707107i) q^{8} +(2.00000 + 2.23607i) q^{9} +1.00000i q^{10} +(1.41421 - 1.41421i) q^{11} +(-0.707107 + 1.58114i) q^{12} +(3.58114 + 0.418861i) q^{13} +(-0.618034 - 1.61803i) q^{15} -1.00000 q^{16} +1.64371 q^{17} +(0.166925 - 2.99535i) q^{18} +(1.16228 - 1.16228i) q^{19} +(0.707107 - 0.707107i) q^{20} -2.00000 q^{22} +4.47214 q^{23} +(1.61803 - 0.618034i) q^{24} +1.00000i q^{25} +(-2.23607 - 2.82843i) q^{26} +(1.58114 + 4.94975i) q^{27} +4.47214i q^{29} +(-0.707107 + 1.58114i) q^{30} +(-3.00000 + 3.00000i) q^{31} +(0.707107 + 0.707107i) q^{32} +(3.23607 - 1.23607i) q^{33} +(-1.16228 - 1.16228i) q^{34} +(-2.23607 + 2.00000i) q^{36} +(-4.00000 - 4.00000i) q^{37} -1.64371 q^{38} +(5.36610 + 3.19453i) q^{39} -1.00000 q^{40} +(-2.23607 - 2.23607i) q^{41} +0.837722i q^{43} +(1.41421 + 1.41421i) q^{44} +(0.166925 - 2.99535i) q^{45} +(-3.16228 - 3.16228i) q^{46} +(1.64371 - 1.64371i) q^{47} +(-1.58114 - 0.707107i) q^{48} -7.00000i q^{49} +(0.707107 - 0.707107i) q^{50} +(2.59893 + 1.16228i) q^{51} +(-0.418861 + 3.58114i) q^{52} +1.41421i q^{53} +(2.38197 - 4.61803i) q^{54} -2.00000 q^{55} +(2.65958 - 1.01587i) q^{57} +(3.16228 - 3.16228i) q^{58} +(3.05792 - 3.05792i) q^{59} +(1.61803 - 0.618034i) q^{60} -14.6491 q^{61} +4.24264 q^{62} -1.00000i q^{64} +(-2.23607 - 2.82843i) q^{65} +(-3.16228 - 1.41421i) q^{66} +(0.837722 - 0.837722i) q^{67} +1.64371i q^{68} +(7.07107 + 3.16228i) q^{69} +(-9.53663 - 9.53663i) q^{71} +(2.99535 + 0.166925i) q^{72} +(1.16228 + 1.16228i) q^{73} +5.65685i q^{74} +(-0.707107 + 1.58114i) q^{75} +(1.16228 + 1.16228i) q^{76} +(-1.53553 - 6.05327i) q^{78} -10.0000 q^{79} +(0.707107 + 0.707107i) q^{80} +(-1.00000 + 8.94427i) q^{81} +3.16228i q^{82} +(5.65685 + 5.65685i) q^{83} +(-1.16228 - 1.16228i) q^{85} +(0.592359 - 0.592359i) q^{86} +(-3.16228 + 7.07107i) q^{87} -2.00000i q^{88} +(-5.06450 + 5.06450i) q^{89} +(-2.23607 + 2.00000i) q^{90} +4.47214i q^{92} +(-6.86474 + 2.62210i) q^{93} -2.32456 q^{94} -1.64371 q^{95} +(0.618034 + 1.61803i) q^{96} +(5.16228 - 5.16228i) q^{97} +(-4.94975 + 4.94975i) q^{98} +(5.99070 + 0.333851i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 4 q^{6} + 16 q^{9} + 16 q^{13} + 4 q^{15} - 8 q^{16} - 16 q^{19} - 16 q^{22} + 4 q^{24} - 24 q^{31} + 8 q^{33} + 16 q^{34} - 32 q^{37} + 20 q^{39} - 8 q^{40} - 16 q^{52} + 28 q^{54} - 16 q^{55} + 40 q^{57}+ \cdots + 16 q^{97}+O(q^{100}) $ 8 * q + 4 * q^6 + 16 * q^9 + 16 * q^13 + 4 * q^15 - 8 * q^16 - 16 * q^19 - 16 * q^22 + 4 * q^24 - 24 * q^31 + 8 * q^33 + 16 * q^34 - 32 * q^37 + 20 * q^39 - 8 * q^40 - 16 * q^52 + 28 * q^54 - 16 * q^55 + 40 * q^57 + 4 * q^60 - 16 * q^61 + 32 * q^67 - 16 * q^73 - 16 * q^76 + 16 * q^78 - 80 * q^79 - 8 * q^81 + 16 * q^85 + 32 * q^94 - 4 * q^96 + 16 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/390\mathbb{Z}\right)^\times$.

$n$	$131$	$157$	$301$
$\chi(n)$	$-1$	$1$	$e\left(\frac{3}{4}\right)$

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 $

$2$	−0.707107	−	0.707107i	−0.500000	−	0.500000i
$2$	−0.707107	−	0.707107i	−0.500000	−	0.500000i
$3$	1.58114	+	0.707107i	0.912871	+	0.408248i
$3$	1.58114	+	0.707107i	0.912871	+	0.408248i
$4$			1.00000i			0.500000i
$5$	−0.707107	−	0.707107i	−0.316228	−	0.316228i
$5$	−0.707107	−	0.707107i	−0.316228	−	0.316228i
$6$	−0.618034	−	1.61803i	−0.252311	−	0.660560i
$7$		0			0		0.707107	−	0.707107i	$-0.250000\pi$
$7$		0			0		−0.707107	+	0.707107i	$0.750000\pi$
$8$	0.707107	−	0.707107i	0.250000	−	0.250000i
$9$	2.00000	+	2.23607i	0.666667	+	0.745356i
$10$			1.00000i			0.316228i
$11$	1.41421	−	1.41421i	0.426401	−	0.426401i	−0.460999	−	0.887401i	$-0.652509\pi$
$11$	1.41421	−	1.41421i	0.426401	−	0.426401i	0.887401	+	0.460999i	$0.152509\pi$
$12$	−0.707107	+	1.58114i	−0.204124	+	0.456435i
$13$	3.58114	+	0.418861i	0.993229	+	0.116171i
$13$	3.58114	+	0.418861i	0.993229	+	0.116171i
$14$		0			0
$15$	−0.618034	−	1.61803i	−0.159576	−	0.417775i
$16$	−1.00000			−0.250000
$17$	1.64371			0.398658			0.199329	−	0.979933i	$-0.436124\pi$
$17$	1.64371			0.398658			0.199329	+	0.979933i	$0.436124\pi$
$18$	0.166925	−	2.99535i	0.0393447	−	0.706011i
$19$	1.16228	−	1.16228i	0.266645	−	0.266645i	−0.561102	−	0.827747i	$-0.689622\pi$
$19$	1.16228	−	1.16228i	0.266645	−	0.266645i	0.827747	+	0.561102i	$0.189622\pi$
$20$	0.707107	−	0.707107i	0.158114	−	0.158114i
$21$		0			0
$22$	−2.00000			−0.426401
$23$	4.47214			0.932505			0.466252	−	0.884652i	$-0.345604\pi$
$23$	4.47214			0.932505			0.466252	+	0.884652i	$0.345604\pi$
$24$	1.61803	−	0.618034i	0.330280	−	0.126156i
$25$			1.00000i			0.200000i
$26$	−2.23607	−	2.82843i	−0.438529	−	0.554700i
$27$	1.58114	+	4.94975i	0.304290	+	0.952579i
$28$		0			0
$29$			4.47214i			0.830455i	0.909718	+	0.415227i	$0.136298\pi$
$29$			4.47214i			0.830455i	−0.909718	+	0.415227i	$0.863702\pi$
$30$	−0.707107	+	1.58114i	−0.129099	+	0.288675i
$31$	−3.00000	+	3.00000i	−0.538816	+	0.538816i	−0.923181	−	0.384365i	$-0.874420\pi$
$31$	−3.00000	+	3.00000i	−0.538816	+	0.538816i	0.384365	+	0.923181i	$0.374420\pi$
$32$	0.707107	+	0.707107i	0.125000	+	0.125000i
$33$	3.23607	−	1.23607i	0.563327	−	0.215172i
$34$	−1.16228	−	1.16228i	−0.199329	−	0.199329i
$35$		0			0
$36$	−2.23607	+	2.00000i	−0.372678	+	0.333333i
$37$	−4.00000	−	4.00000i	−0.657596	−	0.657596i	0.297215	−	0.954811i	$-0.403942\pi$
$37$	−4.00000	−	4.00000i	−0.657596	−	0.657596i	−0.954811	+	0.297215i	$0.903942\pi$
$38$	−1.64371			−0.266645
$39$	5.36610	+	3.19453i	0.859263	+	0.511533i
$40$	−1.00000			−0.158114
$41$	−2.23607	−	2.23607i	−0.349215	−	0.349215i	0.510602	−	0.859817i	$-0.329423\pi$
$41$	−2.23607	−	2.23607i	−0.349215	−	0.349215i	−0.859817	+	0.510602i	$0.829423\pi$
$42$		0			0
$43$			0.837722i			0.127751i	0.997958	+	0.0638757i	$0.0203461\pi$
$43$			0.837722i			0.127751i	−0.997958	+	0.0638757i	$0.979654\pi$
$44$	1.41421	+	1.41421i	0.213201	+	0.213201i
$45$	0.166925	−	2.99535i	0.0248837	−	0.446521i
$46$	−3.16228	−	3.16228i	−0.466252	−	0.466252i
$47$	1.64371	−	1.64371i	0.239760	−	0.239760i	−0.576991	−	0.816751i	$-0.695773\pi$
$47$	1.64371	−	1.64371i	0.239760	−	0.239760i	0.816751	+	0.576991i	$0.195773\pi$
$48$	−1.58114	−	0.707107i	−0.228218	−	0.102062i
$49$		−	7.00000i		−	1.00000i
$50$	0.707107	−	0.707107i	0.100000	−	0.100000i
$51$	2.59893	+	1.16228i	0.363923	+	0.162751i
$52$	−0.418861	+	3.58114i	−0.0580856	+	0.496615i
$53$			1.41421i			0.194257i	0.995272	+	0.0971286i	$0.0309658\pi$
$53$			1.41421i			0.194257i	−0.995272	+	0.0971286i	$0.969034\pi$
$54$	2.38197	−	4.61803i	0.324145	−	0.628435i
$55$	−2.00000			−0.269680
$56$		0			0
$57$	2.65958	−	1.01587i	0.352270	−	0.134555i
$58$	3.16228	−	3.16228i	0.415227	−	0.415227i
$59$	3.05792	−	3.05792i	0.398108	−	0.398108i	−0.479458	−	0.877565i	$-0.659167\pi$
$59$	3.05792	−	3.05792i	0.398108	−	0.398108i	0.877565	+	0.479458i	$0.159167\pi$
$60$	1.61803	−	0.618034i	0.208887	−	0.0797878i
$61$	−14.6491			−1.87563			−0.937813	−	0.347140i	$-0.887153\pi$
$61$	−14.6491			−1.87563			−0.937813	+	0.347140i	$0.887153\pi$
$62$	4.24264			0.538816
$63$		0			0
$64$		−	1.00000i		−	0.125000i
$65$	−2.23607	−	2.82843i	−0.277350	−	0.350823i
$66$	−3.16228	−	1.41421i	−0.389249	−	0.174078i
$67$	0.837722	−	0.837722i	0.102344	−	0.102344i	−0.654081	−	0.756425i	$-0.726944\pi$
$67$	0.837722	−	0.837722i	0.102344	−	0.102344i	0.756425	+	0.654081i	$0.226944\pi$
$68$			1.64371i			0.199329i
$69$	7.07107	+	3.16228i	0.851257	+	0.380693i
$70$		0			0
$71$	−9.53663	−	9.53663i	−1.13179	−	1.13179i	−0.989880	−	0.141910i	$-0.954676\pi$
$71$	−9.53663	−	9.53663i	−1.13179	−	1.13179i	−0.141910	−	0.989880i	$-0.545324\pi$
$72$	2.99535	+	0.166925i	0.353006	+	0.0196723i
$73$	1.16228	+	1.16228i	0.136034	+	0.136034i	0.771845	−	0.635811i	$-0.219334\pi$
$73$	1.16228	+	1.16228i	0.136034	+	0.136034i	−0.635811	+	0.771845i	$0.719334\pi$
$74$			5.65685i			0.657596i
$75$	−0.707107	+	1.58114i	−0.0816497	+	0.182574i
$76$	1.16228	+	1.16228i	0.133322	+	0.133322i
$77$		0			0
$78$	−1.53553	−	6.05327i	−0.173865	−	0.685398i
$79$	−10.0000			−1.12509			−0.562544	−	0.826767i	$-0.690177\pi$
$79$	−10.0000			−1.12509			−0.562544	+	0.826767i	$0.690177\pi$
$80$	0.707107	+	0.707107i	0.0790569	+	0.0790569i
$81$	−1.00000	+	8.94427i	−0.111111	+	0.993808i
$82$			3.16228i			0.349215i
$83$	5.65685	+	5.65685i	0.620920	+	0.620920i	0.945767	−	0.324846i	$-0.105313\pi$
$83$	5.65685	+	5.65685i	0.620920	+	0.620920i	−0.324846	+	0.945767i	$0.605313\pi$
$84$		0			0
$85$	−1.16228	−	1.16228i	−0.126067	−	0.126067i
$86$	0.592359	−	0.592359i	0.0638757	−	0.0638757i
$87$	−3.16228	+	7.07107i	−0.339032	+	0.758098i
$88$		−	2.00000i		−	0.213201i
$89$	−5.06450	+	5.06450i	−0.536835	+	0.536835i	−0.922598	−	0.385763i	$-0.873938\pi$
$89$	−5.06450	+	5.06450i	−0.536835	+	0.536835i	0.385763	+	0.922598i	$0.373938\pi$
$90$	−2.23607	+	2.00000i	−0.235702	+	0.210819i
$91$		0			0
$92$			4.47214i			0.466252i
$93$	−6.86474	+	2.62210i	−0.711840	+	0.271899i
$94$	−2.32456			−0.239760
$95$	−1.64371			−0.168641
$96$	0.618034	+	1.61803i	0.0630778	+	0.165140i
$97$	5.16228	−	5.16228i	0.524150	−	0.524150i	−0.394672	−	0.918822i	$-0.629142\pi$
$97$	5.16228	−	5.16228i	0.524150	−	0.524150i	0.918822	+	0.394672i	$0.129142\pi$
$98$	−4.94975	+	4.94975i	−0.500000	+	0.500000i
$99$	5.99070	+	0.333851i	0.602088	+	0.0335532i
$100$	−1.00000			−0.100000
$101$	−15.7858			−1.57075			−0.785375	−	0.619020i	$-0.787530\pi$
$101$	−15.7858			−1.57075			−0.785375	+	0.619020i	$0.787530\pi$
$102$	−1.01587	−	2.65958i	−0.100586	−	0.263337i
$103$			6.64911i			0.655156i	0.944824	+	0.327578i	$0.106232\pi$
$103$			6.64911i			0.655156i	−0.944824	+	0.327578i	$0.893768\pi$
$104$	2.82843	−	2.23607i	0.277350	−	0.219265i
$105$		0			0
$106$	1.00000	−	1.00000i	0.0971286	−	0.0971286i
$107$			10.3585i			1.00139i	0.865623	+	0.500696i	$0.166923\pi$
$107$			10.3585i			1.00139i	−0.865623	+	0.500696i	$0.833077\pi$
$108$	−4.94975	+	1.58114i	−0.476290	+	0.152145i
$109$	−11.1623	+	11.1623i	−1.06915	+	1.06915i	−0.0717281	+	0.997424i	$0.522851\pi$
$109$	−11.1623	+	11.1623i	−1.06915	+	1.06915i	−0.997424	+	0.0717281i	$0.977149\pi$
$110$	1.41421	+	1.41421i	0.134840	+	0.134840i
$111$	−3.49613	−	9.15298i	−0.331838	−	0.868763i
$112$		0			0
$113$			10.5880i			0.996033i	0.867167	+	0.498017i	$0.165938\pi$
$113$			10.5880i			0.996033i	−0.867167	+	0.498017i	$0.834062\pi$
$114$	−2.59893	−	1.16228i	−0.243412	−	0.108857i
$115$	−3.16228	−	3.16228i	−0.294884	−	0.294884i
$116$	−4.47214			−0.415227
$117$	6.22568	+	8.84539i	0.575564	+	0.817757i
$118$	−4.32456			−0.398108
$119$		0			0
$120$	−1.58114	−	0.707107i	−0.144338	−	0.0645497i
$121$			7.00000i			0.636364i
$122$	10.3585	+	10.3585i	0.937813	+	0.937813i
$123$	−1.95440	−	5.11667i	−0.176222	−	0.461355i
$124$	−3.00000	−	3.00000i	−0.269408	−	0.269408i
$125$	0.707107	−	0.707107i	0.0632456	−	0.0632456i
$126$		0			0
$127$		−	20.9737i		−	1.86111i	−0.366150	−	0.930556i	$-0.619324\pi$
$127$		−	20.9737i		−	1.86111i	0.366150	−	0.930556i	$-0.380676\pi$
$128$	−0.707107	+	0.707107i	−0.0625000	+	0.0625000i
$129$	−0.592359	+	1.32456i	−0.0521543	+	0.116621i
$130$	−0.418861	+	3.58114i	−0.0367366	+	0.314087i
$131$		−	17.4296i		−	1.52283i	−0.648266	−	0.761414i	$-0.724506\pi$
$131$		−	17.4296i		−	1.52283i	0.648266	−	0.761414i	$-0.275494\pi$
$132$	1.23607	+	3.23607i	0.107586	+	0.281664i
$133$		0			0
$134$	−1.18472			−0.102344
$135$	2.38197	−	4.61803i	0.205007	−	0.397457i
$136$	1.16228	−	1.16228i	0.0996645	−	0.0996645i
$137$	−5.42736	+	5.42736i	−0.463691	+	0.463691i	−0.899863	−	0.436173i	$-0.856334\pi$
$137$	−5.42736	+	5.42736i	−0.463691	+	0.463691i	0.436173	+	0.899863i	$0.356334\pi$
$138$	−2.76393	−	7.23607i	−0.235282	−	0.615975i
$139$	−6.32456			−0.536442			−0.268221	−	0.963357i	$-0.586436\pi$
$139$	−6.32456			−0.536442			−0.268221	+	0.963357i	$0.586436\pi$
$140$		0			0
$141$	3.76121	−	1.43665i	0.316751	−	0.120988i
$142$			13.4868i			1.13179i
$143$	5.65685	−	4.47214i	0.473050	−	0.373979i
$144$	−2.00000	−	2.23607i	−0.166667	−	0.186339i
$145$	3.16228	−	3.16228i	0.262613	−	0.262613i
$146$		−	1.64371i		−	0.136034i
$147$	4.94975	−	11.0680i	0.408248	−	0.912871i
$148$	4.00000	−	4.00000i	0.328798	−	0.328798i
$149$	−11.5432	−	11.5432i	−0.945656	−	0.945656i	0.0529415	−	0.998598i	$-0.483140\pi$
$149$	−11.5432	−	11.5432i	−0.945656	−	0.945656i	−0.998598	+	0.0529415i	$0.983140\pi$
$150$	1.61803	−	0.618034i	0.132112	−	0.0504623i
$151$	13.3246	+	13.3246i	1.08434	+	1.08434i	0.996099	+	0.0882375i	$0.0281234\pi$
$151$	13.3246	+	13.3246i	1.08434	+	1.08434i	0.0882375	+	0.996099i	$0.471877\pi$
$152$		−	1.64371i		−	0.133322i
$153$	3.28742	+	3.67544i	0.265772	+	0.297142i
$154$		0			0
$155$	4.24264			0.340777
$156$	−3.19453	+	5.36610i	−0.255767	+	0.429632i
$157$	16.8377			1.34380			0.671898	−	0.740643i	$-0.265479\pi$
$157$	16.8377			1.34380			0.671898	+	0.740643i	$0.265479\pi$
$158$	7.07107	+	7.07107i	0.562544	+	0.562544i
$159$	−1.00000	+	2.23607i	−0.0793052	+	0.177332i
$160$		−	1.00000i		−	0.0790569i
$161$		0			0
$162$	7.03166	−	5.61745i	0.552460	−	0.441348i
$163$	−10.3246	−	10.3246i	−0.808682	−	0.808682i	0.175753	−	0.984434i	$-0.443764\pi$
$163$	−10.3246	−	10.3246i	−0.808682	−	0.808682i	−0.984434	+	0.175753i	$0.943764\pi$
$164$	2.23607	−	2.23607i	0.174608	−	0.174608i
$165$	−3.16228	−	1.41421i	−0.246183	−	0.110096i
$166$		−	8.00000i		−	0.620920i
$167$	7.30056	−	7.30056i	0.564935	−	0.564935i	−0.365771	−	0.930705i	$-0.619195\pi$
$167$	7.30056	−	7.30056i	0.564935	−	0.564935i	0.930705	+	0.365771i	$0.119195\pi$
$168$		0			0
$169$	12.6491	+	3.00000i	0.973009	+	0.230769i
$170$			1.64371i			0.126067i
$171$	4.92349	+	0.274377i	0.376508	+	0.0209821i
$172$	−0.837722			−0.0638757
$173$	−13.6459			−1.03748			−0.518739	−	0.854932i	$-0.673599\pi$
$173$	−13.6459			−1.03748			−0.518739	+	0.854932i	$0.673599\pi$
$174$	7.23607	−	2.76393i	0.548565	−	0.209533i
$175$		0			0
$176$	−1.41421	+	1.41421i	−0.106600	+	0.106600i
$177$	6.99728	−	2.67272i	0.525948	−	0.200894i
$178$	7.16228			0.536835
$179$	17.4296			1.30275			0.651373	−	0.758758i	$-0.274193\pi$
$179$	17.4296			1.30275			0.651373	+	0.758758i	$0.274193\pi$
$180$	2.99535	+	0.166925i	0.223260	+	0.0124419i
$181$			8.32456i			0.618759i	0.950939	+	0.309380i	$0.100121\pi$
$181$			8.32456i			0.618759i	−0.950939	+	0.309380i	$0.899879\pi$
$182$		0			0
$183$	−23.1623	−	10.3585i	−1.71220	−	0.765721i
$184$	3.16228	−	3.16228i	0.233126	−	0.233126i
$185$			5.65685i			0.415900i
$186$	6.70820	+	3.00000i	0.491869	+	0.219971i
$187$	2.32456	−	2.32456i	0.169988	−	0.169988i
$188$	1.64371	+	1.64371i	0.119880	+	0.119880i
$189$		0			0
$190$	1.16228	+	1.16228i	0.0843205	+	0.0843205i
$191$		−	24.7301i		−	1.78941i	−0.446659	−	0.894704i	$-0.647386\pi$
$191$		−	24.7301i		−	1.78941i	0.446659	−	0.894704i	$-0.352614\pi$
$192$	0.707107	−	1.58114i	0.0510310	−	0.114109i
$193$	15.4868	+	15.4868i	1.11477	+	1.11477i	0.992497	+	0.122270i	$0.0390173\pi$
$193$	15.4868	+	15.4868i	1.11477	+	1.11477i	0.122270	+	0.992497i	$0.460983\pi$
$194$	−7.30056			−0.524150
$195$	−1.53553	−	6.05327i	−0.109962	−	0.433484i
$196$	7.00000			0.500000
$197$	−8.94427	−	8.94427i	−0.637253	−	0.637253i	0.312624	−	0.949877i	$-0.398792\pi$
$197$	−8.94427	−	8.94427i	−0.637253	−	0.637253i	−0.949877	+	0.312624i	$0.898792\pi$
$198$	−4.00000	−	4.47214i	−0.284268	−	0.317821i
$199$			2.00000i			0.141776i	0.997484	+	0.0708881i	$0.0225833\pi$
$199$			2.00000i			0.141776i	−0.997484	+	0.0708881i	$0.977417\pi$
$200$	0.707107	+	0.707107i	0.0500000	+	0.0500000i
$201$	1.91691	−	0.732196i	0.135209	−	0.0516451i
$202$	11.1623	+	11.1623i	0.785375	+	0.785375i
$203$		0			0
$204$	−1.16228	+	2.59893i	−0.0813757	+	0.181962i
$205$			3.16228i			0.220863i
$206$	4.70163	−	4.70163i	0.327578	−	0.327578i
$207$	8.94427	+	10.0000i	0.621670	+	0.695048i
$208$	−3.58114	−	0.418861i	−0.248307	−	0.0290428i
$209$		−	3.28742i		−	0.227395i
$210$		0			0
$211$	28.6491			1.97229			0.986143	−	0.165897i	$-0.0530520\pi$
$211$	28.6491			1.97229			0.986143	+	0.165897i	$0.0530520\pi$
$212$	−1.41421			−0.0971286
$213$	−8.33532	−	21.8222i	−0.571127	−	1.49523i
$214$	7.32456	−	7.32456i	0.500696	−	0.500696i
$215$	0.592359	−	0.592359i	0.0403986	−	0.0403986i
$216$	4.61803	+	2.38197i	0.314217	+	0.162072i
$217$		0			0
$218$	15.7858			1.06915
$219$	1.01587	+	2.65958i	0.0686460	+	0.179718i
$220$		−	2.00000i		−	0.134840i
$221$	5.88635	+	0.688486i	0.395959	+	0.0463126i
$222$	−4.00000	+	8.94427i	−0.268462	+	0.600300i
$223$	−8.64911	+	8.64911i	−0.579187	+	0.579187i	−0.934679	−	0.355492i	$-0.884313\pi$
$223$	−8.64911	+	8.64911i	−0.579187	+	0.579187i	0.355492	+	0.934679i	$0.384313\pi$
$224$		0			0
$225$	−2.23607	+	2.00000i	−0.149071	+	0.133333i
$226$	7.48683	−	7.48683i	0.498017	−	0.498017i
$227$	−12.7279	−	12.7279i	−0.844782	−	0.844782i	0.144695	−	0.989476i	$-0.453780\pi$
$227$	−12.7279	−	12.7279i	−0.844782	−	0.844782i	−0.989476	+	0.144695i	$0.953780\pi$
$228$	1.01587	+	2.65958i	0.0672775	+	0.176135i
$229$	17.8114	+	17.8114i	1.17701	+	1.17701i	0.980502	+	0.196507i	$0.0629599\pi$
$229$	17.8114	+	17.8114i	1.17701	+	1.17701i	0.196507	+	0.980502i	$0.437040\pi$
$230$			4.47214i			0.294884i
$231$		0			0
$232$	3.16228	+	3.16228i	0.207614	+	0.207614i
$233$	12.9574			0.848869			0.424434	−	0.905459i	$-0.360473\pi$
$233$	12.9574			0.848869			0.424434	+	0.905459i	$0.360473\pi$
$234$	1.85242	−	10.6569i	0.121096	−	0.696660i
$235$	−2.32456			−0.151637
$236$	3.05792	+	3.05792i	0.199054	+	0.199054i
$237$	−15.8114	−	7.07107i	−1.02706	−	0.459315i
$238$		0			0
$239$	−3.42079	−	3.42079i	−0.221272	−	0.221272i	0.587762	−	0.809034i	$-0.300009\pi$
$239$	−3.42079	−	3.42079i	−0.221272	−	0.221272i	−0.809034	+	0.587762i	$0.800009\pi$
$240$	0.618034	+	1.61803i	0.0398939	+	0.104444i
$241$	−17.6491	−	17.6491i	−1.13688	−	1.13688i	−0.989006	−	0.147873i	$-0.952757\pi$
$241$	−17.6491	−	17.6491i	−1.13688	−	1.13688i	−0.147873	−	0.989006i	$-0.547243\pi$
$242$	4.94975	−	4.94975i	0.318182	−	0.318182i
$243$	−7.90569	+	13.4350i	−0.507151	+	0.861858i
$244$		−	14.6491i		−	0.937813i
$245$	−4.94975	+	4.94975i	−0.316228	+	0.316228i
$246$	−2.23607	+	5.00000i	−0.142566	+	0.318788i
$247$	4.64911	−	3.67544i	0.295816	−	0.233863i
$248$			4.24264i			0.269408i
$249$	4.94427	+	12.9443i	0.313331	+	0.820310i
$250$	−1.00000			−0.0632456
$251$	3.28742			0.207500			0.103750	−	0.994603i	$-0.466916\pi$
$251$	3.28742			0.207500			0.103750	+	0.994603i	$0.466916\pi$
$252$		0			0
$253$	6.32456	−	6.32456i	0.397621	−	0.397621i
$254$	−14.8306	+	14.8306i	−0.930556	+	0.930556i
$255$	−1.01587	−	2.65958i	−0.0636161	−	0.166549i
$256$	1.00000			0.0625000
$257$	−7.30056			−0.455397			−0.227698	−	0.973732i	$-0.573120\pi$
$257$	−7.30056			−0.455397			−0.227698	+	0.973732i	$0.573120\pi$
$258$	1.35546	−	0.517741i	0.0843875	−	0.0322331i
$259$		0			0
$260$	2.82843	−	2.23607i	0.175412	−	0.138675i
$261$	−10.0000	+	8.94427i	−0.618984	+	0.553637i
$262$	−12.3246	+	12.3246i	−0.761414	+	0.761414i
$263$			10.1290i			0.624580i	0.949987	+	0.312290i	$0.101096\pi$
$263$			10.1290i			0.624580i	−0.949987	+	0.312290i	$0.898904\pi$
$264$	1.41421	−	3.16228i	0.0870388	−	0.194625i
$265$	1.00000	−	1.00000i	0.0614295	−	0.0614295i
$266$		0			0
$267$	−11.5888	+	4.42653i	−0.709224	+	0.270899i
$268$	0.837722	+	0.837722i	0.0511720	+	0.0511720i
$269$			4.47214i			0.272671i	0.990663	+	0.136335i	$0.0435325\pi$
$269$			4.47214i			0.272671i	−0.990663	+	0.136335i	$0.956467\pi$
$270$	−4.94975	+	1.58114i	−0.301232	+	0.0962250i
$271$	5.32456	+	5.32456i	0.323444	+	0.323444i	0.850087	−	0.526643i	$-0.176549\pi$
$271$	5.32456	+	5.32456i	0.323444	+	0.323444i	−0.526643	+	0.850087i	$0.676549\pi$
$272$	−1.64371			−0.0996645
$273$		0			0
$274$	7.67544			0.463691
$275$	1.41421	+	1.41421i	0.0852803	+	0.0852803i
$276$	−3.16228	+	7.07107i	−0.190347	+	0.425628i
$277$		−	3.16228i		−	0.190003i	−0.995477	−	0.0950014i	$-0.969714\pi$
$277$		−	3.16228i		−	0.190003i	0.995477	−	0.0950014i	$-0.0302856\pi$
$278$	4.47214	+	4.47214i	0.268221	+	0.268221i
$279$	−12.7082	−	0.708204i	−0.760820	−	0.0423991i
$280$		0			0
$281$	−22.0351	+	22.0351i	−1.31450	+	1.31450i	−0.396441	+	0.918060i	$0.629755\pi$
$281$	−22.0351	+	22.0351i	−1.31450	+	1.31450i	−0.918060	+	0.396441i	$0.870245\pi$
$282$	−3.67544	−	1.64371i	−0.218870	−	0.0978814i
$283$		−	19.1623i		−	1.13908i	−0.821964	−	0.569540i	$-0.807122\pi$
$283$		−	19.1623i		−	1.13908i	0.821964	−	0.569540i	$-0.192878\pi$
$284$	9.53663	−	9.53663i	0.565895	−	0.565895i
$285$	−2.59893	−	1.16228i	−0.153947	−	0.0688474i
$286$	−7.16228	−	0.837722i	−0.423514	−	0.0495356i
$287$		0			0
$288$	−0.166925	+	2.99535i	−0.00983617	+	0.176503i
$289$	−14.2982			−0.841072
$290$	−4.47214			−0.262613
$291$	11.8126	−	4.51200i	0.692464	−	0.264498i
$292$	−1.16228	+	1.16228i	−0.0680172	+	0.0680172i
$293$	−2.82843	+	2.82843i	−0.165238	+	0.165238i	−0.784883	−	0.619644i	$-0.787277\pi$
$293$	−2.82843	+	2.82843i	−0.165238	+	0.165238i	0.619644	+	0.784883i	$0.287277\pi$
$294$	−11.3262	+	4.32624i	−0.660560	+	0.252311i
$295$	−4.32456			−0.251785
$296$	−5.65685			−0.328798
$297$	9.23607	+	4.76393i	0.535931	+	0.276431i
$298$			16.3246i			0.945656i
$299$	16.0153	+	1.87320i	0.926191	+	0.108330i
$300$	−1.58114	−	0.707107i	−0.0912871	−	0.0408248i
$301$		0			0
$302$		−	18.8438i		−	1.08434i
$303$	−24.9596	−	11.1623i	−1.43389	−	0.641256i
$304$	−1.16228	+	1.16228i	−0.0666612	+	0.0666612i
$305$	10.3585	+	10.3585i	0.593125	+	0.593125i
$306$	0.274377	−	4.92349i	0.0156851	−	0.281457i
$307$	0.837722	+	0.837722i	0.0478113	+	0.0478113i	0.730608	−	0.682797i	$-0.239237\pi$
$307$	0.837722	+	0.837722i	0.0478113	+	0.0478113i	−0.682797	+	0.730608i	$0.739237\pi$
$308$		0			0
$309$	−4.70163	+	10.5132i	−0.267466	+	0.598073i
$310$	−3.00000	−	3.00000i	−0.170389	−	0.170389i
$311$	32.4897			1.84232			0.921160	−	0.389184i	$-0.127243\pi$
$311$	32.4897			1.84232			0.921160	+	0.389184i	$0.127243\pi$
$312$	6.05327	−	1.53553i	0.342699	−	0.0869325i
$313$	6.64911			0.375830			0.187915	−	0.982185i	$-0.439827\pi$
$313$	6.64911			0.375830			0.187915	+	0.982185i	$0.439827\pi$
$314$	−11.9061	−	11.9061i	−0.671898	−	0.671898i
$315$		0			0
$316$		−	10.0000i		−	0.562544i
$317$	−17.8885	−	17.8885i	−1.00472	−	1.00472i	−0.999989	−	0.00473191i	$-0.998494\pi$
$317$	−17.8885	−	17.8885i	−1.00472	−	1.00472i	−0.00473191	−	0.999989i	$-0.501506\pi$
$318$	2.28825	−	0.874032i	0.128318	−	0.0490133i
$319$	6.32456	+	6.32456i	0.354107	+	0.354107i
$320$	−0.707107	+	0.707107i	−0.0395285	+	0.0395285i
$321$	−7.32456	+	16.3782i	−0.408817	+	0.914142i
$322$		0			0
$323$	1.91045	−	1.91045i	0.106300	−	0.106300i
$324$	−8.94427	−	1.00000i	−0.496904	−	0.0555556i
$325$	−0.418861	+	3.58114i	−0.0232342	+	0.198646i
$326$			14.6011i			0.808682i
$327$	−25.5420	+	9.75619i	−1.41248	+	0.539518i
$328$	−3.16228			−0.174608
$329$		0			0
$330$	1.23607	+	3.23607i	0.0680433	+	0.178140i
$331$	9.48683	−	9.48683i	0.521443	−	0.521443i	−0.396564	−	0.918007i	$-0.629797\pi$
$331$	9.48683	−	9.48683i	0.521443	−	0.521443i	0.918007	+	0.396564i	$0.129797\pi$
$332$	−5.65685	+	5.65685i	−0.310460	+	0.310460i
$333$	0.944272	−	16.9443i	0.0517458	−	0.928540i
$334$	−10.3246			−0.564935
$335$	−1.18472			−0.0647281
$336$		0			0
$337$		−	5.35089i		−	0.291482i	−0.989323	−	0.145741i	$-0.953443\pi$
$337$		−	5.35089i		−	0.291482i	0.989323	−	0.145741i	$-0.0465565\pi$
$338$	−6.82295	−	11.0656i	−0.371120	−	0.601889i
$339$	−7.48683	+	16.7411i	−0.406629	+	0.909250i
$340$	1.16228	−	1.16228i	0.0630334	−	0.0630334i
$341$			8.48528i			0.459504i
$342$	−3.28742	−	3.67544i	−0.177763	−	0.198745i
$343$		0			0
$344$	0.592359	+	0.592359i	0.0319379	+	0.0319379i
$345$	−2.76393	−	7.23607i	−0.148805	−	0.389577i
$346$	9.64911	+	9.64911i	0.518739	+	0.518739i
$347$		−	10.3585i		−	0.556073i	−0.960571	−	0.278036i	$-0.910316\pi$
$347$		−	10.3585i		−	0.556073i	0.960571	−	0.278036i	$-0.0896836\pi$
$348$	−7.07107	−	3.16228i	−0.379049	−	0.169516i
$349$	−7.16228	−	7.16228i	−0.383388	−	0.383388i	0.488933	−	0.872321i	$-0.337386\pi$
$349$	−7.16228	−	7.16228i	−0.383388	−	0.383388i	−0.872321	+	0.488933i	$0.837386\pi$
$350$		0			0
$351$	3.58902	+	18.3880i	0.191568	+	0.981479i
$352$	2.00000			0.106600
$353$	17.6590	+	17.6590i	0.939896	+	0.939896i	0.998293	−	0.0583971i	$-0.0185990\pi$
$353$	17.6590	+	17.6590i	0.939896	+	0.939896i	−0.0583971	+	0.998293i	$0.518599\pi$
$354$	−6.83772	−	3.05792i	−0.363421	−	0.162527i
$355$			13.4868i			0.715807i
$356$	−5.06450	−	5.06450i	−0.268418	−	0.268418i
$357$		0			0
$358$	−12.3246	−	12.3246i	−0.651373	−	0.651373i
$359$	0.133369	−	0.133369i	0.00703893	−	0.00703893i	−0.703579	−	0.710617i	$-0.748416\pi$
$359$	0.133369	−	0.133369i	0.00703893	−	0.00703893i	0.710617	+	0.703579i	$0.248416\pi$
$360$	−2.00000	−	2.23607i	−0.105409	−	0.117851i
$361$			16.2982i			0.857801i
$362$	5.88635	−	5.88635i	0.309380	−	0.309380i
$363$	−4.94975	+	11.0680i	−0.259794	+	0.580918i
$364$		0			0
$365$		−	1.64371i		−	0.0860357i
$366$	9.05365	+	23.7028i	0.473242	+	1.23896i
$367$	−6.64911			−0.347081			−0.173540	−	0.984827i	$-0.555521\pi$
$367$	−6.64911			−0.347081			−0.173540	+	0.984827i	$0.555521\pi$
$368$	−4.47214			−0.233126
$369$	0.527864	−	9.47214i	0.0274795	−	0.493100i
$370$	4.00000	−	4.00000i	0.207950	−	0.207950i
$371$		0			0
$372$	−2.62210	−	6.86474i	−0.135949	−	0.355920i
$373$	8.83772			0.457600			0.228800	−	0.973473i	$-0.426520\pi$
$373$	8.83772			0.457600			0.228800	+	0.973473i	$0.426520\pi$
$374$	−3.28742			−0.169988
$375$	1.61803	−	0.618034i	0.0835549	−	0.0319151i
$376$		−	2.32456i		−	0.119880i
$377$	−1.87320	+	16.0153i	−0.0964749	+	0.824832i
$378$		0			0
$379$	−6.83772	+	6.83772i	−0.351230	+	0.351230i	−0.860567	−	0.509337i	$-0.829891\pi$
$379$	−6.83772	+	6.83772i	−0.351230	+	0.351230i	0.509337	+	0.860567i	$0.329891\pi$
$380$		−	1.64371i		−	0.0843205i
$381$	14.8306	−	33.1623i	0.759796	−	1.69895i
$382$	−17.4868	+	17.4868i	−0.894704	+	0.894704i
$383$	21.9017	+	21.9017i	1.11912	+	1.11912i	0.991870	+	0.127254i	$0.0406163\pi$
$383$	21.9017	+	21.9017i	1.11912	+	1.11912i	0.127254	+	0.991870i	$0.459384\pi$
$384$	−1.61803	+	0.618034i	−0.0825700	+	0.0315389i
$385$		0			0
$386$		−	21.9017i		−	1.11477i
$387$	−1.87320	+	1.67544i	−0.0952203	+	0.0851676i
$388$	5.16228	+	5.16228i	0.262075	+	0.262075i
$389$	20.9837			1.06392			0.531958	−	0.846771i	$-0.321456\pi$
$389$	20.9837			1.06392			0.531958	+	0.846771i	$0.321456\pi$
$390$	−3.19453	+	5.36610i	−0.161761	+	0.271723i
$391$	7.35089			0.371750
$392$	−4.94975	−	4.94975i	−0.250000	−	0.250000i
$393$	12.3246	−	27.5585i	0.621692	−	1.39014i
$394$			12.6491i			0.637253i
$395$	7.07107	+	7.07107i	0.355784	+	0.355784i
$396$	−0.333851	+	5.99070i	−0.0167766	+	0.301044i
$397$	−19.1623	−	19.1623i	−0.961727	−	0.961727i	0.0375670	−	0.999294i	$-0.488039\pi$
$397$	−19.1623	−	19.1623i	−0.961727	−	0.961727i	−0.999294	+	0.0375670i	$0.988039\pi$
$398$	1.41421	−	1.41421i	0.0708881	−	0.0708881i
$399$		0			0
$400$		−	1.00000i		−	0.0500000i
$401$	−1.77708	+	1.77708i	−0.0887430	+	0.0887430i	−0.750085	−	0.661342i	$-0.769987\pi$
$401$	−1.77708	+	1.77708i	−0.0887430	+	0.0887430i	0.661342	+	0.750085i	$0.269987\pi$
$402$	−1.87320	−	0.837722i	−0.0934269	−	0.0417818i
$403$	−12.0000	+	9.48683i	−0.597763	+	0.472573i
$404$		−	15.7858i		−	0.785375i
$405$	7.03166	−	5.61745i	0.349406	−	0.279133i
$406$		0			0
$407$	−11.3137			−0.560800
$408$	2.65958	−	1.01587i	0.131669	−	0.0502930i
$409$	23.3246	−	23.3246i	1.15333	−	1.15333i	0.167443	−	0.985882i	$-0.446449\pi$
$409$	23.3246	−	23.3246i	1.15333	−	1.15333i	0.985882	−	0.167443i	$-0.0535511\pi$
$410$	2.23607	−	2.23607i	0.110432	−	0.110432i
$411$	−12.4191	+	4.74369i	−0.612591	+	0.233989i
$412$	−6.64911			−0.327578
$413$		0			0
$414$	0.746512	−	13.3956i	0.0366891	−	0.658359i
$415$		−	8.00000i		−	0.392705i
$416$	2.23607	+	2.82843i	0.109632	+	0.138675i
$417$	−10.0000	−	4.47214i	−0.489702	−	0.219001i
$418$	−2.32456	+	2.32456i	−0.113698	+	0.113698i
$419$			4.73887i			0.231509i	0.993278	+	0.115755i	$0.0369286\pi$
$419$			4.73887i			0.231509i	−0.993278	+	0.115755i	$0.963071\pi$
$420$		0			0
$421$	−19.1623	+	19.1623i	−0.933912	+	0.933912i	−0.997948	−	0.0640354i	$-0.979603\pi$
$421$	−19.1623	+	19.1623i	−0.933912	+	0.933912i	0.0640354	+	0.997948i	$0.479603\pi$
$422$	−20.2580	−	20.2580i	−0.986143	−	0.986143i
$423$	6.96286	+	0.388027i	0.338546	+	0.0188665i
$424$	1.00000	+	1.00000i	0.0485643	+	0.0485643i
$425$			1.64371i			0.0797316i
$426$	−9.53663	+	21.3246i	−0.462051	+	1.03318i
$427$		0			0
$428$	−10.3585			−0.500696
$429$	12.1065	−	3.07107i	0.584510	−	0.148273i
$430$	−0.837722			−0.0403986
$431$	15.1935	+	15.1935i	0.731844	+	0.731844i	0.970985	−	0.239141i	$-0.0768657\pi$
$431$	15.1935	+	15.1935i	0.731844	+	0.731844i	−0.239141	+	0.970985i	$0.576866\pi$
$432$	−1.58114	−	4.94975i	−0.0760726	−	0.238145i
$433$		−	11.2982i		−	0.542958i	−0.962444	−	0.271479i	$-0.912487\pi$
$433$		−	11.2982i		−	0.542958i	0.962444	−	0.271479i	$-0.0875127\pi$
$434$		0			0
$435$	7.23607	−	2.76393i	0.346943	−	0.132520i
$436$	−11.1623	−	11.1623i	−0.534576	−	0.534576i
$437$	5.19786	−	5.19786i	0.248648	−	0.248648i
$438$	1.16228	−	2.59893i	0.0555358	−	0.124182i
$439$		−	28.6491i		−	1.36735i	−0.729788	−	0.683674i	$-0.760381\pi$
$439$		−	28.6491i		−	1.36735i	0.729788	−	0.683674i	$-0.239619\pi$
$440$	−1.41421	+	1.41421i	−0.0674200	+	0.0674200i
$441$	15.6525	−	14.0000i	0.745356	−	0.666667i
$442$	−3.67544	−	4.64911i	−0.174823	−	0.221136i
$443$		−	7.53006i		−	0.357764i	−0.983871	−	0.178882i	$-0.942752\pi$
$443$		−	7.53006i		−	0.357764i	0.983871	−	0.178882i	$-0.0572480\pi$
$444$	9.15298	−	3.49613i	0.434381	−	0.165919i
$445$	7.16228			0.339525
$446$	12.2317			0.579187
$447$	−10.0891	−	26.4137i	−0.477199	−	1.24932i
$448$		0			0
$449$	8.35191	−	8.35191i	0.394151	−	0.394151i	−0.482013	−	0.876164i	$-0.660094\pi$
$449$	8.35191	−	8.35191i	0.394151	−	0.394151i	0.876164	+	0.482013i	$0.160094\pi$
$450$	2.99535	+	0.166925i	0.141202	+	0.00786893i
$451$	−6.32456			−0.297812
$452$	−10.5880			−0.498017
$453$	11.6461	+	30.4899i	0.547181	+	1.43254i
$454$			18.0000i			0.844782i
$455$		0			0
$456$	1.16228	−	2.59893i	0.0544286	−	0.121706i
$457$	−15.4868	+	15.4868i	−0.724443	+	0.724443i	−0.969507	−	0.245064i	$-0.921191\pi$
$457$	−15.4868	+	15.4868i	−0.724443	+	0.724443i	0.245064	+	0.969507i	$0.421191\pi$
$458$		−	25.1891i		−	1.17701i
$459$	2.59893	+	8.13594i	0.121308	+	0.379753i
$460$	3.16228	−	3.16228i	0.147442	−	0.147442i
$461$	3.78365	+	3.78365i	0.176222	+	0.176222i	0.789707	−	0.613485i	$-0.210233\pi$
$461$	3.78365	+	3.78365i	0.176222	+	0.176222i	−0.613485	+	0.789707i	$0.710233\pi$
$462$		0			0
$463$	−4.32456	−	4.32456i	−0.200979	−	0.200979i	0.599440	−	0.800419i	$-0.295390\pi$
$463$	−4.32456	−	4.32456i	−0.200979	−	0.200979i	−0.800419	+	0.599440i	$0.795390\pi$
$464$		−	4.47214i		−	0.207614i
$465$	6.70820	+	3.00000i	0.311086	+	0.139122i
$466$	−9.16228	−	9.16228i	−0.424434	−	0.424434i
$467$	19.7617			0.914465			0.457232	−	0.889347i	$-0.348841\pi$
$467$	19.7617			0.914465			0.457232	+	0.889347i	$0.348841\pi$
$468$	−8.84539	+	6.22568i	−0.408878	+	0.287782i
$469$		0			0
$470$	1.64371	+	1.64371i	0.0758186	+	0.0758186i
$471$	26.6228	+	11.9061i	1.22671	+	0.548603i
$472$		−	4.32456i		−	0.199054i
$473$	1.18472	+	1.18472i	0.0544734	+	0.0544734i
$474$	6.18034	+	16.1803i	0.283872	+	0.743188i
$475$	1.16228	+	1.16228i	0.0533290	+	0.0533290i
$476$		0			0
$477$	−3.16228	+	2.82843i	−0.144791	+	0.129505i
$478$			4.83772i			0.221272i
$479$	−22.4940	+	22.4940i	−1.02778	+	1.02778i	−0.0281763	+	0.999603i	$0.508970\pi$
$479$	−22.4940	+	22.4940i	−1.02778	+	1.02778i	−0.999603	+	0.0281763i	$0.991030\pi$
$480$	0.707107	−	1.58114i	0.0322749	−	0.0721688i
$481$	−12.6491	−	16.0000i	−0.576750	−	0.729537i
$482$			24.9596i			1.13688i
$483$		0			0
$484$	−7.00000			−0.318182
$485$	−7.30056			−0.331501
$486$	15.0902	−	3.90983i	0.684504	−	0.177353i
$487$	−18.0000	+	18.0000i	−0.815658	+	0.815658i	−0.985476	−	0.169818i	$-0.945682\pi$
$487$	−18.0000	+	18.0000i	−0.815658	+	0.815658i	0.169818	+	0.985476i	$0.445682\pi$
$488$	−10.3585	+	10.3585i	−0.468907	+	0.468907i
$489$	−9.02399	−	23.6251i	−0.408079	−	1.06836i
$490$	7.00000			0.316228
$491$	−28.2843			−1.27645			−0.638226	−	0.769849i	$-0.720331\pi$
$491$	−28.2843			−1.27645			−0.638226	+	0.769849i	$0.720331\pi$
$492$	5.11667	−	1.95440i	0.230677	−	0.0881109i
$493$			7.35089i			0.331067i
$494$	−5.88635	−	0.688486i	−0.264839	−	0.0309764i
$495$	−4.00000	−	4.47214i	−0.179787	−	0.201008i
$496$	3.00000	−	3.00000i	0.134704	−	0.134704i
$497$		0			0
$498$	5.65685	−	12.6491i	0.253490	−	0.566820i
$499$	−4.83772	+	4.83772i	−0.216566	+	0.216566i	−0.807050	−	0.590484i	$-0.798937\pi$
$499$	−4.83772	+	4.83772i	−0.216566	+	0.216566i	0.590484	+	0.807050i	$0.298937\pi$
$500$	0.707107	+	0.707107i	0.0316228	+	0.0316228i
$501$	16.7055	−	6.38093i	0.746346	−	0.285079i
$502$	−2.32456	−	2.32456i	−0.103750	−	0.103750i
$503$			19.5323i			0.870900i	0.900213	+	0.435450i	$0.143411\pi$
$503$			19.5323i			0.870900i	−0.900213	+	0.435450i	$0.856589\pi$
$504$		0			0
$505$	11.1623	+	11.1623i	0.496715	+	0.496715i
$506$	−8.94427			−0.397621
$507$	17.8787	+	13.6877i	0.794020	+	0.607892i
$508$	20.9737			0.930556
$509$	−5.42736	−	5.42736i	−0.240563	−	0.240563i	0.576520	−	0.817083i	$-0.304410\pi$
$509$	−5.42736	−	5.42736i	−0.240563	−	0.240563i	−0.817083	+	0.576520i	$0.804410\pi$
$510$	−1.16228	+	2.59893i	−0.0514665	+	0.115083i
$511$		0			0
$512$	−0.707107	−	0.707107i	−0.0312500	−	0.0312500i
$513$	7.59070	+	3.91526i	0.335138	+	0.172863i
$514$	5.16228	+	5.16228i	0.227698	+	0.227698i
$515$	4.70163	−	4.70163i	0.207179	−	0.207179i
$516$	−1.32456	−	0.592359i	−0.0583103	−	0.0260772i
$517$		−	4.64911i		−	0.204468i
$518$		0			0
$519$	−21.5761	−	9.64911i	−0.947084	−	0.423549i
$520$	−3.58114	−	0.418861i	−0.157043	−	0.0183683i
$521$			24.7301i			1.08345i	0.840557	+	0.541723i	$0.182228\pi$
$521$			24.7301i			1.08345i	−0.840557	+	0.541723i	$0.817772\pi$
$522$	13.3956	+	0.746512i	0.586310	+	0.0326740i
$523$	−4.18861			−0.183155			−0.0915776	−	0.995798i	$-0.529191\pi$
$523$	−4.18861			−0.183155			−0.0915776	+	0.995798i	$0.529191\pi$
$524$	17.4296			0.761414
$525$		0			0
$526$	7.16228	−	7.16228i	0.312290	−	0.312290i
$527$	−4.93113	+	4.93113i	−0.214803	+	0.214803i
$528$	−3.23607	+	1.23607i	−0.140832	+	0.0537930i
$529$	−3.00000			−0.130435
$530$	−1.41421			−0.0614295
$531$	12.9536	+	0.721878i	0.562137	+	0.0313268i
$532$		0			0
$533$	−7.07107	−	8.94427i	−0.306282	−	0.387419i
$534$	11.3246	+	5.06450i	0.490061	+	0.219162i
$535$	7.32456	−	7.32456i	0.316668	−	0.316668i
$536$		−	1.18472i		−	0.0511720i
$537$	27.5585	+	12.3246i	1.18924	+	0.531844i
$538$	3.16228	−	3.16228i	0.136335	−	0.136335i
$539$	−9.89949	−	9.89949i	−0.426401	−	0.426401i
$540$	4.61803	+	2.38197i	0.198729	+	0.102503i
$541$	−1.81139	−	1.81139i	−0.0778777	−	0.0778777i	0.667095	−	0.744973i	$-0.267538\pi$
$541$	−1.81139	−	1.81139i	−0.0778777	−	0.0778777i	−0.744973	+	0.667095i	$0.767538\pi$
$542$		−	7.53006i		−	0.323444i
$543$	−5.88635	+	13.1623i	−0.252607	+	0.564847i
$544$	1.16228	+	1.16228i	0.0498322	+	0.0498322i
$545$	15.7858			0.676191
$546$		0			0
$547$	9.48683			0.405628			0.202814	−	0.979217i	$-0.434991\pi$
$547$	9.48683			0.405628			0.202814	+	0.979217i	$0.434991\pi$
$548$	−5.42736	−	5.42736i	−0.231845	−	0.231845i
$549$	−29.2982	−	32.7564i	−1.25042	−	1.39801i
$550$		−	2.00000i		−	0.0852803i
$551$	5.19786	+	5.19786i	0.221436	+	0.221436i
$552$	7.23607	−	2.76393i	0.307988	−	0.117641i
$553$		0			0
$554$	−2.23607	+	2.23607i	−0.0950014	+	0.0950014i
$555$	−4.00000	+	8.94427i	−0.169791	+	0.379663i
$556$		−	6.32456i		−	0.268221i
$557$	−6.11584	+	6.11584i	−0.259137	+	0.259137i	−0.824703	−	0.565566i	$-0.808658\pi$
$557$	−6.11584	+	6.11584i	−0.259137	+	0.259137i	0.565566	+	0.824703i	$0.308658\pi$
$558$	8.48528	+	9.48683i	0.359211	+	0.401610i
$559$	−0.350889	+	3.00000i	−0.0148410	+	0.126886i
$560$		0			0
$561$	5.31915	−	2.03174i	0.224575	−	0.0857800i
$562$	31.1623			1.31450
$563$	−42.3892			−1.78649			−0.893245	−	0.449570i	$-0.851577\pi$
$563$	−42.3892			−1.78649			−0.893245	+	0.449570i	$0.851577\pi$
$564$	1.43665	+	3.76121i	0.0604941	+	0.158375i
$565$	7.48683	−	7.48683i	0.314973	−	0.314973i
$566$	−13.5498	+	13.5498i	−0.569540	+	0.569540i
$567$		0			0
$568$	−13.4868			−0.565895
$569$	−24.7301			−1.03674			−0.518370	−	0.855156i	$-0.673461\pi$
$569$	−24.7301			−1.03674			−0.518370	+	0.855156i	$0.673461\pi$
$570$	1.01587	+	2.65958i	0.0425500	+	0.111397i
$571$			18.9737i			0.794023i	0.917814	+	0.397012i	$0.129953\pi$
$571$			18.9737i			0.794023i	−0.917814	+	0.397012i	$0.870047\pi$
$572$	4.47214	+	5.65685i	0.186989	+	0.236525i
$573$	17.4868	−	39.1017i	0.730523	−	1.63350i
$574$		0			0
$575$			4.47214i			0.186501i
$576$	2.23607	−	2.00000i	0.0931695	−	0.0833333i
$577$	−14.8377	+	14.8377i	−0.617702	+	0.617702i	−0.944942	−	0.327239i	$-0.893882\pi$
$577$	−14.8377	+	14.8377i	−0.617702	+	0.617702i	0.327239	+	0.944942i	$0.393882\pi$
$578$	10.1104	+	10.1104i	0.420536	+	0.420536i
$579$	13.5360	+	35.4377i	0.562536	+	1.47274i
$580$	3.16228	+	3.16228i	0.131306	+	0.131306i
$581$		0			0
$582$	−11.5432	−	5.16228i	−0.478481	−	0.213983i
$583$	2.00000	+	2.00000i	0.0828315	+	0.0828315i
$584$	1.64371			0.0680172
$585$	1.85242	−	10.6569i	0.0765881	−	0.440607i
$586$	4.00000			0.165238
$587$	−17.4296	−	17.4296i	−0.719395	−	0.719395i	0.249087	−	0.968481i	$-0.419870\pi$
$587$	−17.4296	−	17.4296i	−0.719395	−	0.719395i	−0.968481	+	0.249087i	$0.919870\pi$
$588$	11.0680	+	4.94975i	0.456435	+	0.204124i
$589$			6.97367i			0.287345i
$590$	3.05792	+	3.05792i	0.125893	+	0.125893i
$591$	−7.81758	−	20.4667i	−0.321572	−	0.841887i
$592$	4.00000	+	4.00000i	0.164399	+	0.164399i
$593$	22.5902	−	22.5902i	0.927667	−	0.927667i	−0.0698876	−	0.997555i	$-0.522264\pi$
$593$	22.5902	−	22.5902i	0.927667	−	0.927667i	0.997555	+	0.0698876i	$0.0222641\pi$
$594$	−3.16228	−	9.89949i	−0.129750	−	0.406181i
$595$		0			0
$596$	11.5432	−	11.5432i	0.472828	−	0.472828i
$597$	−1.41421	+	3.16228i	−0.0578799	+	0.129423i
$598$	−10.0000	−	12.6491i	−0.408930	−	0.517261i
$599$		−	14.8679i		−	0.607484i	−0.952754	−	0.303742i	$-0.901764\pi$
$599$		−	14.8679i		−	0.607484i	0.952754	−	0.303742i	$-0.0982362\pi$
$600$	0.618034	+	1.61803i	0.0252311	+	0.0660560i
$601$	0.649111			0.0264778			0.0132389	−	0.999912i	$-0.495786\pi$
$601$	0.649111			0.0264778			0.0132389	+	0.999912i	$0.495786\pi$
$602$		0			0
$603$	3.54865	+	0.197759i	0.144512	+	0.00805339i
$604$	−13.3246	+	13.3246i	−0.542168	+	0.542168i
$605$	4.94975	−	4.94975i	0.201236	−	0.201236i
$606$	9.75619	+	25.5420i	0.396318	+	1.03757i
$607$	41.6228			1.68942			0.844708	−	0.535227i	$-0.179774\pi$
$607$	41.6228			1.68942			0.844708	+	0.535227i	$0.179774\pi$
$608$	1.64371			0.0666612
$609$		0			0
$610$		−	14.6491i		−	0.593125i
$611$	6.57484	−	5.19786i	0.265989	−	0.210283i
$612$	−3.67544	+	3.28742i	−0.148571	+	0.132886i
$613$	−9.67544	+	9.67544i	−0.390788	+	0.390788i	−0.874968	−	0.484181i	$-0.839118\pi$
$613$	−9.67544	+	9.67544i	−0.390788	+	0.390788i	0.484181	+	0.874968i	$0.339118\pi$
$614$		−	1.18472i		−	0.0478113i
$615$	−2.23607	+	5.00000i	−0.0901670	+	0.201619i
$616$		0			0
$617$	18.3848	+	18.3848i	0.740143	+	0.740143i	0.972605	−	0.232462i	$-0.0746782\pi$
$617$	18.3848	+	18.3848i	0.740143	+	0.740143i	−0.232462	+	0.972605i	$0.574678\pi$
$618$	10.7585	−	4.10938i	0.432770	−	0.165303i
$619$	10.5132	+	10.5132i	0.422560	+	0.422560i	0.886084	−	0.463524i	$-0.153415\pi$
$619$	10.5132	+	10.5132i	0.422560	+	0.422560i	−0.463524	+	0.886084i	$0.653415\pi$
$620$			4.24264i			0.170389i
$621$	7.07107	+	22.1359i	0.283752	+	0.888285i
$622$	−22.9737	−	22.9737i	−0.921160	−	0.921160i
$623$		0			0
$624$	−5.36610	−	3.19453i	−0.214816	−	0.127883i
$625$	−1.00000			−0.0400000
$626$	−4.70163	−	4.70163i	−0.187915	−	0.187915i
$627$	2.32456	−	5.19786i	0.0928338	−	0.207583i
$628$			16.8377i			0.671898i
$629$	−6.57484	−	6.57484i	−0.262156	−	0.262156i
$630$		0			0
$631$	0.675445	+	0.675445i	0.0268890	+	0.0268890i	0.720423	−	0.693534i	$-0.243947\pi$
$631$	0.675445	+	0.675445i	0.0268890	+	0.0268890i	−0.693534	+	0.720423i	$0.743947\pi$
$632$	−7.07107	+	7.07107i	−0.281272	+	0.281272i
$633$	45.2982	+	20.2580i	1.80044	+	0.805182i
$634$			25.2982i			1.00472i
$635$	−14.8306	+	14.8306i	−0.588535	+	0.588535i
$636$	−2.23607	−	1.00000i	−0.0886659	−	0.0396526i
$637$	2.93203	−	25.0680i	0.116171	−	0.993229i
$638$		−	8.94427i		−	0.354107i
$639$	2.25129	−	40.3978i	0.0890598	−	1.59811i
$640$	1.00000			0.0395285
$641$	35.7771			1.41311			0.706555	−	0.707658i	$-0.250248\pi$
$641$	35.7771			1.41311			0.706555	+	0.707658i	$0.250248\pi$
$642$	16.7604	−	6.40190i	0.661479	−	0.252663i
$643$	7.35089	−	7.35089i	0.289891	−	0.289891i	−0.547146	−	0.837037i	$-0.684286\pi$
$643$	7.35089	−	7.35089i	0.289891	−	0.289891i	0.837037	+	0.547146i	$0.184286\pi$
$644$		0			0
$645$	1.35546	−	0.517741i	0.0533713	−	0.0203860i
$646$	−2.70178			−0.106300
$647$	37.9543			1.49214			0.746068	−	0.665870i	$-0.231939\pi$
$647$	37.9543			1.49214			0.746068	+	0.665870i	$0.231939\pi$
$648$	5.61745	+	7.03166i	0.220674	+	0.276230i
$649$		−	8.64911i		−	0.339507i
$650$	2.82843	−	2.23607i	0.110940	−	0.0877058i
$651$		0			0
$652$	10.3246	−	10.3246i	0.404341	−	0.404341i
$653$		−	48.0460i		−	1.88019i	−0.340918	−	0.940093i	$-0.610738\pi$
$653$		−	48.0460i		−	1.88019i	0.340918	−	0.940093i	$-0.389262\pi$
$654$	24.9596	+	11.1623i	0.975998	+	0.436480i
$655$	−12.3246	+	12.3246i	−0.481560	+	0.481560i
$656$	2.23607	+	2.23607i	0.0873038	+	0.0873038i
$657$	−0.274377	+	4.92349i	−0.0107044	+	0.192084i
$658$		0			0
$659$		−	8.94427i		−	0.348419i	−0.984709	−	0.174210i	$-0.944263\pi$
$659$		−	8.94427i		−	0.348419i	0.984709	−	0.174210i	$-0.0557371\pi$
$660$	1.41421	−	3.16228i	0.0550482	−	0.123091i
$661$	−17.1623	−	17.1623i	−0.667535	−	0.667535i	0.289610	−	0.957145i	$-0.406475\pi$
$661$	−17.1623	−	17.1623i	−0.667535	−	0.667535i	−0.957145	+	0.289610i	$0.906475\pi$
$662$	−13.4164			−0.521443
$663$	8.82030	+	5.25087i	0.342552	+	0.203927i
$664$	8.00000			0.310460
$665$		0			0
$666$	−12.6491	+	11.3137i	−0.490143	+	0.438397i
$667$			20.0000i			0.774403i
$668$	7.30056	+	7.30056i	0.282467	+	0.282467i
$669$	−19.7913	+	7.55960i	−0.765175	+	0.292271i
$670$	0.837722	+	0.837722i	0.0323640	+	0.0323640i
$671$	−20.7170	+	20.7170i	−0.799770	+	0.799770i
$672$		0			0
$673$		−	32.3246i		−	1.24602i	−0.782214	−	0.623010i	$-0.785910\pi$
$673$		−	32.3246i		−	1.24602i	0.782214	−	0.623010i	$-0.214090\pi$
$674$	−3.78365	+	3.78365i	−0.145741	+	0.145741i
$675$	−4.94975	+	1.58114i	−0.190516	+	0.0608581i
$676$	−3.00000	+	12.6491i	−0.115385	+	0.486504i
$677$		−	13.1869i		−	0.506814i	−0.967360	−	0.253407i	$-0.918449\pi$
$677$		−	13.1869i		−	0.506814i	0.967360	−	0.253407i	$-0.0815512\pi$
$678$	17.1317	−	6.54373i	0.657939	−	0.251311i
$679$		0			0
$680$	−1.64371			−0.0630334
$681$	−11.1246	−	29.1246i	−0.426296	−	1.11606i
$682$	6.00000	−	6.00000i	0.229752	−	0.229752i
$683$	−4.24264	+	4.24264i	−0.162340	+	0.162340i	−0.783603	−	0.621262i	$-0.786620\pi$
$683$	−4.24264	+	4.24264i	−0.162340	+	0.162340i	0.621262	+	0.783603i	$0.286620\pi$
$684$	−0.274377	+	4.92349i	−0.0104910	+	0.188254i
$685$	7.67544			0.293264
$686$		0			0
$687$	15.5677	+	40.7568i	0.593946	+	1.55497i
$688$		−	0.837722i		−	0.0319379i
$689$	−0.592359	+	5.06450i	−0.0225671	+	0.192942i
$690$	−3.16228	+	7.07107i	−0.120386	+	0.269191i
$691$	−4.18861	+	4.18861i	−0.159342	+	0.159342i	−0.782275	−	0.622933i	$-0.785941\pi$
$691$	−4.18861	+	4.18861i	−0.159342	+	0.159342i	0.622933	+	0.782275i	$0.285941\pi$
$692$		−	13.6459i		−	0.518739i
$693$		0			0
$694$	−7.32456	+	7.32456i	−0.278036	+	0.278036i
$695$	4.47214	+	4.47214i	0.169638	+	0.169638i
$696$	2.76393	+	7.23607i	0.104767	+	0.274282i
$697$	−3.67544	−	3.67544i	−0.139217	−	0.139217i
$698$			10.1290i			0.383388i
$699$	20.4875	+	9.16228i	0.774907	+	0.346549i
$700$		0			0
$701$	−5.39012			−0.203582			−0.101791	−	0.994806i	$-0.532457\pi$
$701$	−5.39012			−0.203582			−0.101791	+	0.994806i	$0.532457\pi$
$702$	10.4645	−	15.5401i	0.394956	−	0.586524i
$703$	−9.29822			−0.350689
$704$	−1.41421	−	1.41421i	−0.0533002	−	0.0533002i
$705$	−3.67544	−	1.64371i	−0.138425	−	0.0619057i
$706$		−	24.9737i		−	0.939896i
$707$		0			0
$708$	2.67272	+	6.99728i	0.100447	+	0.262974i
$709$	3.48683	+	3.48683i	0.130951	+	0.130951i	0.769544	−	0.638593i	$-0.220483\pi$
$709$	3.48683	+	3.48683i	0.130951	+	0.130951i	−0.638593	+	0.769544i	$0.720483\pi$
$710$	9.53663	−	9.53663i	0.357903	−	0.357903i
$711$	−20.0000	−	22.3607i	−0.750059	−	0.838591i
$712$			7.16228i			0.268418i
$713$	−13.4164	+	13.4164i	−0.502448	+	0.502448i
$714$		0			0
$715$	−7.16228	−	0.837722i	−0.267854	−	0.0313290i
$716$			17.4296i			0.651373i
$717$	−2.98988	−	7.82760i	−0.111659	−	0.292327i
$718$	−0.188612			−0.00703893
$719$	−24.7301			−0.922278			−0.461139	−	0.887328i	$-0.652559\pi$
$719$	−24.7301			−0.922278			−0.461139	+	0.887328i	$0.652559\pi$
$720$	−0.166925	+	2.99535i	−0.00622094	+	0.111630i
$721$		0			0
$722$	11.5246	−	11.5246i	0.428901	−	0.428901i
$723$	−15.4259	−	40.3855i	−0.573695	−	1.50195i
$724$	−8.32456			−0.309380
$725$	−4.47214			−0.166091
$726$	11.3262	−	4.32624i	0.420356	−	0.160562i
$727$		−	32.9737i		−	1.22293i	−0.791273	−	0.611463i	$-0.790581\pi$
$727$		−	32.9737i		−	1.22293i	0.791273	−	0.611463i	$-0.209419\pi$
$728$		0			0
$729$	−22.0000	+	15.6525i	−0.814815	+	0.579721i
$730$	−1.16228	+	1.16228i	−0.0430178	+	0.0430178i
$731$			1.37697i			0.0509291i
$732$	10.3585	−	23.1623i	0.382861	−	0.856102i
$733$	−14.5132	+	14.5132i	−0.536056	+	0.536056i	−0.922368	−	0.386312i	$-0.873749\pi$
$733$	−14.5132	+	14.5132i	−0.536056	+	0.536056i	0.386312	+	0.922368i	$0.373749\pi$
$734$	4.70163	+	4.70163i	0.173540	+	0.173540i
$735$	−11.3262	+	4.32624i	−0.417775	+	0.159576i
$736$	3.16228	+	3.16228i	0.116563	+	0.116563i
$737$		−	2.36944i		−	0.0872793i
$738$	−7.07107	+	6.32456i	−0.260290	+	0.232810i
$739$	−32.1359	−	32.1359i	−1.18214	−	1.18214i	−0.979189	−	0.202951i	$-0.934947\pi$
$739$	−32.1359	−	32.1359i	−1.18214	−	1.18214i	−0.202951	−	0.979189i	$-0.565053\pi$
$740$	−5.65685			−0.207950
$741$	9.94982	−	2.52397i	0.365516	−	0.0927204i
$742$		0			0
$743$	0.725728	+	0.725728i	0.0266244	+	0.0266244i	0.720294	−	0.693669i	$-0.244007\pi$
$743$	0.725728	+	0.725728i	0.0266244	+	0.0266244i	−0.693669	+	0.720294i	$0.744007\pi$
$744$	−3.00000	+	6.70820i	−0.109985	+	0.245935i
$745$			16.3246i			0.598085i
$746$	−6.24921	−	6.24921i	−0.228800	−	0.228800i
$747$	−1.33540	+	23.9628i	−0.0488598	+	0.876754i
$748$	2.32456	+	2.32456i	0.0849942	+	0.0849942i
$749$		0			0
$750$	−1.58114	−	0.707107i	−0.0577350	−	0.0258199i
$751$			28.0000i			1.02173i	0.859660	+	0.510867i	$0.170676\pi$
$751$			28.0000i			1.02173i	−0.859660	+	0.510867i	$0.829324\pi$
$752$	−1.64371	+	1.64371i	−0.0599399	+	0.0599399i
$753$	5.19786	+	2.32456i	0.189421	+	0.0847115i
$754$	12.6491	−	10.0000i	0.460653	−	0.364179i
$755$		−	18.8438i		−	0.685795i
$756$		0			0
$757$	−23.8114			−0.865440			−0.432720	−	0.901528i	$-0.642446\pi$
$757$	−23.8114			−0.865440			−0.432720	+	0.901528i	$0.642446\pi$
$758$	9.67000			0.351230
$759$	14.4721	−	5.52786i	0.525305	−	0.200649i
$760$	−1.16228	+	1.16228i	−0.0421602	+	0.0421602i
$761$	29.7946	−	29.7946i	1.08005	−	1.08005i	0.0835503	−	0.996504i	$-0.473374\pi$
$761$	29.7946	−	29.7946i	1.08005	−	1.08005i	0.996504	−	0.0835503i	$-0.0266259\pi$
$762$	−33.9361	+	12.9624i	−1.22938	+	0.469580i
$763$		0			0
$764$	24.7301			0.894704
$765$	0.274377	−	4.92349i	0.00992010	−	0.178009i
$766$		−	30.9737i		−	1.11912i
$767$	12.2317	−	9.67000i	0.441661	−	0.349163i
$768$	1.58114	+	0.707107i	0.0570544	+	0.0255155i
$769$	31.6491	−	31.6491i	1.14130	−	1.14130i	0.153083	−	0.988213i	$-0.451080\pi$
$769$	31.6491	−	31.6491i	1.14130	−	1.14130i	0.988213	−	0.153083i	$-0.0489201\pi$
$770$		0			0
$771$	−11.5432	−	5.16228i	−0.415718	−	0.185915i
$772$	−15.4868	+	15.4868i	−0.557383	+	0.557383i
$773$	16.9706	+	16.9706i	0.610389	+	0.610389i	0.943047	−	0.332659i	$-0.107946\pi$
$773$	16.9706	+	16.9706i	0.610389	+	0.610389i	−0.332659	+	0.943047i	$0.607946\pi$
$774$	2.50927	+	0.139837i	0.0901940	+	0.00502634i
$775$	−3.00000	−	3.00000i	−0.107763	−	0.107763i
$776$		−	7.30056i		−	0.262075i
$777$		0			0
$778$	−14.8377	−	14.8377i	−0.531958	−	0.531958i
$779$	−5.19786			−0.186233
$780$	6.05327	−	1.53553i	0.216742	−	0.0549809i
$781$	−26.9737			−0.965194
$782$	−5.19786	−	5.19786i	−0.185875	−	0.185875i
$783$	−22.1359	+	7.07107i	−0.791074	+	0.252699i
$784$			7.00000i			0.250000i
$785$	−11.9061	−	11.9061i	−0.424946	−	0.424946i
$786$	−28.2016	+	10.7721i	−1.00592	+	0.384227i
$787$	9.48683	+	9.48683i	0.338169	+	0.338169i	0.855678	−	0.517509i	$-0.173141\pi$
$787$	9.48683	+	9.48683i	0.338169	+	0.338169i	−0.517509	+	0.855678i	$0.673141\pi$
$788$	8.94427	−	8.94427i	0.318626	−	0.318626i
$789$	−7.16228	+	16.0153i	−0.254984	+	0.570161i
$790$		−	10.0000i		−	0.355784i
$791$		0			0
$792$	4.47214	−	4.00000i	0.158910	−	0.142134i
$793$	−52.4605	−	6.13594i	−1.86293	−	0.217894i
$794$			27.0996i			0.961727i
$795$	2.28825	−	0.874032i	0.0811557	−	0.0309987i
$796$	−2.00000			−0.0708881
$797$	40.0197			1.41757			0.708786	−	0.705424i	$-0.249243\pi$
$797$	40.0197			1.41757			0.708786	+	0.705424i	$0.249243\pi$
$798$		0			0
$799$	2.70178	−	2.70178i	0.0955821	−	0.0955821i
$800$	−0.707107	+	0.707107i	−0.0250000	+	0.0250000i
$801$	−21.4535	−	1.19557i	−0.758024	−	0.0422432i
$802$	2.51317			0.0887430
$803$	3.28742			0.116010
$804$	0.732196	+	1.91691i	0.0258226	+	0.0676044i
$805$		0			0
$806$	15.1935	+	1.77708i	0.535168	+	0.0625949i
$807$	−3.16228	+	7.07107i	−0.111317	+	0.248913i
$808$	−11.1623	+	11.1623i	−0.392688	+	0.392688i
$809$			37.2285i			1.30889i	0.756111	+	0.654443i	$0.227097\pi$
$809$			37.2285i			1.30889i	−0.756111	+	0.654443i	$0.772903\pi$
$810$	−8.94427	−	1.00000i	−0.314270	−	0.0351364i
$811$	−11.4868	+	11.4868i	−0.403357	+	0.403357i	−0.879414	−	0.476057i	$-0.842066\pi$
$811$	−11.4868	+	11.4868i	−0.403357	+	0.403357i	0.476057	+	0.879414i	$0.342066\pi$
$812$		0			0
$813$	4.65383	+	12.1839i	0.163217	+	0.427308i
$814$	8.00000	+	8.00000i	0.280400	+	0.280400i
$815$			14.6011i			0.511455i
$816$	−2.59893	−	1.16228i	−0.0909808	−	0.0406879i
$817$	0.973666	+	0.973666i	0.0340643	+	0.0340643i
$818$	−32.9859			−1.15333
$819$		0			0
$820$	−3.16228			−0.110432
$821$	−14.1049	−	14.1049i	−0.492264	−	0.492264i	0.416755	−	0.909019i	$-0.363167\pi$
$821$	−14.1049	−	14.1049i	−0.492264	−	0.492264i	−0.909019	+	0.416755i	$0.863167\pi$
$822$	12.1359	+	5.42736i	0.423290	+	0.189301i
$823$			44.9737i			1.56768i	0.620961	+	0.783842i	$0.286743\pi$
$823$			44.9737i			1.56768i	−0.620961	+	0.783842i	$0.713257\pi$
$824$	4.70163	+	4.70163i	0.163789	+	0.163789i
$825$	1.23607	+	3.23607i	0.0430344	+	0.112665i
$826$		0			0
$827$	−24.9596	+	24.9596i	−0.867931	+	0.867931i	−0.992243	−	0.124312i	$-0.960328\pi$
$827$	−24.9596	+	24.9596i	−0.867931	+	0.867931i	0.124312	+	0.992243i	$0.460328\pi$
$828$	−10.0000	+	8.94427i	−0.347524	+	0.310835i
$829$		−	14.0000i		−	0.486240i	−0.969996	−	0.243120i	$-0.921829\pi$
$829$		−	14.0000i		−	0.486240i	0.969996	−	0.243120i	$-0.0781709\pi$
$830$	−5.65685	+	5.65685i	−0.196352	+	0.196352i
$831$	2.23607	−	5.00000i	0.0775683	−	0.173448i
$832$	0.418861	−	3.58114i	0.0145214	−	0.124154i
$833$		−	11.5060i		−	0.398658i
$834$	3.90879	+	10.2333i	0.135350	+	0.354352i
$835$	−10.3246			−0.357296
$836$	3.28742			0.113698
$837$	−19.5927	−	10.1058i	−0.677221	−	0.349308i
$838$	3.35089	−	3.35089i	0.115755	−	0.115755i
$839$	23.2198	−	23.2198i	0.801636	−	0.801636i	−0.181715	−	0.983351i	$-0.558165\pi$
$839$	23.2198	−	23.2198i	0.801636	−	0.801636i	0.983351	+	0.181715i	$0.0581650\pi$
$840$		0			0
$841$	9.00000			0.310345
$842$	27.0996			0.933912
$843$	−50.4216	+	19.2593i	−1.73661	+	0.663327i
$844$			28.6491i			0.986143i
$845$	−6.82295	−	11.0656i	−0.234717	−	0.380668i
$846$	−4.64911	−	5.19786i	−0.159840	−	0.178706i
$847$		0			0
$848$		−	1.41421i		−	0.0485643i
$849$	13.5498	−	30.2982i	0.465027	−	1.03983i
$850$	1.16228	−	1.16228i	0.0398658	−	0.0398658i
$851$	−17.8885	−	17.8885i	−0.613211	−	0.613211i
$852$	21.8222	−	8.33532i	0.747615	−	0.285563i
$853$	−4.64911	−	4.64911i	−0.159183	−	0.159183i	0.623022	−	0.782204i	$-0.285905\pi$
$853$	−4.64911	−	4.64911i	−0.159183	−	0.159183i	−0.782204	+	0.623022i	$0.785905\pi$
$854$		0			0
$855$	−3.28742	−	3.67544i	−0.112427	−	0.125698i
$856$	7.32456	+	7.32456i	0.250348	+	0.250348i
$857$	−9.21101			−0.314642			−0.157321	−	0.987548i	$-0.550286\pi$
$857$	−9.21101			−0.314642			−0.157321	+	0.987548i	$0.550286\pi$
$858$	−10.7322	−	6.38905i	−0.366391	−	0.218119i
$859$	14.3246			0.488748			0.244374	−	0.969681i	$-0.421418\pi$
$859$	14.3246			0.488748			0.244374	+	0.969681i	$0.421418\pi$
$860$	0.592359	+	0.592359i	0.0201993	+	0.0201993i
$861$		0			0
$862$		−	21.4868i		−	0.731844i
$863$	36.9618	+	36.9618i	1.25819	+	1.25819i	0.951954	+	0.306240i	$0.0990711\pi$
$863$	36.9618	+	36.9618i	1.25819	+	1.25819i	0.306240	+	0.951954i	$0.400929\pi$
$864$	−2.38197	+	4.61803i	−0.0810361	+	0.157109i
$865$	9.64911	+	9.64911i	0.328080	+	0.328080i
$866$	−7.98905	+	7.98905i	−0.271479	+	0.271479i
$867$	−22.6075	−	10.1104i	−0.767790	−	0.343366i
$868$		0			0
$869$	−14.1421	+	14.1421i	−0.479739	+	0.479739i
$870$	−7.07107	−	3.16228i	−0.239732	−	0.107211i
$871$	3.35089	−	2.64911i	0.113541	−	0.0897617i
$872$			15.7858i			0.534576i
$873$	21.8678	+	1.21865i	0.740112	+	0.0412450i
$874$	−7.35089			−0.248648
$875$		0			0
$876$	−2.65958	+	1.01587i	−0.0898588	+	0.0343230i
$877$	−35.8114	+	35.8114i	−1.20926	+	1.20926i	−0.237999	+	0.971265i	$0.576492\pi$
$877$	−35.8114	+	35.8114i	−1.20926	+	1.20926i	−0.971265	+	0.237999i	$0.923508\pi$
$878$	−20.2580	+	20.2580i	−0.683674	+	0.683674i
$879$	−6.47214	+	2.47214i	−0.218300	+	0.0833831i
$880$	2.00000			0.0674200
$881$	−8.67753			−0.292354			−0.146177	−	0.989258i	$-0.546697\pi$
$881$	−8.67753			−0.292354			−0.146177	+	0.989258i	$0.546697\pi$
$882$	−20.9675	−	1.16848i	−0.706011	−	0.0393447i
$883$		−	20.1886i		−	0.679401i	−0.940534	−	0.339700i	$-0.889674\pi$
$883$		−	20.1886i		−	0.679401i	0.940534	−	0.339700i	$-0.110326\pi$
$884$	−0.688486	+	5.88635i	−0.0231563	+	0.197979i
$885$	−6.83772	−	3.05792i	−0.229848	−	0.102791i
$886$	−5.32456	+	5.32456i	−0.178882	+	0.178882i
$887$			53.9324i			1.81087i	0.424483	+	0.905436i	$0.360456\pi$
$887$			53.9324i			1.81087i	−0.424483	+	0.905436i	$0.639544\pi$
$888$	−8.94427	−	4.00000i	−0.300150	−	0.134231i
$889$		0			0
$890$	−5.06450	−	5.06450i	−0.169762	−	0.169762i
$891$	11.2349	+	14.0633i	0.376383	+	0.471139i
$892$	−8.64911	−	8.64911i	−0.289594	−	0.289594i
$893$		−	3.82089i		−	0.127861i
$894$	−11.5432	+	25.8114i	−0.386062	+	0.863262i
$895$	−12.3246	−	12.3246i	−0.411964	−	0.411964i
$896$		0			0
$897$	23.9979	+	14.2864i	0.801267	+	0.477007i
$898$	−11.8114			−0.394151
$899$	−13.4164	−	13.4164i	−0.447462	−	0.447462i
$900$	−2.00000	−	2.23607i	−0.0666667	−	0.0745356i
$901$			2.32456i			0.0774422i
$902$	4.47214	+	4.47214i	0.148906	+	0.148906i
$903$		0			0
$904$	7.48683	+	7.48683i	0.249008	+	0.249008i
$905$	5.88635	−	5.88635i	0.195669	−	0.195669i
$906$	13.3246	−	29.7946i	0.442679	−	0.989860i
$907$			22.7851i			0.756565i	0.925690	+	0.378283i	$0.123485\pi$
$907$			22.7851i			0.756565i	−0.925690	+	0.378283i	$0.876515\pi$
$908$	12.7279	−	12.7279i	0.422391	−	0.422391i
$909$	−31.5717	−	35.2982i	−1.04717	−	1.17077i
$910$		0			0
$911$			8.67753i			0.287500i	0.989614	+	0.143750i	$0.0459160\pi$
$911$			8.67753i			0.287500i	−0.989614	+	0.143750i	$0.954084\pi$
$912$	−2.65958	+	1.01587i	−0.0880674	+	0.0336387i
$913$	16.0000			0.529523
$914$	21.9017			0.724443
$915$	9.05365	+	23.7028i	0.299304	+	0.783589i
$916$	−17.8114	+	17.8114i	−0.588505	+	0.588505i
$917$		0			0
$918$	3.91526	−	7.59070i	0.129223	−	0.250531i
$919$	21.2982			0.702563			0.351282	−	0.936270i	$-0.385746\pi$
$919$	21.2982			0.702563			0.351282	+	0.936270i	$0.385746\pi$
$920$	−4.47214			−0.147442
$921$	0.732196	+	1.91691i	0.0241267	+	0.0631645i
$922$		−	5.35089i		−	0.176222i
$923$	−30.1575	−	38.1465i	−0.992645	−	1.25561i
$924$		0			0
$925$	4.00000	−	4.00000i	0.131519	−	0.131519i
$926$			6.11584i			0.200979i
$927$	−14.8679	+	13.2982i	−0.488325	+	0.436771i
$928$	−3.16228	+	3.16228i	−0.103807	+	0.103807i
$929$	22.0351	+	22.0351i	0.722947	+	0.722947i	0.969204	−	0.246258i	$-0.0792009\pi$
$929$	22.0351	+	22.0351i	0.722947	+	0.722947i	−0.246258	+	0.969204i	$0.579201\pi$
$930$	−2.62210	−	6.86474i	−0.0859819	−	0.225104i
$931$	−8.13594	−	8.13594i	−0.266645	−	0.266645i
$932$			12.9574i			0.424434i
$933$	51.3707	+	22.9737i	1.68180	+	0.752124i
$934$	−13.9737	−	13.9737i	−0.457232	−	0.457232i
$935$	−3.28742			−0.107510
$936$	10.6569	+	1.85242i	0.348330	+	0.0605482i
$937$	23.2982			0.761120			0.380560	−	0.924756i	$-0.375731\pi$
$937$	23.2982			0.761120			0.380560	+	0.924756i	$0.375731\pi$
$938$		0			0
$939$	10.5132	+	4.70163i	0.343084	+	0.153432i
$940$		−	2.32456i		−	0.0758186i
$941$	−32.2602	−	32.2602i	−1.05165	−	1.05165i	−0.998591	−	0.0530603i	$-0.983102\pi$
$941$	−32.2602	−	32.2602i	−1.05165	−	1.05165i	−0.0530603	−	0.998591i	$-0.516898\pi$
$942$	−10.4063	−	27.2440i	−0.339055	−	0.887658i
$943$	−10.0000	−	10.0000i	−0.325645	−	0.325645i
$944$	−3.05792	+	3.05792i	−0.0995269	+	0.0995269i
$945$		0			0
$946$		−	1.67544i		−	0.0544734i
$947$	28.2470	−	28.2470i	0.917905	−	0.917905i	−0.0789717	−	0.996877i	$-0.525164\pi$
$947$	28.2470	−	28.2470i	0.917905	−	0.917905i	0.996877	+	0.0789717i	$0.0251637\pi$
$948$	7.07107	−	15.8114i	0.229658	−	0.513530i
$949$	3.67544	+	4.64911i	0.119310	+	0.150917i
$950$		−	1.64371i		−	0.0533290i
$951$	−15.6352	−	40.9334i	−0.507005	−	1.32736i
$952$		0			0
$953$	−53.9324			−1.74704			−0.873520	−	0.486788i	$-0.838169\pi$
$953$	−53.9324			−1.74704			−0.873520	+	0.486788i	$0.838169\pi$
$954$	4.23607	+	0.236068i	0.137148	+	0.00764298i
$955$	−17.4868	+	17.4868i	−0.565861	+	0.565861i
$956$	3.42079	−	3.42079i	0.110636	−	0.110636i
$957$	5.52786	+	14.4721i	0.178690	+	0.467818i
$958$	31.8114			1.02778
$959$		0			0
$960$	−1.61803	+	0.618034i	−0.0522218	+	0.0199470i
$961$			13.0000i			0.419355i
$962$	−2.36944	+	20.2580i	−0.0763937	+	0.653144i
$963$	−23.1623	+	20.7170i	−0.746394	+	0.667595i
$964$	17.6491	−	17.6491i	0.568440	−	0.568440i
$965$		−	21.9017i		−	0.705040i
$966$		0			0
$967$	12.3246	−	12.3246i	0.396331	−	0.396331i	−0.480606	−	0.876937i	$-0.659583\pi$
$967$	12.3246	−	12.3246i	0.396331	−	0.396331i	0.876937	+	0.480606i	$0.159583\pi$
$968$	4.94975	+	4.94975i	0.159091	+	0.159091i
$969$	4.37157	−	1.66979i	0.140435	−	0.0536414i
$970$	5.16228	+	5.16228i	0.165751	+	0.165751i
$971$		−	35.3181i		−	1.13341i	−0.823920	−	0.566706i	$-0.808218\pi$
$971$		−	35.3181i		−	1.13341i	0.823920	−	0.566706i	$-0.191782\pi$
$972$	−13.4350	−	7.90569i	−0.430929	−	0.253575i
$973$		0			0
$974$	25.4558			0.815658
$975$	−3.19453	+	5.36610i	−0.102307	+	0.171853i
$976$	14.6491			0.468907
$977$	30.6165	+	30.6165i	0.979508	+	0.979508i	0.999794	−	0.0202867i	$-0.00645789\pi$
$977$	30.6165	+	30.6165i	0.979508	+	0.979508i	−0.0202867	+	0.999794i	$0.506458\pi$
$978$	−10.3246	+	23.0864i	−0.330143	+	0.738222i
$979$			14.3246i			0.457815i
$980$	−4.94975	−	4.94975i	−0.158114	−	0.158114i
$981$	−47.2842	−	2.63506i	−1.50967	−	0.0841309i
$982$	20.0000	+	20.0000i	0.638226	+	0.638226i
$983$	24.0044	−	24.0044i	0.765621	−	0.765621i	−0.211711	−	0.977332i	$-0.567904\pi$
$983$	24.0044	−	24.0044i	0.765621	−	0.765621i	0.977332	+	0.211711i	$0.0679036\pi$
$984$	−5.00000	−	2.23607i	−0.159394	−	0.0712832i
$985$			12.6491i			0.403034i
$986$	5.19786	−	5.19786i	0.165534	−	0.165534i
$987$		0			0
$988$	3.67544	+	4.64911i	0.116931	+	0.147908i
$989$			3.74641i			0.119129i
$990$	−0.333851	+	5.99070i	−0.0106105	+	0.190397i
$991$	55.2982			1.75661			0.878303	−	0.478105i	$-0.158676\pi$
$991$	55.2982			1.75661			0.878303	+	0.478105i	$0.158676\pi$
$992$	−4.24264			−0.134704
$993$	21.7082	−	8.29180i	0.688889	−	0.263132i
$994$		0			0
$995$	1.41421	−	1.41421i	0.0448336	−	0.0448336i
$996$	−12.9443	+	4.94427i	−0.410155	+	0.156665i
$997$	32.4605			1.02803			0.514017	−	0.857780i	$-0.328157\pi$
$997$	32.4605			1.02803			0.514017	+	0.857780i	$0.328157\pi$
$998$	6.84157			0.216566
$999$	13.4744	−	26.1235i	0.426312	−	0.826512i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	390.2.p.g.161.2	✓	8
3.2	odd	2	inner	390.2.p.g.161.4	yes	8
13.8	odd	4	inner	390.2.p.g.281.4	yes	8
39.8	even	4	inner	390.2.p.g.281.2	yes	8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
390.2.p.g.161.2	✓	8	1.1	even	1	trivial
390.2.p.g.161.4	yes	8	3.2	odd	2	inner
390.2.p.g.281.2	yes	8	39.8	even	4	inner
390.2.p.g.281.4	yes	8	13.8	odd	4	inner

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:	\( N \)	\(=\)	\( 390 = 2 \cdot 3 \cdot 5 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	390.p (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.707107 - 0.707107i) q^{2} +(1.58114 + 0.707107i) q^{3} +1.00000i q^{4} +(-0.707107 - 0.707107i) q^{5} +(-0.618034 - 1.61803i) q^{6} +(0.707107 - 0.707107i) q^{8} +(2.00000 + 2.23607i) q^{9} +1.00000i q^{10} +(1.41421 - 1.41421i) q^{11} +(-0.707107 + 1.58114i) q^{12} +(3.58114 + 0.418861i) q^{13} +(-0.618034 - 1.61803i) q^{15} -1.00000 q^{16} +1.64371 q^{17} +(0.166925 - 2.99535i) q^{18} +(1.16228 - 1.16228i) q^{19} +(0.707107 - 0.707107i) q^{20} -2.00000 q^{22} +4.47214 q^{23} +(1.61803 - 0.618034i) q^{24} +1.00000i q^{25} +(-2.23607 - 2.82843i) q^{26} +(1.58114 + 4.94975i) q^{27} +4.47214i q^{29} +(-0.707107 + 1.58114i) q^{30} +(-3.00000 + 3.00000i) q^{31} +(0.707107 + 0.707107i) q^{32} +(3.23607 - 1.23607i) q^{33} +(-1.16228 - 1.16228i) q^{34} +(-2.23607 + 2.00000i) q^{36} +(-4.00000 - 4.00000i) q^{37} -1.64371 q^{38} +(5.36610 + 3.19453i) q^{39} -1.00000 q^{40} +(-2.23607 - 2.23607i) q^{41} +0.837722i q^{43} +(1.41421 + 1.41421i) q^{44} +(0.166925 - 2.99535i) q^{45} +(-3.16228 - 3.16228i) q^{46} +(1.64371 - 1.64371i) q^{47} +(-1.58114 - 0.707107i) q^{48} -7.00000i q^{49} +(0.707107 - 0.707107i) q^{50} +(2.59893 + 1.16228i) q^{51} +(-0.418861 + 3.58114i) q^{52} +1.41421i q^{53} +(2.38197 - 4.61803i) q^{54} -2.00000 q^{55} +(2.65958 - 1.01587i) q^{57} +(3.16228 - 3.16228i) q^{58} +(3.05792 - 3.05792i) q^{59} +(1.61803 - 0.618034i) q^{60} -14.6491 q^{61} +4.24264 q^{62} -1.00000i q^{64} +(-2.23607 - 2.82843i) q^{65} +(-3.16228 - 1.41421i) q^{66} +(0.837722 - 0.837722i) q^{67} +1.64371i q^{68} +(7.07107 + 3.16228i) q^{69} +(-9.53663 - 9.53663i) q^{71} +(2.99535 + 0.166925i) q^{72} +(1.16228 + 1.16228i) q^{73} +5.65685i q^{74} +(-0.707107 + 1.58114i) q^{75} +(1.16228 + 1.16228i) q^{76} +(-1.53553 - 6.05327i) q^{78} -10.0000 q^{79} +(0.707107 + 0.707107i) q^{80} +(-1.00000 + 8.94427i) q^{81} +3.16228i q^{82} +(5.65685 + 5.65685i) q^{83} +(-1.16228 - 1.16228i) q^{85} +(0.592359 - 0.592359i) q^{86} +(-3.16228 + 7.07107i) q^{87} -2.00000i q^{88} +(-5.06450 + 5.06450i) q^{89} +(-2.23607 + 2.00000i) q^{90} +4.47214i q^{92} +(-6.86474 + 2.62210i) q^{93} -2.32456 q^{94} -1.64371 q^{95} +(0.618034 + 1.61803i) q^{96} +(5.16228 - 5.16228i) q^{97} +(-4.94975 + 4.94975i) q^{98} +(5.99070 + 0.333851i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 4 q^{6} + 16 q^{9} + 16 q^{13} + 4 q^{15} - 8 q^{16} - 16 q^{19} - 16 q^{22} + 4 q^{24} - 24 q^{31} + 8 q^{33} + 16 q^{34} - 32 q^{37} + 20 q^{39} - 8 q^{40} - 16 q^{52} + 28 q^{54} - 16 q^{55} + 40 q^{57}+ \cdots + 16 q^{97}+O(q^{100}) \) 8 * q + 4 * q^6 + 16 * q^9 + 16 * q^13 + 4 * q^15 - 8 * q^16 - 16 * q^19 - 16 * q^22 + 4 * q^24 - 24 * q^31 + 8 * q^33 + 16 * q^34 - 32 * q^37 + 20 * q^39 - 8 * q^40 - 16 * q^52 + 28 * q^54 - 16 * q^55 + 40 * q^57 + 4 * q^60 - 16 * q^61 + 32 * q^67 - 16 * q^73 - 16 * q^76 + 16 * q^78 - 80 * q^79 - 8 * q^81 + 16 * q^85 + 32 * q^94 - 4 * q^96 + 16 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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