LMFDB - Embedded newform 390.2.p.g.161.4

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			161.4
Root			$-0.437016 + 0.437016i$ of defining polynomial
Character	$\chi$	$=$	390.161
Dual form			390.2.p.g.281.4

$q$-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} +(1.61803 + 0.618034i) 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} +(1.61803 + 0.618034i) q^{15} -1.00000 q^{16} -1.64371 q^{17} +(2.99535 - 0.166925i) q^{18} +(1.16228 - 1.16228i) q^{19} +(-0.707107 + 0.707107i) q^{20} -2.00000 q^{22} -4.47214 q^{23} +(-0.618034 + 1.61803i) 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} +(-1.23607 + 3.23607i) q^{33} +(-1.16228 - 1.16228i) q^{34} +(2.23607 + 2.00000i) q^{36} +(-4.00000 - 4.00000i) q^{37} +1.64371 q^{38} +(5.95846 - 1.86997i) q^{39} -1.00000 q^{40} +(2.23607 + 2.23607i) q^{41} +0.837722i q^{43} +(-1.41421 - 1.41421i) q^{44} +(2.99535 - 0.166925i) 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} +(4.61803 - 2.38197i) q^{54} -2.00000 q^{55} +(1.01587 - 2.65958i) q^{57} +(3.16228 - 3.16228i) q^{58} +(-3.05792 + 3.05792i) q^{59} +(-0.618034 + 1.61803i) 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} +(0.166925 + 2.99535i) q^{72} +(1.16228 + 1.16228i) q^{73} -5.65685i q^{74} +(0.707107 + 1.58114i) q^{75} +(1.16228 + 1.16228i) q^{76} +(5.53553 + 2.89100i) 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} +(-2.62210 + 6.86474i) q^{93} -2.32456 q^{94} +1.64371 q^{95} +(-1.61803 - 0.618034i) q^{96} +(5.16228 - 5.16228i) q^{97} +(4.94975 - 4.94975i) q^{98} +(0.333851 + 5.99070i) 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
$6$	1.61803	+	0.618034i	0.660560	+	0.252311i
$7$		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	−0.887401	−	0.460999i	$-0.847491\pi$
$11$	−1.41421	+	1.41421i	−0.426401	+	0.426401i	0.460999	+	0.887401i	$0.347491\pi$
$12$	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
$15$	1.61803	+	0.618034i	0.417775	+	0.159576i
$16$	−1.00000			−0.250000
$17$	−1.64371			−0.398658			−0.199329	−	0.979933i	$-0.563876\pi$
$17$	−1.64371			−0.398658			−0.199329	+	0.979933i	$0.563876\pi$
$18$	2.99535	−	0.166925i	0.706011	−	0.0393447i
$19$	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	$-0.654396\pi$
$23$	−4.47214			−0.932505			−0.466252	+	0.884652i	$0.654396\pi$
$24$	−0.618034	+	1.61803i	−0.126156	+	0.330280i
$25$			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	$-0.863702\pi$
$29$		−	4.47214i		−	0.830455i	0.909718	−	0.415227i	$-0.136298\pi$
$30$	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
$33$	−1.23607	+	3.23607i	−0.215172	+	0.563327i
$34$	−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
$39$	5.95846	−	1.86997i	0.954117	−	0.299435i
$40$	−1.00000			−0.158114
$41$	2.23607	+	2.23607i	0.349215	+	0.349215i	0.859817	−	0.510602i	$-0.170577\pi$
$41$	2.23607	+	2.23607i	0.349215	+	0.349215i	−0.510602	+	0.859817i	$0.670577\pi$
$42$		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
$45$	2.99535	−	0.166925i	0.446521	−	0.0248837i
$46$	−3.16228	−	3.16228i	−0.466252	−	0.466252i
$47$	−1.64371	+	1.64371i	−0.239760	+	0.239760i	−0.816751	−	0.576991i	$-0.804227\pi$
$47$	−1.64371	+	1.64371i	−0.239760	+	0.239760i	0.576991	+	0.816751i	$0.304227\pi$
$48$	−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	$-0.969034\pi$
$53$		−	1.41421i		−	0.194257i	0.995272	−	0.0971286i	$-0.0309658\pi$
$54$	4.61803	−	2.38197i	0.628435	−	0.324145i
$55$	−2.00000			−0.269680
$56$		0			0
$57$	1.01587	−	2.65958i	0.134555	−	0.352270i
$58$	3.16228	−	3.16228i	0.415227	−	0.415227i
$59$	−3.05792	+	3.05792i	−0.398108	+	0.398108i	−0.877565	−	0.479458i	$-0.840833\pi$
$59$	−3.05792	+	3.05792i	−0.398108	+	0.398108i	0.479458	+	0.877565i	$0.340833\pi$
$60$	−0.618034	+	1.61803i	−0.0797878	+	0.208887i
$61$	−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	$0.0453245\pi$
$71$	9.53663	+	9.53663i	1.13179	+	1.13179i	0.141910	+	0.989880i	$0.454676\pi$
$72$	0.166925	+	2.99535i	0.0196723	+	0.353006i
$73$	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
$78$	5.53553	+	2.89100i	0.626776	+	0.327341i
$79$	−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	0.324846	−	0.945767i	$-0.394687\pi$
$83$	−5.65685	−	5.65685i	−0.620920	−	0.620920i	−0.945767	+	0.324846i	$0.894687\pi$
$84$		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	−0.385763	−	0.922598i	$-0.626062\pi$
$89$	5.06450	−	5.06450i	0.536835	−	0.536835i	0.922598	+	0.385763i	$0.126062\pi$
$90$	2.23607	+	2.00000i	0.235702	+	0.210819i
$91$		0			0
$92$		−	4.47214i		−	0.466252i
$93$	−2.62210	+	6.86474i	−0.271899	+	0.711840i
$94$	−2.32456			−0.239760
$95$	1.64371			0.168641
$96$	−1.61803	−	0.618034i	−0.165140	−	0.0630778i
$97$	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
$99$	0.333851	+	5.99070i	0.0335532	+	0.602088i
$100$	−1.00000			−0.100000
$101$	15.7858			1.57075			0.785375	−	0.619020i	$-0.212470\pi$
$101$	15.7858			1.57075			0.785375	+	0.619020i	$0.212470\pi$
$102$	−2.65958	−	1.01587i	−0.263337	−	0.100586i
$103$			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	$-0.833077\pi$
$107$		−	10.3585i		−	1.00139i	0.865623	−	0.500696i	$-0.166923\pi$
$108$	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
$111$	−9.15298	−	3.49613i	−0.868763	−	0.331838i
$112$		0			0
$113$		−	10.5880i		−	0.996033i	−0.867167	−	0.498017i	$-0.834062\pi$
$113$		−	10.5880i		−	0.996033i	0.867167	−	0.498017i	$-0.165938\pi$
$114$	2.59893	−	1.16228i	0.243412	−	0.108857i
$115$	−3.16228	−	3.16228i	−0.294884	−	0.294884i
$116$	4.47214			0.415227
$117$	8.09888	−	7.16995i	0.748742	−	0.662862i
$118$	−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
$123$	5.11667	+	1.95440i	0.461355	+	0.176222i
$124$	−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	$0.275494\pi$
$131$			17.4296i			1.52283i	−0.648266	+	0.761414i	$0.724506\pi$
$132$	−3.23607	−	1.23607i	−0.281664	−	0.107586i
$133$		0			0
$134$	1.18472			0.102344
$135$	4.61803	−	2.38197i	0.397457	−	0.205007i
$136$	1.16228	−	1.16228i	0.0996645	−	0.0996645i
$137$	5.42736	−	5.42736i	0.463691	−	0.463691i	−0.436173	−	0.899863i	$-0.643666\pi$
$137$	5.42736	−	5.42736i	0.463691	−	0.463691i	0.899863	+	0.436173i	$0.143666\pi$
$138$	−7.23607	−	2.76393i	−0.615975	−	0.235282i
$139$	−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
$141$	−1.43665	+	3.76121i	−0.120988	+	0.316751i
$142$			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	0.998598	−	0.0529415i	$-0.0168597\pi$
$149$	11.5432	+	11.5432i	0.945656	+	0.945656i	−0.0529415	+	0.998598i	$0.516860\pi$
$150$	−0.618034	+	1.61803i	−0.0504623	+	0.132112i
$151$	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
$156$	1.86997	+	5.95846i	0.149717	+	0.477058i
$157$	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
$162$	5.61745	−	7.03166i	0.441348	−	0.552460i
$163$	−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	−0.930705	−	0.365771i	$-0.880805\pi$
$167$	−7.30056	+	7.30056i	−0.564935	+	0.564935i	0.365771	+	0.930705i	$0.380805\pi$
$168$		0			0
$169$	12.6491	+	3.00000i	0.973009	+	0.230769i
$170$		−	1.64371i		−	0.126067i
$171$	−0.274377	−	4.92349i	−0.0209821	−	0.376508i
$172$	−0.837722			−0.0638757
$173$	13.6459			1.03748			0.518739	−	0.854932i	$-0.326401\pi$
$173$	13.6459			1.03748			0.518739	+	0.854932i	$0.326401\pi$
$174$	2.76393	−	7.23607i	0.209533	−	0.548565i
$175$		0			0
$176$	1.41421	−	1.41421i	0.106600	−	0.106600i
$177$	−2.67272	+	6.99728i	−0.200894	+	0.525948i
$178$	7.16228			0.536835
$179$	−17.4296			−1.30275			−0.651373	−	0.758758i	$-0.725807\pi$
$179$	−17.4296			−1.30275			−0.651373	+	0.758758i	$0.725807\pi$
$180$	0.166925	+	2.99535i	0.0124419	+	0.223260i
$181$			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	$0.352614\pi$
$191$			24.7301i			1.78941i	−0.446659	+	0.894704i	$0.647386\pi$
$192$	−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
$195$	5.53553	+	2.89100i	0.396408	+	0.207029i
$196$	7.00000			0.500000
$197$	8.94427	+	8.94427i	0.637253	+	0.637253i	0.949877	−	0.312624i	$-0.101208\pi$
$197$	8.94427	+	8.94427i	0.637253	+	0.637253i	−0.312624	+	0.949877i	$0.601208\pi$
$198$	−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
$201$	0.732196	−	1.91691i	0.0516451	−	0.135209i
$202$	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
$213$	21.8222	+	8.33532i	1.49523	+	0.571127i
$214$	7.32456	−	7.32456i	0.500696	−	0.500696i
$215$	−0.592359	+	0.592359i	−0.0403986	+	0.0403986i
$216$	2.38197	+	4.61803i	0.162072	+	0.314217i
$217$		0			0
$218$	−15.7858			−1.06915
$219$	2.65958	+	1.01587i	0.179718	+	0.0686460i
$220$		−	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	0.989476	−	0.144695i	$-0.0462199\pi$
$227$	12.7279	+	12.7279i	0.844782	+	0.844782i	−0.144695	+	0.989476i	$0.546220\pi$
$228$	2.65958	+	1.01587i	0.176135	+	0.0672775i
$229$	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	$-0.639527\pi$
$233$	−12.9574			−0.848869			−0.424434	+	0.905459i	$0.639527\pi$
$234$	10.7967	+	0.656854i	0.705802	+	0.0429399i
$235$	−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	0.809034	−	0.587762i	$-0.199991\pi$
$239$	3.42079	+	3.42079i	0.221272	+	0.221272i	−0.587762	+	0.809034i	$0.699991\pi$
$240$	−1.61803	−	0.618034i	−0.104444	−	0.0398939i
$241$	−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
$249$	−12.9443	−	4.94427i	−0.820310	−	0.313331i
$250$	−1.00000			−0.0632456
$251$	−3.28742			−0.207500			−0.103750	−	0.994603i	$-0.533084\pi$
$251$	−3.28742			−0.207500			−0.103750	+	0.994603i	$0.533084\pi$
$252$		0			0
$253$	6.32456	−	6.32456i	0.397621	−	0.397621i
$254$	14.8306	−	14.8306i	0.930556	−	0.930556i
$255$	−2.65958	−	1.01587i	−0.166549	−	0.0636161i
$256$	1.00000			0.0625000
$257$	7.30056			0.455397			0.227698	−	0.973732i	$-0.426880\pi$
$257$	7.30056			0.455397			0.227698	+	0.973732i	$0.426880\pi$
$258$	−0.517741	+	1.35546i	−0.0322331	+	0.0843875i
$259$		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	$-0.898904\pi$
$263$		−	10.1290i		−	0.624580i	0.949987	−	0.312290i	$-0.101096\pi$
$264$	−1.41421	−	3.16228i	−0.0870388	−	0.194625i
$265$	1.00000	−	1.00000i	0.0614295	−	0.0614295i
$266$		0			0
$267$	4.42653	−	11.5888i	0.270899	−	0.709224i
$268$	0.837722	+	0.837722i	0.0511720	+	0.0511720i
$269$		−	4.47214i		−	0.272671i	−0.990663	−	0.136335i	$-0.956467\pi$
$269$		−	4.47214i		−	0.272671i	0.990663	−	0.136335i	$-0.0435325\pi$
$270$	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
$279$	0.708204	+	12.7082i	0.0423991	+	0.760820i
$280$		0			0
$281$	22.0351	−	22.0351i	1.31450	−	1.31450i	0.396441	−	0.918060i	$-0.370245\pi$
$281$	22.0351	−	22.0351i	1.31450	−	1.31450i	0.918060	−	0.396441i	$-0.129755\pi$
$282$	−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
$288$	−2.99535	+	0.166925i	−0.176503	+	0.00983617i
$289$	−14.2982			−0.841072
$290$	4.47214			0.262613
$291$	4.51200	−	11.8126i	0.264498	−	0.692464i
$292$	−1.16228	+	1.16228i	−0.0680172	+	0.0680172i
$293$	2.82843	−	2.82843i	0.165238	−	0.165238i	−0.619644	−	0.784883i	$-0.712723\pi$
$293$	2.82843	−	2.82843i	0.165238	−	0.165238i	0.784883	+	0.619644i	$0.212723\pi$
$294$	4.32624	−	11.3262i	0.252311	−	0.660560i
$295$	−4.32456			−0.251785
$296$	5.65685			0.328798
$297$	4.76393	+	9.23607i	0.276431	+	0.535931i
$298$			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
$306$	−4.92349	+	0.274377i	−0.281457	+	0.0156851i
$307$	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	$-0.872757\pi$
$311$	−32.4897			−1.84232			−0.921160	+	0.389184i	$0.872757\pi$
$312$	−2.89100	+	5.53553i	−0.163670	+	0.313388i
$313$	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	$0.00150622\pi$
$317$	17.8885	+	17.8885i	1.00472	+	1.00472i	0.00473191	+	0.999989i	$0.498494\pi$
$318$	0.874032	−	2.28825i	0.0490133	−	0.128318i
$319$	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
$327$	−9.75619	+	25.5420i	−0.539518	+	1.41248i
$328$	−3.16228			−0.174608
$329$		0			0
$330$	−3.23607	−	1.23607i	−0.178140	−	0.0680433i
$331$	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
$333$	−16.9443	+	0.944272i	−0.928540	+	0.0517458i
$334$	−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
$345$	−7.23607	−	2.76393i	−0.389577	−	0.148805i
$346$	9.64911	+	9.64911i	0.518739	+	0.518739i
$347$			10.3585i			0.556073i	0.960571	+	0.278036i	$0.0896836\pi$
$347$			10.3585i			0.556073i	−0.960571	+	0.278036i	$0.910316\pi$
$348$	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
$351$	7.73553	−	17.0635i	0.412892	−	0.910780i
$352$	2.00000			0.106600
$353$	−17.6590	−	17.6590i	−0.939896	−	0.939896i	0.0583971	−	0.998293i	$-0.481401\pi$
$353$	−17.6590	−	17.6590i	−0.939896	−	0.939896i	−0.998293	+	0.0583971i	$0.981401\pi$
$354$	−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	−0.710617	−	0.703579i	$-0.751584\pi$
$359$	−0.133369	+	0.133369i	−0.00703893	+	0.00703893i	0.703579	+	0.710617i	$0.251584\pi$
$360$	−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
$366$	−23.7028	−	9.05365i	−1.23896	−	0.473242i
$367$	−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
$369$	9.47214	−	0.527864i	0.493100	−	0.0274795i
$370$	4.00000	−	4.00000i	0.207950	−	0.207950i
$371$		0			0
$372$	−6.86474	−	2.62210i	−0.355920	−	0.135949i
$373$	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
$375$	−0.618034	+	1.61803i	−0.0319151	+	0.0835549i
$376$		−	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	$-0.959384\pi$
$383$	−21.9017	−	21.9017i	−1.11912	−	1.11912i	−0.127254	−	0.991870i	$-0.540616\pi$
$384$	0.618034	−	1.61803i	0.0315389	−	0.0825700i
$385$		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	$-0.678544\pi$
$389$	−20.9837			−1.06392			−0.531958	+	0.846771i	$0.678544\pi$
$390$	1.86997	+	5.95846i	0.0946896	+	0.301718i
$391$	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
$396$	−5.99070	+	0.333851i	−0.301044	+	0.0167766i
$397$	−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	−0.661342	−	0.750085i	$-0.730013\pi$
$401$	1.77708	−	1.77708i	0.0887430	−	0.0887430i	0.750085	+	0.661342i	$0.230013\pi$
$402$	1.87320	−	0.837722i	0.0934269	−	0.0417818i
$403$	−12.0000	+	9.48683i	−0.597763	+	0.472573i
$404$			15.7858i			0.785375i
$405$	5.61745	−	7.03166i	0.279133	−	0.349406i
$406$		0			0
$407$	11.3137			0.560800
$408$	1.01587	−	2.65958i	0.0502930	−	0.131669i
$409$	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
$411$	4.74369	−	12.4191i	0.233989	−	0.612591i
$412$	−6.64911			−0.327578
$413$		0			0
$414$	−13.3956	+	0.746512i	−0.658359	+	0.0366891i
$415$		−	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	$-0.963071\pi$
$419$		−	4.73887i		−	0.231509i	0.993278	−	0.115755i	$-0.0369286\pi$
$420$		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
$423$	0.388027	+	6.96286i	0.0188665	+	0.338546i
$424$	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
$429$	−5.78199	+	11.0711i	−0.279157	+	0.534516i
$430$	−0.837722			−0.0403986
$431$	−15.1935	−	15.1935i	−0.731844	−	0.731844i	0.239141	−	0.970985i	$-0.423134\pi$
$431$	−15.1935	−	15.1935i	−0.731844	−	0.731844i	−0.970985	+	0.239141i	$0.923134\pi$
$432$	−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
$435$	2.76393	−	7.23607i	0.132520	−	0.346943i
$436$	−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	$0.0572480\pi$
$443$			7.53006i			0.357764i	−0.983871	+	0.178882i	$0.942752\pi$
$444$	3.49613	−	9.15298i	0.165919	−	0.434381i
$445$	7.16228			0.339525
$446$	−12.2317			−0.579187
$447$	26.4137	+	10.0891i	1.24932	+	0.477199i
$448$		0			0
$449$	−8.35191	+	8.35191i	−0.394151	+	0.394151i	−0.876164	−	0.482013i	$-0.839906\pi$
$449$	−8.35191	+	8.35191i	−0.394151	+	0.394151i	0.482013	+	0.876164i	$0.339906\pi$
$450$	0.166925	+	2.99535i	0.00786893	+	0.141202i
$451$	−6.32456			−0.297812
$452$	10.5880			0.498017
$453$	30.4899	+	11.6461i	1.43254	+	0.547181i
$454$			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	0.613485	−	0.789707i	$-0.289767\pi$
$461$	−3.78365	−	3.78365i	−0.176222	−	0.176222i	−0.789707	+	0.613485i	$0.789767\pi$
$462$		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	$-0.651159\pi$
$467$	−19.7617			−0.914465			−0.457232	+	0.889347i	$0.651159\pi$
$468$	7.16995	+	8.09888i	0.331431	+	0.374371i
$469$		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
$474$	−16.1803	−	6.18034i	−0.743188	−	0.283872i
$475$	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	$-0.491030\pi$
$479$	22.4940	−	22.4940i	1.02778	−	1.02778i	0.999603	−	0.0281763i	$-0.00896999\pi$
$480$	−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
$486$	3.90983	−	15.0902i	0.177353	−	0.684504i
$487$	−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
$489$	−23.6251	−	9.02399i	−1.06836	−	0.408079i
$490$	7.00000			0.316228
$491$	28.2843			1.27645			0.638226	−	0.769849i	$-0.279669\pi$
$491$	28.2843			1.27645			0.638226	+	0.769849i	$0.279669\pi$
$492$	−1.95440	+	5.11667i	−0.0881109	+	0.230677i
$493$			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
$501$	−6.38093	+	16.7055i	−0.285079	+	0.746346i
$502$	−2.32456	−	2.32456i	−0.103750	−	0.103750i
$503$		−	19.5323i		−	0.870900i	−0.900213	−	0.435450i	$-0.856589\pi$
$503$		−	19.5323i		−	0.870900i	0.900213	−	0.435450i	$-0.143411\pi$
$504$		0			0
$505$	11.1623	+	11.1623i	0.496715	+	0.496715i
$506$	8.94427			0.397621
$507$	22.1213	−	4.20086i	0.982442	−	0.186567i
$508$	20.9737			0.930556
$509$	5.42736	+	5.42736i	0.240563	+	0.240563i	0.817083	−	0.576520i	$-0.195590\pi$
$509$	5.42736	+	5.42736i	0.240563	+	0.240563i	−0.576520	+	0.817083i	$0.695590\pi$
$510$	−1.16228	−	2.59893i	−0.0514665	−	0.115083i
$511$		0			0
$512$	0.707107	+	0.707107i	0.0312500	+	0.0312500i
$513$	−3.91526	−	7.59070i	−0.172863	−	0.335138i
$514$	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	$-0.817772\pi$
$521$		−	24.7301i		−	1.08345i	0.840557	−	0.541723i	$-0.182228\pi$
$522$	−0.746512	−	13.3956i	−0.0326740	−	0.586310i
$523$	−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
$528$	1.23607	−	3.23607i	0.0537930	−	0.140832i
$529$	−3.00000			−0.130435
$530$	1.41421			0.0614295
$531$	0.721878	+	12.9536i	0.0313268	+	0.562137i
$532$		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
$540$	2.38197	+	4.61803i	0.102503	+	0.198729i
$541$	−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
$552$	2.76393	−	7.23607i	0.117641	−	0.307988i
$553$		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	−0.565566	−	0.824703i	$-0.691342\pi$
$557$	6.11584	−	6.11584i	0.259137	−	0.259137i	0.824703	+	0.565566i	$0.191342\pi$
$558$	−8.48528	+	9.48683i	−0.359211	+	0.401610i
$559$	−0.350889	+	3.00000i	−0.0148410	+	0.126886i
$560$		0			0
$561$	2.03174	−	5.31915i	0.0857800	−	0.224575i
$562$	31.1623			1.31450
$563$	42.3892			1.78649			0.893245	−	0.449570i	$-0.148423\pi$
$563$	42.3892			1.78649			0.893245	+	0.449570i	$0.148423\pi$
$564$	−3.76121	−	1.43665i	−0.158375	−	0.0604941i
$565$	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	$-0.326539\pi$
$569$	24.7301			1.03674			0.518370	+	0.855156i	$0.326539\pi$
$570$	2.65958	+	1.01587i	0.111397	+	0.0425500i
$571$			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
$579$	35.4377	+	13.5360i	1.47274	+	0.562536i
$580$	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
$585$	10.7967	+	0.656854i	0.446388	+	0.0271576i
$586$	4.00000			0.165238
$587$	17.4296	+	17.4296i	0.719395	+	0.719395i	0.968481	−	0.249087i	$-0.0801304\pi$
$587$	17.4296	+	17.4296i	0.719395	+	0.719395i	−0.249087	+	0.968481i	$0.580130\pi$
$588$	11.0680	−	4.94975i	0.456435	−	0.204124i
$589$			6.97367i			0.287345i
$590$	−3.05792	−	3.05792i	−0.125893	−	0.125893i
$591$	20.4667	+	7.81758i	0.841887	+	0.321572i
$592$	4.00000	+	4.00000i	0.164399	+	0.164399i
$593$	−22.5902	+	22.5902i	−0.927667	+	0.927667i	−0.997555	−	0.0698876i	$-0.977736\pi$
$593$	−22.5902	+	22.5902i	−0.927667	+	0.927667i	0.0698876	+	0.997555i	$0.477736\pi$
$594$	−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	$0.0982362\pi$
$599$			14.8679i			0.607484i	−0.952754	+	0.303742i	$0.901764\pi$
$600$	−1.61803	−	0.618034i	−0.0660560	−	0.0252311i
$601$	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
$603$	−0.197759	−	3.54865i	−0.00805339	−	0.144512i
$604$	−13.3246	+	13.3246i	−0.542168	+	0.542168i
$605$	−4.94975	+	4.94975i	−0.201236	+	0.201236i
$606$	25.5420	+	9.75619i	1.03757	+	0.396318i
$607$	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	0.232462	−	0.972605i	$-0.425322\pi$
$617$	−18.3848	−	18.3848i	−0.740143	−	0.740143i	−0.972605	+	0.232462i	$0.925322\pi$
$618$	−4.10938	+	10.7585i	−0.165303	+	0.432770i
$619$	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
$624$	−5.95846	+	1.86997i	−0.238529	+	0.0748587i
$625$	−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
$639$	40.3978	−	2.25129i	1.59811	−	0.0890598i
$640$	1.00000			0.0395285
$641$	−35.7771			−1.41311			−0.706555	−	0.707658i	$-0.749752\pi$
$641$	−35.7771			−1.41311			−0.706555	+	0.707658i	$0.749752\pi$
$642$	6.40190	−	16.7604i	0.252663	−	0.661479i
$643$	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
$645$	−0.517741	+	1.35546i	−0.0203860	+	0.0533713i
$646$	−2.70178			−0.106300
$647$	−37.9543			−1.49214			−0.746068	−	0.665870i	$-0.768061\pi$
$647$	−37.9543			−1.49214			−0.746068	+	0.665870i	$0.768061\pi$
$648$	7.03166	+	5.61745i	0.276230	+	0.220674i
$649$		−	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	$0.389262\pi$
$653$			48.0460i			1.88019i	−0.340918	+	0.940093i	$0.610738\pi$
$654$	−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
$657$	4.92349	−	0.274377i	0.192084	−	0.0107044i
$658$		0			0
$659$			8.94427i			0.348419i	0.984709	+	0.174210i	$0.0557371\pi$
$659$			8.94427i			0.348419i	−0.984709	+	0.174210i	$0.944263\pi$
$660$	−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
$663$	−9.79397	+	3.07369i	−0.380366	+	0.119372i
$664$	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
$669$	−7.55960	+	19.7913i	−0.292271	+	0.765175i
$670$	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	$0.0815512\pi$
$677$			13.1869i			0.506814i	−0.967360	+	0.253407i	$0.918449\pi$
$678$	6.54373	−	17.1317i	0.251311	−	0.657939i
$679$		0			0
$680$	1.64371			0.0630334
$681$	29.1246	+	11.1246i	1.11606	+	0.426296i
$682$	6.00000	−	6.00000i	0.229752	−	0.229752i
$683$	4.24264	−	4.24264i	0.162340	−	0.162340i	−0.621262	−	0.783603i	$-0.713380\pi$
$683$	4.24264	−	4.24264i	0.162340	−	0.162340i	0.783603	+	0.621262i	$0.213380\pi$
$684$	4.92349	−	0.274377i	0.188254	−	0.0104910i
$685$	7.67544			0.293264
$686$		0			0
$687$	40.7568	+	15.5677i	1.55497	+	0.593946i
$688$		−	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
$696$	7.23607	+	2.76393i	0.274282	+	0.104767i
$697$	−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	$-0.467543\pi$
$701$	5.39012			0.203582			0.101791	+	0.994806i	$0.467543\pi$
$702$	17.5355	−	6.59584i	0.661836	−	0.248944i
$703$	−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
$708$	−6.99728	−	2.67272i	−0.262974	−	0.100447i
$709$	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
$717$	7.82760	+	2.98988i	0.292327	+	0.111659i
$718$	−0.188612			−0.00703893
$719$	24.7301			0.922278			0.461139	−	0.887328i	$-0.347441\pi$
$719$	24.7301			0.922278			0.461139	+	0.887328i	$0.347441\pi$
$720$	−2.99535	+	0.166925i	−0.111630	+	0.00622094i
$721$		0			0
$722$	−11.5246	+	11.5246i	−0.428901	+	0.428901i
$723$	−40.3855	−	15.4259i	−1.50195	−	0.573695i
$724$	−8.32456			−0.309380
$725$	4.47214			0.166091
$726$	−4.32624	+	11.3262i	−0.160562	+	0.420356i
$727$		−	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
$735$	4.32624	−	11.3262i	0.159576	−	0.417775i
$736$	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
$741$	4.75196	−	9.09881i	0.174568	−	0.334253i
$742$		0			0
$743$	−0.725728	−	0.725728i	−0.0266244	−	0.0266244i	0.693669	−	0.720294i	$-0.255993\pi$
$743$	−0.725728	−	0.725728i	−0.0266244	−	0.0266244i	−0.720294	+	0.693669i	$0.755993\pi$
$744$	−3.00000	−	6.70820i	−0.109985	−	0.245935i
$745$			16.3246i			0.598085i
$746$	6.24921	+	6.24921i	0.228800	+	0.228800i
$747$	−23.9628	+	1.33540i	−0.876754	+	0.0488598i
$748$	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
$759$	5.52786	−	14.4721i	0.200649	−	0.525305i
$760$	−1.16228	+	1.16228i	−0.0421602	+	0.0421602i
$761$	−29.7946	+	29.7946i	−1.08005	+	1.08005i	−0.0835503	+	0.996504i	$0.526626\pi$
$761$	−29.7946	+	29.7946i	−1.08005	+	1.08005i	−0.996504	+	0.0835503i	$0.973374\pi$
$762$	12.9624	−	33.9361i	0.469580	−	1.22938i
$763$		0			0
$764$	−24.7301			−0.894704
$765$	−4.92349	+	0.274377i	−0.178009	+	0.00992010i
$766$		−	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	0.332659	−	0.943047i	$-0.392054\pi$
$773$	−16.9706	−	16.9706i	−0.610389	−	0.610389i	−0.943047	+	0.332659i	$0.892054\pi$
$774$	0.139837	+	2.50927i	0.00502634	+	0.0901940i
$775$	−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
$780$	−2.89100	+	5.53553i	−0.103514	+	0.198204i
$781$	−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
$786$	−10.7721	+	28.2016i	−0.384227	+	1.00592i
$787$	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
$795$	0.874032	−	2.28825i	0.0309987	−	0.0811557i
$796$	−2.00000			−0.0708881
$797$	−40.0197			−1.41757			−0.708786	−	0.705424i	$-0.750757\pi$
$797$	−40.0197			−1.41757			−0.708786	+	0.705424i	$0.750757\pi$
$798$		0			0
$799$	2.70178	−	2.70178i	0.0955821	−	0.0955821i
$800$	0.707107	−	0.707107i	0.0250000	−	0.0250000i
$801$	−1.19557	−	21.4535i	−0.0422432	−	0.758024i
$802$	2.51317			0.0887430
$803$	−3.28742			−0.116010
$804$	1.91691	+	0.732196i	0.0676044	+	0.0258226i
$805$		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	$-0.772903\pi$
$809$		−	37.2285i		−	1.30889i	0.756111	−	0.654443i	$-0.227097\pi$
$810$	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
$813$	12.1839	+	4.65383i	0.427308	+	0.163217i
$814$	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	0.909019	−	0.416755i	$-0.136833\pi$
$821$	14.1049	+	14.1049i	0.492264	+	0.492264i	−0.416755	+	0.909019i	$0.636833\pi$
$822$	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
$825$	−3.23607	−	1.23607i	−0.112665	−	0.0430344i
$826$		0			0
$827$	24.9596	−	24.9596i	0.867931	−	0.867931i	−0.124312	−	0.992243i	$-0.539672\pi$
$827$	24.9596	−	24.9596i	0.867931	−	0.867931i	0.992243	+	0.124312i	$0.0396725\pi$
$828$	−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
$834$	−10.2333	−	3.90879i	−0.354352	−	0.135350i
$835$	−10.3246			−0.357296
$836$	−3.28742			−0.113698
$837$	10.1058	+	19.5927i	0.349308	+	0.677221i
$838$	3.35089	−	3.35089i	0.115755	−	0.115755i
$839$	−23.2198	+	23.2198i	−0.801636	+	0.801636i	−0.983351	−	0.181715i	$-0.941835\pi$
$839$	−23.2198	+	23.2198i	−0.801636	+	0.801636i	0.181715	+	0.983351i	$0.441835\pi$
$840$		0			0
$841$	9.00000			0.310345
$842$	−27.0996			−0.933912
$843$	19.2593	−	50.4216i	0.663327	−	1.73661i
$844$			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
$852$	−8.33532	+	21.8222i	−0.285563	+	0.747615i
$853$	−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	$-0.449714\pi$
$857$	9.21101			0.314642			0.157321	+	0.987548i	$0.449714\pi$
$858$	−11.9169	+	3.73994i	−0.406837	+	0.127679i
$859$	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	$-0.900929\pi$
$863$	−36.9618	−	36.9618i	−1.25819	−	1.25819i	−0.306240	−	0.951954i	$-0.599071\pi$
$864$	−4.61803	+	2.38197i	−0.157109	+	0.0810361i
$865$	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
$873$	−1.21865	−	21.8678i	−0.0412450	−	0.740112i
$874$	−7.35089			−0.248648
$875$		0			0
$876$	−1.01587	+	2.65958i	−0.0343230	+	0.0898588i
$877$	−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
$879$	2.47214	−	6.47214i	0.0833831	−	0.218300i
$880$	2.00000			0.0674200
$881$	8.67753			0.292354			0.146177	−	0.989258i	$-0.453303\pi$
$881$	8.67753			0.292354			0.146177	+	0.989258i	$0.453303\pi$
$882$	−1.16848	−	20.9675i	−0.0393447	−	0.706011i
$883$		−	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	$-0.639544\pi$
$887$		−	53.9324i		−	1.81087i	0.424483	−	0.905436i	$-0.360456\pi$
$888$	8.94427	−	4.00000i	0.300150	−	0.134231i
$889$		0			0
$890$	5.06450	+	5.06450i	0.169762	+	0.169762i
$891$	14.0633	+	11.2349i	0.471139	+	0.376383i
$892$	−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
$897$	−26.6470	+	8.36276i	−0.889718	+	0.279224i
$898$	−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	$-0.954084\pi$
$911$		−	8.67753i		−	0.287500i	0.989614	−	0.143750i	$-0.0459160\pi$
$912$	−1.01587	+	2.65958i	−0.0336387	+	0.0880674i
$913$	16.0000			0.529523
$914$	−21.9017			−0.724443
$915$	−23.7028	−	9.05365i	−0.783589	−	0.299304i
$916$	−17.8114	+	17.8114i	−0.588505	+	0.588505i
$917$		0			0
$918$	−7.59070	+	3.91526i	−0.250531	+	0.129223i
$919$	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
$921$	1.91691	+	0.732196i	0.0631645	+	0.0241267i
$922$		−	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	0.246258	−	0.969204i	$-0.420799\pi$
$929$	−22.0351	−	22.0351i	−0.722947	−	0.722947i	−0.969204	+	0.246258i	$0.920799\pi$
$930$	−6.86474	−	2.62210i	−0.225104	−	0.0859819i
$931$	−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
$936$	−0.656854	+	10.7967i	−0.0214700	+	0.352901i
$937$	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	$0.0168976\pi$
$941$	32.2602	+	32.2602i	1.05165	+	1.05165i	0.0530603	+	0.998591i	$0.483102\pi$
$942$	27.2440	+	10.4063i	0.887658	+	0.339055i
$943$	−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	−0.996877	−	0.0789717i	$-0.974836\pi$
$947$	−28.2470	+	28.2470i	−0.917905	+	0.917905i	0.0789717	+	0.996877i	$0.474836\pi$
$948$	−7.07107	−	15.8114i	−0.229658	−	0.513530i
$949$	3.67544	+	4.64911i	0.119310	+	0.150917i
$950$			1.64371i			0.0533290i
$951$	40.9334	+	15.6352i	1.32736	+	0.507005i
$952$		0			0
$953$	53.9324			1.74704			0.873520	−	0.486788i	$-0.161831\pi$
$953$	53.9324			1.74704			0.873520	+	0.486788i	$0.161831\pi$
$954$	−0.236068	−	4.23607i	−0.00764298	−	0.137148i
$955$	−17.4868	+	17.4868i	−0.565861	+	0.565861i
$956$	−3.42079	+	3.42079i	−0.110636	+	0.110636i
$957$	14.4721	+	5.52786i	0.467818	+	0.178690i
$958$	31.8114			1.02778
$959$		0			0
$960$	0.618034	−	1.61803i	0.0199470	−	0.0522218i
$961$			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
$969$	−1.66979	+	4.37157i	−0.0536414	+	0.140435i
$970$	5.16228	+	5.16228i	0.165751	+	0.165751i
$971$			35.3181i			1.13341i	0.823920	+	0.566706i	$0.191782\pi$
$971$			35.3181i			1.13341i	−0.823920	+	0.566706i	$0.808218\pi$
$972$	13.4350	−	7.90569i	0.430929	−	0.253575i
$973$		0			0
$974$	−25.4558			−0.815658
$975$	1.86997	+	5.95846i	0.0598870	+	0.190823i
$976$	14.6491			0.468907
$977$	−30.6165	−	30.6165i	−0.979508	−	0.979508i	0.0202867	−	0.999794i	$-0.493542\pi$
$977$	−30.6165	−	30.6165i	−0.979508	−	0.979508i	−0.999794	+	0.0202867i	$0.993542\pi$
$978$	−10.3246	−	23.0864i	−0.330143	−	0.738222i
$979$			14.3246i			0.457815i
$980$	4.94975	+	4.94975i	0.158114	+	0.158114i
$981$	2.63506	+	47.2842i	0.0841309	+	1.50967i
$982$	20.0000	+	20.0000i	0.638226	+	0.638226i
$983$	−24.0044	+	24.0044i	−0.765621	+	0.765621i	−0.977332	−	0.211711i	$-0.932096\pi$
$983$	−24.0044	+	24.0044i	−0.765621	+	0.765621i	0.211711	+	0.977332i	$0.432096\pi$
$984$	−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
$990$	−5.99070	+	0.333851i	−0.190397	+	0.0106105i
$991$	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
$993$	8.29180	−	21.7082i	0.263132	−	0.688889i
$994$		0			0
$995$	−1.41421	+	1.41421i	−0.0448336	+	0.0448336i
$996$	4.94427	−	12.9443i	0.156665	−	0.410155i
$997$	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
$999$	−26.1235	+	13.4744i	−0.826512	+	0.426312i

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
390.2.p.g.161.2	✓	8	3.2	odd	2	inner
390.2.p.g.161.4	yes	8	1.1	even	1	trivial
390.2.p.g.281.2	yes	8	13.8	odd	4	inner
390.2.p.g.281.4	yes	8	39.8	even	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} +(1.61803 + 0.618034i) 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} +(1.61803 + 0.618034i) q^{15} -1.00000 q^{16} -1.64371 q^{17} +(2.99535 - 0.166925i) q^{18} +(1.16228 - 1.16228i) q^{19} +(-0.707107 + 0.707107i) q^{20} -2.00000 q^{22} -4.47214 q^{23} +(-0.618034 + 1.61803i) 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} +(-1.23607 + 3.23607i) q^{33} +(-1.16228 - 1.16228i) q^{34} +(2.23607 + 2.00000i) q^{36} +(-4.00000 - 4.00000i) q^{37} +1.64371 q^{38} +(5.95846 - 1.86997i) q^{39} -1.00000 q^{40} +(2.23607 + 2.23607i) q^{41} +0.837722i q^{43} +(-1.41421 - 1.41421i) q^{44} +(2.99535 - 0.166925i) 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} +(4.61803 - 2.38197i) q^{54} -2.00000 q^{55} +(1.01587 - 2.65958i) q^{57} +(3.16228 - 3.16228i) q^{58} +(-3.05792 + 3.05792i) q^{59} +(-0.618034 + 1.61803i) 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} +(0.166925 + 2.99535i) q^{72} +(1.16228 + 1.16228i) q^{73} -5.65685i q^{74} +(0.707107 + 1.58114i) q^{75} +(1.16228 + 1.16228i) q^{76} +(5.53553 + 2.89100i) 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} +(-2.62210 + 6.86474i) q^{93} -2.32456 q^{94} +1.64371 q^{95} +(-1.61803 - 0.618034i) q^{96} +(5.16228 - 5.16228i) q^{97} +(4.94975 - 4.94975i) q^{98} +(0.333851 + 5.99070i) 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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