LMFDB - Embedded newform 1950.2.z.d.1849.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [1950,2,Mod(1699,1950)] 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("1950.1699"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(1950, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([0, 3, 4])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 1950 = 2 \cdot 3 \cdot 5^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1950.z (of order $6$, degree $2$, not minimal)

Newform invariants

comment:select newform

sage:traces = [4,0,0,2,0,-2,0,0,2,0,6,0,0,12] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(14)] == traces)

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

Self dual:	no
Analytic conductor:	$15.5708283941$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(\zeta_{6})$
Coefficient field:	$\Q(\zeta_{12})$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{2} + 1 $ x^4 - x^2 + 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 390)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			1849.1
Root			$-0.866025 - 0.500000i$ of defining polynomial
Character	$\chi$	$=$	1950.1849
Dual form			1950.2.z.d.1699.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.866025 + 0.500000i) q^{2} +(0.866025 - 0.500000i) q^{3} +(0.500000 - 0.866025i) q^{4} +(-0.500000 + 0.866025i) q^{6} +(-2.59808 - 1.50000i) q^{7} +1.00000i q^{8} +(0.500000 - 0.866025i) q^{9} +(1.50000 + 2.59808i) q^{11} -1.00000i q^{12} +(-2.59808 + 2.50000i) q^{13} +3.00000 q^{14} +(-0.500000 - 0.866025i) q^{16} +1.00000i q^{18} +(1.50000 - 2.59808i) q^{19} -3.00000 q^{21} +(-2.59808 - 1.50000i) q^{22} +(3.46410 - 2.00000i) q^{23} +(0.500000 + 0.866025i) q^{24} +(1.00000 - 3.46410i) q^{26} -1.00000i q^{27} +(-2.59808 + 1.50000i) q^{28} +(-2.00000 - 3.46410i) q^{29} +6.00000 q^{31} +(0.866025 + 0.500000i) q^{32} +(2.59808 + 1.50000i) q^{33} +(-0.500000 - 0.866025i) q^{36} +(7.79423 - 4.50000i) q^{37} +3.00000i q^{38} +(-1.00000 + 3.46410i) q^{39} +(5.00000 + 8.66025i) q^{41} +(2.59808 - 1.50000i) q^{42} +(-8.66025 - 5.00000i) q^{43} +3.00000 q^{44} +(-2.00000 + 3.46410i) q^{46} -3.00000i q^{47} +(-0.866025 - 0.500000i) q^{48} +(1.00000 + 1.73205i) q^{49} +(0.866025 + 3.50000i) q^{52} -9.00000i q^{53} +(0.500000 + 0.866025i) q^{54} +(1.50000 - 2.59808i) q^{56} -3.00000i q^{57} +(3.46410 + 2.00000i) q^{58} +(6.00000 - 10.3923i) q^{59} +(3.00000 - 5.19615i) q^{61} +(-5.19615 + 3.00000i) q^{62} +(-2.59808 + 1.50000i) q^{63} -1.00000 q^{64} -3.00000 q^{66} +(-6.92820 + 4.00000i) q^{67} +(2.00000 - 3.46410i) q^{69} +(7.00000 - 12.1244i) q^{71} +(0.866025 + 0.500000i) q^{72} +8.00000i q^{73} +(-4.50000 + 7.79423i) q^{74} +(-1.50000 - 2.59808i) q^{76} -9.00000i q^{77} +(-0.866025 - 3.50000i) q^{78} -6.00000 q^{79} +(-0.500000 - 0.866025i) q^{81} +(-8.66025 - 5.00000i) q^{82} -16.0000i q^{83} +(-1.50000 + 2.59808i) q^{84} +10.0000 q^{86} +(-3.46410 - 2.00000i) q^{87} +(-2.59808 + 1.50000i) q^{88} +(-1.50000 - 2.59808i) q^{89} +(10.5000 - 2.59808i) q^{91} -4.00000i q^{92} +(5.19615 - 3.00000i) q^{93} +(1.50000 + 2.59808i) q^{94} +1.00000 q^{96} +(-6.92820 - 4.00000i) q^{97} +(-1.73205 - 1.00000i) q^{98} +3.00000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 2 q^{4} - 2 q^{6} + 2 q^{9} + 6 q^{11} + 12 q^{14} - 2 q^{16} + 6 q^{19} - 12 q^{21} + 2 q^{24} + 4 q^{26} - 8 q^{29} + 24 q^{31} - 2 q^{36} - 4 q^{39} + 20 q^{41} + 12 q^{44} - 8 q^{46} + 4 q^{49}+ \cdots + 12 q^{99}+O(q^{100}) $ 4 * q + 2 * q^4 - 2 * q^6 + 2 * q^9 + 6 * q^11 + 12 * q^14 - 2 * q^16 + 6 * q^19 - 12 * q^21 + 2 * q^24 + 4 * q^26 - 8 * q^29 + 24 * q^31 - 2 * q^36 - 4 * q^39 + 20 * q^41 + 12 * q^44 - 8 * q^46 + 4 * q^49 + 2 * q^54 + 6 * q^56 + 24 * q^59 + 12 * q^61 - 4 * q^64 - 12 * q^66 + 8 * q^69 + 28 * q^71 - 18 * q^74 - 6 * q^76 - 24 * q^79 - 2 * q^81 - 6 * q^84 + 40 * q^86 - 6 * q^89 + 42 * q^91 + 6 * q^94 + 4 * q^96 + 12 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1950\mathbb{Z}\right)^\times$.

$n$	$301$	$1301$	$1327$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$1$	$-1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−0.866025	+	0.500000i	−0.612372	+	0.353553i
$2$	−0.866025	+	0.500000i	−0.612372	+	0.353553i
$3$	0.866025	−	0.500000i	0.500000	−	0.288675i
$3$	0.866025	−	0.500000i	0.500000	−	0.288675i
$4$	0.500000	−	0.866025i	0.250000	−	0.433013i
$5$		0			0
$5$		0			0
$6$	−0.500000	+	0.866025i	−0.204124	+	0.353553i
$7$	−2.59808	−	1.50000i	−0.981981	−	0.566947i	−0.0791130	−	0.996866i	$-0.525209\pi$
$7$	−2.59808	−	1.50000i	−0.981981	−	0.566947i	−0.902867	+	0.429919i	$0.858542\pi$
$8$			1.00000i			0.353553i
$9$	0.500000	−	0.866025i	0.166667	−	0.288675i
$10$		0			0
$11$	1.50000	+	2.59808i	0.452267	+	0.783349i	0.998526	−	0.0542666i	$-0.0172821\pi$
$11$	1.50000	+	2.59808i	0.452267	+	0.783349i	−0.546259	+	0.837616i	$0.683949\pi$
$12$		−	1.00000i		−	0.288675i
$13$	−2.59808	+	2.50000i	−0.720577	+	0.693375i
$13$	−2.59808	+	2.50000i	−0.720577	+	0.693375i
$14$	3.00000			0.801784
$15$		0			0
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$17$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$18$			1.00000i			0.235702i
$19$	1.50000	−	2.59808i	0.344124	−	0.596040i	−0.641071	−	0.767482i	$-0.721509\pi$
$19$	1.50000	−	2.59808i	0.344124	−	0.596040i	0.985194	+	0.171442i	$0.0548427\pi$
$20$		0			0
$21$	−3.00000			−0.654654
$22$	−2.59808	−	1.50000i	−0.553912	−	0.319801i
$23$	3.46410	−	2.00000i	0.722315	−	0.417029i	−0.0932891	−	0.995639i	$-0.529738\pi$
$23$	3.46410	−	2.00000i	0.722315	−	0.417029i	0.815604	+	0.578610i	$0.196405\pi$
$24$	0.500000	+	0.866025i	0.102062	+	0.176777i
$25$		0			0
$26$	1.00000	−	3.46410i	0.196116	−	0.679366i
$27$		−	1.00000i		−	0.192450i
$28$	−2.59808	+	1.50000i	−0.490990	+	0.283473i
$29$	−2.00000	−	3.46410i	−0.371391	−	0.643268i	0.618389	−	0.785872i	$-0.287786\pi$
$29$	−2.00000	−	3.46410i	−0.371391	−	0.643268i	−0.989780	+	0.142605i	$0.954452\pi$
$30$		0			0
$31$	6.00000			1.07763			0.538816	−	0.842424i	$-0.318872\pi$
$31$	6.00000			1.07763			0.538816	+	0.842424i	$0.318872\pi$
$32$	0.866025	+	0.500000i	0.153093	+	0.0883883i
$33$	2.59808	+	1.50000i	0.452267	+	0.261116i
$34$		0			0
$35$		0			0
$36$	−0.500000	−	0.866025i	−0.0833333	−	0.144338i
$37$	7.79423	−	4.50000i	1.28136	−	0.739795i	0.304266	−	0.952587i	$-0.401589\pi$
$37$	7.79423	−	4.50000i	1.28136	−	0.739795i	0.977098	+	0.212792i	$0.0682556\pi$
$38$			3.00000i			0.486664i
$39$	−1.00000	+	3.46410i	−0.160128	+	0.554700i
$40$		0			0
$41$	5.00000	+	8.66025i	0.780869	+	1.35250i	0.931436	+	0.363905i	$0.118557\pi$
$41$	5.00000	+	8.66025i	0.780869	+	1.35250i	−0.150567	+	0.988600i	$0.548110\pi$
$42$	2.59808	−	1.50000i	0.400892	−	0.231455i
$43$	−8.66025	−	5.00000i	−1.32068	−	0.762493i	−0.336840	−	0.941562i	$-0.609358\pi$
$43$	−8.66025	−	5.00000i	−1.32068	−	0.762493i	−0.983836	+	0.179069i	$0.942691\pi$
$44$	3.00000			0.452267
$45$		0			0
$46$	−2.00000	+	3.46410i	−0.294884	+	0.510754i
$47$		−	3.00000i		−	0.437595i	−0.975770	−	0.218797i	$-0.929787\pi$
$47$		−	3.00000i		−	0.437595i	0.975770	−	0.218797i	$-0.0702134\pi$
$48$	−0.866025	−	0.500000i	−0.125000	−	0.0721688i
$49$	1.00000	+	1.73205i	0.142857	+	0.247436i
$50$		0			0
$51$		0			0
$52$	0.866025	+	3.50000i	0.120096	+	0.485363i
$53$		−	9.00000i		−	1.23625i	−0.786082	−	0.618123i	$-0.787894\pi$
$53$		−	9.00000i		−	1.23625i	0.786082	−	0.618123i	$-0.212106\pi$
$54$	0.500000	+	0.866025i	0.0680414	+	0.117851i
$55$		0			0
$56$	1.50000	−	2.59808i	0.200446	−	0.347183i
$57$		−	3.00000i		−	0.397360i
$58$	3.46410	+	2.00000i	0.454859	+	0.262613i
$59$	6.00000	−	10.3923i	0.781133	−	1.35296i	−0.150148	−	0.988663i	$-0.547975\pi$
$59$	6.00000	−	10.3923i	0.781133	−	1.35296i	0.931282	−	0.364299i	$-0.118692\pi$
$60$		0			0
$61$	3.00000	−	5.19615i	0.384111	−	0.665299i	−0.607535	−	0.794293i	$-0.707841\pi$
$61$	3.00000	−	5.19615i	0.384111	−	0.665299i	0.991645	+	0.128994i	$0.0411748\pi$
$62$	−5.19615	+	3.00000i	−0.659912	+	0.381000i
$63$	−2.59808	+	1.50000i	−0.327327	+	0.188982i
$64$	−1.00000			−0.125000
$65$		0			0
$66$	−3.00000			−0.369274
$67$	−6.92820	+	4.00000i	−0.846415	+	0.488678i	−0.859440	−	0.511237i	$-0.829187\pi$
$67$	−6.92820	+	4.00000i	−0.846415	+	0.488678i	0.0130248	+	0.999915i	$0.495854\pi$
$68$		0			0
$69$	2.00000	−	3.46410i	0.240772	−	0.417029i
$70$		0			0
$71$	7.00000	−	12.1244i	0.830747	−	1.43890i	−0.0666994	−	0.997773i	$-0.521247\pi$
$71$	7.00000	−	12.1244i	0.830747	−	1.43890i	0.897447	−	0.441123i	$-0.145420\pi$
$72$	0.866025	+	0.500000i	0.102062	+	0.0589256i
$73$			8.00000i			0.936329i	0.883641	+	0.468165i	$0.155085\pi$
$73$			8.00000i			0.936329i	−0.883641	+	0.468165i	$0.844915\pi$
$74$	−4.50000	+	7.79423i	−0.523114	+	0.906061i
$75$		0			0
$76$	−1.50000	−	2.59808i	−0.172062	−	0.298020i
$77$		−	9.00000i		−	1.02565i
$78$	−0.866025	−	3.50000i	−0.0980581	−	0.396297i
$79$	−6.00000			−0.675053			−0.337526	−	0.941316i	$-0.609590\pi$
$79$	−6.00000			−0.675053			−0.337526	+	0.941316i	$0.609590\pi$
$80$		0			0
$81$	−0.500000	−	0.866025i	−0.0555556	−	0.0962250i
$82$	−8.66025	−	5.00000i	−0.956365	−	0.552158i
$83$		−	16.0000i		−	1.75623i	−0.478451	−	0.878114i	$-0.658802\pi$
$83$		−	16.0000i		−	1.75623i	0.478451	−	0.878114i	$-0.341198\pi$
$84$	−1.50000	+	2.59808i	−0.163663	+	0.283473i
$85$		0			0
$86$	10.0000			1.07833
$87$	−3.46410	−	2.00000i	−0.371391	−	0.214423i
$88$	−2.59808	+	1.50000i	−0.276956	+	0.159901i
$89$	−1.50000	−	2.59808i	−0.159000	−	0.275396i	0.775509	−	0.631337i	$-0.217494\pi$
$89$	−1.50000	−	2.59808i	−0.159000	−	0.275396i	−0.934508	+	0.355942i	$0.884160\pi$
$90$		0			0
$91$	10.5000	−	2.59808i	1.10070	−	0.272352i
$92$		−	4.00000i		−	0.417029i
$93$	5.19615	−	3.00000i	0.538816	−	0.311086i
$94$	1.50000	+	2.59808i	0.154713	+	0.267971i
$95$		0			0
$96$	1.00000			0.102062
$97$	−6.92820	−	4.00000i	−0.703452	−	0.406138i	0.105180	−	0.994453i	$-0.466458\pi$
$97$	−6.92820	−	4.00000i	−0.703452	−	0.406138i	−0.808632	+	0.588315i	$0.799792\pi$
$98$	−1.73205	−	1.00000i	−0.174964	−	0.101015i
$99$	3.00000			0.301511
$100$		0			0
$101$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$101$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$102$		0			0
$103$			15.0000i			1.47799i	0.673709	+	0.738997i	$0.264700\pi$
$103$			15.0000i			1.47799i	−0.673709	+	0.738997i	$0.735300\pi$
$104$	−2.50000	−	2.59808i	−0.245145	−	0.254762i
$105$		0			0
$106$	4.50000	+	7.79423i	0.437079	+	0.757042i
$107$	1.73205	−	1.00000i	0.167444	−	0.0966736i	−0.413936	−	0.910306i	$-0.635846\pi$
$107$	1.73205	−	1.00000i	0.167444	−	0.0966736i	0.581380	+	0.813632i	$0.302513\pi$
$108$	−0.866025	−	0.500000i	−0.0833333	−	0.0481125i
$109$	2.00000			0.191565			0.0957826	−	0.995402i	$-0.469465\pi$
$109$	2.00000			0.191565			0.0957826	+	0.995402i	$0.469465\pi$
$110$		0			0
$111$	4.50000	−	7.79423i	0.427121	−	0.739795i
$112$			3.00000i			0.283473i
$113$	−6.92820	−	4.00000i	−0.651751	−	0.376288i	0.137376	−	0.990519i	$-0.456133\pi$
$113$	−6.92820	−	4.00000i	−0.651751	−	0.376288i	−0.789127	+	0.614231i	$0.789466\pi$
$114$	1.50000	+	2.59808i	0.140488	+	0.243332i
$115$		0			0
$116$	−4.00000			−0.371391
$117$	0.866025	+	3.50000i	0.0800641	+	0.323575i
$118$			12.0000i			1.10469i
$119$		0			0
$120$		0			0
$121$	1.00000	−	1.73205i	0.0909091	−	0.157459i
$122$			6.00000i			0.543214i
$123$	8.66025	+	5.00000i	0.780869	+	0.450835i
$124$	3.00000	−	5.19615i	0.269408	−	0.466628i
$125$		0			0
$126$	1.50000	−	2.59808i	0.133631	−	0.231455i
$127$	2.59808	−	1.50000i	0.230542	−	0.133103i	−0.380280	−	0.924871i	$-0.624172\pi$
$127$	2.59808	−	1.50000i	0.230542	−	0.133103i	0.610822	+	0.791768i	$0.290839\pi$
$128$	0.866025	−	0.500000i	0.0765466	−	0.0441942i
$129$	−10.0000			−0.880451
$130$		0			0
$131$	−3.00000			−0.262111			−0.131056	−	0.991375i	$-0.541837\pi$
$131$	−3.00000			−0.262111			−0.131056	+	0.991375i	$0.541837\pi$
$132$	2.59808	−	1.50000i	0.226134	−	0.130558i
$133$	−7.79423	+	4.50000i	−0.675845	+	0.390199i
$134$	4.00000	−	6.92820i	0.345547	−	0.598506i
$135$		0			0
$136$		0			0
$137$	−10.3923	−	6.00000i	−0.887875	−	0.512615i	−0.0146279	−	0.999893i	$-0.504656\pi$
$137$	−10.3923	−	6.00000i	−0.887875	−	0.512615i	−0.873247	+	0.487278i	$0.837990\pi$
$138$			4.00000i			0.340503i
$139$	−8.50000	+	14.7224i	−0.720961	+	1.24874i	0.239655	+	0.970858i	$0.422966\pi$
$139$	−8.50000	+	14.7224i	−0.720961	+	1.24874i	−0.960615	+	0.277882i	$0.910368\pi$
$140$		0			0
$141$	−1.50000	−	2.59808i	−0.126323	−	0.218797i
$142$			14.0000i			1.17485i
$143$	−10.3923	−	3.00000i	−0.869048	−	0.250873i
$144$	−1.00000			−0.0833333
$145$		0			0
$146$	−4.00000	−	6.92820i	−0.331042	−	0.573382i
$147$	1.73205	+	1.00000i	0.142857	+	0.0824786i
$148$		−	9.00000i		−	0.739795i
$149$	−1.00000	+	1.73205i	−0.0819232	+	0.141895i	−0.904076	−	0.427372i	$-0.859440\pi$
$149$	−1.00000	+	1.73205i	−0.0819232	+	0.141895i	0.822153	+	0.569267i	$0.192773\pi$
$150$		0			0
$151$	14.0000			1.13930			0.569652	−	0.821886i	$-0.307078\pi$
$151$	14.0000			1.13930			0.569652	+	0.821886i	$0.307078\pi$
$152$	2.59808	+	1.50000i	0.210732	+	0.121666i
$153$		0			0
$154$	4.50000	+	7.79423i	0.362620	+	0.628077i
$155$		0			0
$156$	2.50000	+	2.59808i	0.200160	+	0.208013i
$157$		−	17.0000i		−	1.35675i	−0.734717	−	0.678374i	$-0.762685\pi$
$157$		−	17.0000i		−	1.35675i	0.734717	−	0.678374i	$-0.237315\pi$
$158$	5.19615	−	3.00000i	0.413384	−	0.238667i
$159$	−4.50000	−	7.79423i	−0.356873	−	0.618123i
$160$		0			0
$161$	−12.0000			−0.945732
$162$	0.866025	+	0.500000i	0.0680414	+	0.0392837i
$163$	17.3205	+	10.0000i	1.35665	+	0.783260i	0.989170	−	0.146772i	$-0.0468885\pi$
$163$	17.3205	+	10.0000i	1.35665	+	0.783260i	0.367477	+	0.930033i	$0.380222\pi$
$164$	10.0000			0.780869
$165$		0			0
$166$	8.00000	+	13.8564i	0.620920	+	1.07547i
$167$	7.79423	−	4.50000i	0.603136	−	0.348220i	−0.167139	−	0.985933i	$-0.553453\pi$
$167$	7.79423	−	4.50000i	0.603136	−	0.348220i	0.770274	+	0.637713i	$0.220119\pi$
$168$		−	3.00000i		−	0.231455i
$169$	0.500000	−	12.9904i	0.0384615	−	0.999260i
$170$		0			0
$171$	−1.50000	−	2.59808i	−0.114708	−	0.198680i
$172$	−8.66025	+	5.00000i	−0.660338	+	0.381246i
$173$	11.2583	+	6.50000i	0.855955	+	0.494186i	0.862656	−	0.505792i	$-0.168800\pi$
$173$	11.2583	+	6.50000i	0.855955	+	0.494186i	−0.00670064	+	0.999978i	$0.502133\pi$
$174$	4.00000			0.303239
$175$		0			0
$176$	1.50000	−	2.59808i	0.113067	−	0.195837i
$177$		−	12.0000i		−	0.901975i
$178$	2.59808	+	1.50000i	0.194734	+	0.112430i
$179$	2.00000	+	3.46410i	0.149487	+	0.258919i	0.931038	−	0.364922i	$-0.118904\pi$
$179$	2.00000	+	3.46410i	0.149487	+	0.258919i	−0.781551	+	0.623841i	$0.785571\pi$
$180$		0			0
$181$	−10.0000			−0.743294			−0.371647	−	0.928374i	$-0.621207\pi$
$181$	−10.0000			−0.743294			−0.371647	+	0.928374i	$0.621207\pi$
$182$	−7.79423	+	7.50000i	−0.577747	+	0.555937i
$183$		−	6.00000i		−	0.443533i
$184$	2.00000	+	3.46410i	0.147442	+	0.255377i
$185$		0			0
$186$	−3.00000	+	5.19615i	−0.219971	+	0.381000i
$187$		0			0
$188$	−2.59808	−	1.50000i	−0.189484	−	0.109399i
$189$	−1.50000	+	2.59808i	−0.109109	+	0.188982i
$190$		0			0
$191$	3.00000	−	5.19615i	0.217072	−	0.375980i	−0.736839	−	0.676068i	$-0.763683\pi$
$191$	3.00000	−	5.19615i	0.217072	−	0.375980i	0.953912	+	0.300088i	$0.0970159\pi$
$192$	−0.866025	+	0.500000i	−0.0625000	+	0.0360844i
$193$	−6.92820	+	4.00000i	−0.498703	+	0.287926i	−0.728178	−	0.685388i	$-0.759632\pi$
$193$	−6.92820	+	4.00000i	−0.498703	+	0.287926i	0.229475	+	0.973315i	$0.426299\pi$
$194$	8.00000			0.574367
$195$		0			0
$196$	2.00000			0.142857
$197$	9.52628	−	5.50000i	0.678719	−	0.391859i	−0.120653	−	0.992695i	$-0.538499\pi$
$197$	9.52628	−	5.50000i	0.678719	−	0.391859i	0.799372	+	0.600836i	$0.205166\pi$
$198$	−2.59808	+	1.50000i	−0.184637	+	0.106600i
$199$	−5.00000	+	8.66025i	−0.354441	+	0.613909i	−0.987022	−	0.160585i	$-0.948662\pi$
$199$	−5.00000	+	8.66025i	−0.354441	+	0.613909i	0.632581	+	0.774494i	$0.281995\pi$
$200$		0			0
$201$	−4.00000	+	6.92820i	−0.282138	+	0.488678i
$202$		0			0
$203$			12.0000i			0.842235i
$204$		0			0
$205$		0			0
$206$	−7.50000	−	12.9904i	−0.522550	−	0.905083i
$207$		−	4.00000i		−	0.278019i
$208$	3.46410	+	1.00000i	0.240192	+	0.0693375i
$209$	9.00000			0.622543
$210$		0			0
$211$	−4.50000	−	7.79423i	−0.309793	−	0.536577i	0.668524	−	0.743690i	$-0.266926\pi$
$211$	−4.50000	−	7.79423i	−0.309793	−	0.536577i	−0.978317	+	0.207114i	$0.933593\pi$
$212$	−7.79423	−	4.50000i	−0.535310	−	0.309061i
$213$		−	14.0000i		−	0.959264i
$214$	−1.00000	+	1.73205i	−0.0683586	+	0.118401i
$215$		0			0
$216$	1.00000			0.0680414
$217$	−15.5885	−	9.00000i	−1.05821	−	0.610960i
$218$	−1.73205	+	1.00000i	−0.117309	+	0.0677285i
$219$	4.00000	+	6.92820i	0.270295	+	0.468165i
$220$		0			0
$221$		0			0
$222$			9.00000i			0.604040i
$223$	9.52628	−	5.50000i	0.637927	−	0.368307i	−0.145889	−	0.989301i	$-0.546604\pi$
$223$	9.52628	−	5.50000i	0.637927	−	0.368307i	0.783815	+	0.620994i	$0.213271\pi$
$224$	−1.50000	−	2.59808i	−0.100223	−	0.173591i
$225$		0			0
$226$	8.00000			0.532152
$227$	13.8564	+	8.00000i	0.919682	+	0.530979i	0.883534	−	0.468368i	$-0.155158\pi$
$227$	13.8564	+	8.00000i	0.919682	+	0.530979i	0.0361484	+	0.999346i	$0.488491\pi$
$228$	−2.59808	−	1.50000i	−0.172062	−	0.0993399i
$229$	10.0000			0.660819			0.330409	−	0.943838i	$-0.392813\pi$
$229$	10.0000			0.660819			0.330409	+	0.943838i	$0.392813\pi$
$230$		0			0
$231$	−4.50000	−	7.79423i	−0.296078	−	0.512823i
$232$	3.46410	−	2.00000i	0.227429	−	0.131306i
$233$			6.00000i			0.393073i	0.980497	+	0.196537i	$0.0629694\pi$
$233$			6.00000i			0.393073i	−0.980497	+	0.196537i	$0.937031\pi$
$234$	−2.50000	−	2.59808i	−0.163430	−	0.169842i
$235$		0			0
$236$	−6.00000	−	10.3923i	−0.390567	−	0.676481i
$237$	−5.19615	+	3.00000i	−0.337526	+	0.194871i
$238$		0			0
$239$	26.0000			1.68180			0.840900	−	0.541190i	$-0.182026\pi$
$239$	26.0000			1.68180			0.840900	+	0.541190i	$0.182026\pi$
$240$		0			0
$241$	−3.50000	+	6.06218i	−0.225455	+	0.390499i	−0.956456	−	0.291877i	$-0.905720\pi$
$241$	−3.50000	+	6.06218i	−0.225455	+	0.390499i	0.731001	+	0.682376i	$0.239053\pi$
$242$			2.00000i			0.128565i
$243$	−0.866025	−	0.500000i	−0.0555556	−	0.0320750i
$244$	−3.00000	−	5.19615i	−0.192055	−	0.332650i
$245$		0			0
$246$	−10.0000			−0.637577
$247$	2.59808	+	10.5000i	0.165312	+	0.668099i
$248$			6.00000i			0.381000i
$249$	−8.00000	−	13.8564i	−0.506979	−	0.878114i
$250$		0			0
$251$	0.500000	−	0.866025i	0.0315597	−	0.0546630i	−0.849814	−	0.527082i	$-0.823286\pi$
$251$	0.500000	−	0.866025i	0.0315597	−	0.0546630i	0.881374	+	0.472419i	$0.156619\pi$
$252$			3.00000i			0.188982i
$253$	10.3923	+	6.00000i	0.653359	+	0.377217i
$254$	−1.50000	+	2.59808i	−0.0941184	+	0.163018i
$255$		0			0
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	10.3923	−	6.00000i	0.648254	−	0.374270i	−0.139533	−	0.990217i	$-0.544560\pi$
$257$	10.3923	−	6.00000i	0.648254	−	0.374270i	0.787787	+	0.615948i	$0.211227\pi$
$258$	8.66025	−	5.00000i	0.539164	−	0.311286i
$259$	−27.0000			−1.67770
$260$		0			0
$261$	−4.00000			−0.247594
$262$	2.59808	−	1.50000i	0.160510	−	0.0926703i
$263$	26.8468	−	15.5000i	1.65544	−	0.955771i	0.680666	−	0.732594i	$-0.261691\pi$
$263$	26.8468	−	15.5000i	1.65544	−	0.955771i	0.974778	−	0.223177i	$-0.0716428\pi$
$264$	−1.50000	+	2.59808i	−0.0923186	+	0.159901i
$265$		0			0
$266$	4.50000	−	7.79423i	0.275913	−	0.477895i
$267$	−2.59808	−	1.50000i	−0.159000	−	0.0917985i
$268$			8.00000i			0.488678i
$269$	−2.00000	+	3.46410i	−0.121942	+	0.211210i	−0.920534	−	0.390664i	$-0.872246\pi$
$269$	−2.00000	+	3.46410i	−0.121942	+	0.211210i	0.798591	+	0.601874i	$0.205579\pi$
$270$		0			0
$271$	6.00000	+	10.3923i	0.364474	+	0.631288i	0.988692	−	0.149963i	$-0.0479155\pi$
$271$	6.00000	+	10.3923i	0.364474	+	0.631288i	−0.624218	+	0.781251i	$0.714582\pi$
$272$		0			0
$273$	7.79423	−	7.50000i	0.471728	−	0.453921i
$274$	12.0000			0.724947
$275$		0			0
$276$	−2.00000	−	3.46410i	−0.120386	−	0.208514i
$277$	26.8468	+	15.5000i	1.61307	+	0.931305i	0.988654	+	0.150210i	$0.0479951\pi$
$277$	26.8468	+	15.5000i	1.61307	+	0.931305i	0.624413	+	0.781094i	$0.285338\pi$
$278$		−	17.0000i		−	1.01959i
$279$	3.00000	−	5.19615i	0.179605	−	0.311086i
$280$		0			0
$281$	−30.0000			−1.78965			−0.894825	−	0.446417i	$-0.852700\pi$
$281$	−30.0000			−1.78965			−0.894825	+	0.446417i	$0.852700\pi$
$282$	2.59808	+	1.50000i	0.154713	+	0.0893237i
$283$	−5.19615	+	3.00000i	−0.308879	+	0.178331i	−0.646425	−	0.762978i	$-0.723737\pi$
$283$	−5.19615	+	3.00000i	−0.308879	+	0.178331i	0.337546	+	0.941309i	$0.390403\pi$
$284$	−7.00000	−	12.1244i	−0.415374	−	0.719448i
$285$		0			0
$286$	10.5000	−	2.59808i	0.620878	−	0.153627i
$287$		−	30.0000i		−	1.77084i
$288$	0.866025	−	0.500000i	0.0510310	−	0.0294628i
$289$	−8.50000	−	14.7224i	−0.500000	−	0.866025i
$290$		0			0
$291$	−8.00000			−0.468968
$292$	6.92820	+	4.00000i	0.405442	+	0.234082i
$293$	−0.866025	−	0.500000i	−0.0505937	−	0.0292103i	0.474490	−	0.880261i	$-0.342633\pi$
$293$	−0.866025	−	0.500000i	−0.0505937	−	0.0292103i	−0.525084	+	0.851051i	$0.675966\pi$
$294$	−2.00000			−0.116642
$295$		0			0
$296$	4.50000	+	7.79423i	0.261557	+	0.453030i
$297$	2.59808	−	1.50000i	0.150756	−	0.0870388i
$298$		−	2.00000i		−	0.115857i
$299$	−4.00000	+	13.8564i	−0.231326	+	0.801337i
$300$		0			0
$301$	15.0000	+	25.9808i	0.864586	+	1.49751i
$302$	−12.1244	+	7.00000i	−0.697678	+	0.402805i
$303$		0			0
$304$	−3.00000			−0.172062
$305$		0			0
$306$		0			0
$307$			26.0000i			1.48390i	0.670456	+	0.741949i	$0.266098\pi$
$307$			26.0000i			1.48390i	−0.670456	+	0.741949i	$0.733902\pi$
$308$	−7.79423	−	4.50000i	−0.444117	−	0.256411i
$309$	7.50000	+	12.9904i	0.426660	+	0.738997i
$310$		0			0
$311$	−4.00000			−0.226819			−0.113410	−	0.993548i	$-0.536177\pi$
$311$	−4.00000			−0.226819			−0.113410	+	0.993548i	$0.536177\pi$
$312$	−3.46410	−	1.00000i	−0.196116	−	0.0566139i
$313$		−	26.0000i		−	1.46961i	−0.678280	−	0.734803i	$-0.737274\pi$
$313$		−	26.0000i		−	1.46961i	0.678280	−	0.734803i	$-0.262726\pi$
$314$	8.50000	+	14.7224i	0.479683	+	0.830835i
$315$		0			0
$316$	−3.00000	+	5.19615i	−0.168763	+	0.292306i
$317$			17.0000i			0.954815i	0.878682	+	0.477408i	$0.158423\pi$
$317$			17.0000i			0.954815i	−0.878682	+	0.477408i	$0.841577\pi$
$318$	7.79423	+	4.50000i	0.437079	+	0.252347i
$319$	6.00000	−	10.3923i	0.335936	−	0.581857i
$320$		0			0
$321$	1.00000	−	1.73205i	0.0558146	−	0.0966736i
$322$	10.3923	−	6.00000i	0.579141	−	0.334367i
$323$		0			0
$324$	−1.00000			−0.0555556
$325$		0			0
$326$	−20.0000			−1.10770
$327$	1.73205	−	1.00000i	0.0957826	−	0.0553001i
$328$	−8.66025	+	5.00000i	−0.478183	+	0.276079i
$329$	−4.50000	+	7.79423i	−0.248093	+	0.429710i
$330$		0			0
$331$	14.0000	−	24.2487i	0.769510	−	1.33283i	−0.168320	−	0.985732i	$-0.553834\pi$
$331$	14.0000	−	24.2487i	0.769510	−	1.33283i	0.937829	−	0.347097i	$-0.112833\pi$
$332$	−13.8564	−	8.00000i	−0.760469	−	0.439057i
$333$		−	9.00000i		−	0.493197i
$334$	−4.50000	+	7.79423i	−0.246229	+	0.426481i
$335$		0			0
$336$	1.50000	+	2.59808i	0.0818317	+	0.141737i
$337$			6.00000i			0.326841i	0.986557	+	0.163420i	$0.0522527\pi$
$337$			6.00000i			0.326841i	−0.986557	+	0.163420i	$0.947747\pi$
$338$	6.06218	+	11.5000i	0.329739	+	0.625518i
$339$	−8.00000			−0.434500
$340$		0			0
$341$	9.00000	+	15.5885i	0.487377	+	0.844162i
$342$	2.59808	+	1.50000i	0.140488	+	0.0811107i
$343$			15.0000i			0.809924i
$344$	5.00000	−	8.66025i	0.269582	−	0.466930i
$345$		0			0
$346$	−13.0000			−0.698884
$347$	20.7846	+	12.0000i	1.11578	+	0.644194i	0.940319	−	0.340293i	$-0.110526\pi$
$347$	20.7846	+	12.0000i	1.11578	+	0.644194i	0.175457	+	0.984487i	$0.443860\pi$
$348$	−3.46410	+	2.00000i	−0.185695	+	0.107211i
$349$	8.00000	+	13.8564i	0.428230	+	0.741716i	0.996716	−	0.0809766i	$-0.0258039\pi$
$349$	8.00000	+	13.8564i	0.428230	+	0.741716i	−0.568486	+	0.822693i	$0.692471\pi$
$350$		0			0
$351$	2.50000	+	2.59808i	0.133440	+	0.138675i
$352$			3.00000i			0.159901i
$353$	6.92820	−	4.00000i	0.368751	−	0.212899i	−0.304162	−	0.952620i	$-0.598376\pi$
$353$	6.92820	−	4.00000i	0.368751	−	0.212899i	0.672913	+	0.739722i	$0.265043\pi$
$354$	6.00000	+	10.3923i	0.318896	+	0.552345i
$355$		0			0
$356$	−3.00000			−0.159000
$357$		0			0
$358$	−3.46410	−	2.00000i	−0.183083	−	0.105703i
$359$	−30.0000			−1.58334			−0.791670	−	0.610949i	$-0.790788\pi$
$359$	−30.0000			−1.58334			−0.791670	+	0.610949i	$0.790788\pi$
$360$		0			0
$361$	5.00000	+	8.66025i	0.263158	+	0.455803i
$362$	8.66025	−	5.00000i	0.455173	−	0.262794i
$363$		−	2.00000i		−	0.104973i
$364$	3.00000	−	10.3923i	0.157243	−	0.544705i
$365$		0			0
$366$	3.00000	+	5.19615i	0.156813	+	0.271607i
$367$	6.92820	−	4.00000i	0.361649	−	0.208798i	−0.308155	−	0.951336i	$-0.599711\pi$
$367$	6.92820	−	4.00000i	0.361649	−	0.208798i	0.669804	+	0.742538i	$0.266378\pi$
$368$	−3.46410	−	2.00000i	−0.180579	−	0.104257i
$369$	10.0000			0.520579
$370$		0			0
$371$	−13.5000	+	23.3827i	−0.700885	+	1.21397i
$372$		−	6.00000i		−	0.311086i
$373$	−22.5167	−	13.0000i	−1.16587	−	0.673114i	−0.213165	−	0.977016i	$-0.568377\pi$
$373$	−22.5167	−	13.0000i	−1.16587	−	0.673114i	−0.952703	+	0.303902i	$0.901711\pi$
$374$		0			0
$375$		0			0
$376$	3.00000			0.154713
$377$	13.8564	+	4.00000i	0.713641	+	0.206010i
$378$		−	3.00000i		−	0.154303i
$379$	−16.5000	−	28.5788i	−0.847548	−	1.46800i	−0.883390	−	0.468639i	$-0.844745\pi$
$379$	−16.5000	−	28.5788i	−0.847548	−	1.46800i	0.0358418	−	0.999357i	$-0.488589\pi$
$380$		0			0
$381$	1.50000	−	2.59808i	0.0768473	−	0.133103i
$382$			6.00000i			0.306987i
$383$	3.46410	+	2.00000i	0.177007	+	0.102195i	0.585886	−	0.810394i	$-0.300747\pi$
$383$	3.46410	+	2.00000i	0.177007	+	0.102195i	−0.408879	+	0.912589i	$0.634080\pi$
$384$	0.500000	−	0.866025i	0.0255155	−	0.0441942i
$385$		0			0
$386$	4.00000	−	6.92820i	0.203595	−	0.352636i
$387$	−8.66025	+	5.00000i	−0.440225	+	0.254164i
$388$	−6.92820	+	4.00000i	−0.351726	+	0.203069i
$389$	−24.0000			−1.21685			−0.608424	−	0.793612i	$-0.708198\pi$
$389$	−24.0000			−1.21685			−0.608424	+	0.793612i	$0.708198\pi$
$390$		0			0
$391$		0			0
$392$	−1.73205	+	1.00000i	−0.0874818	+	0.0505076i
$393$	−2.59808	+	1.50000i	−0.131056	+	0.0756650i
$394$	−5.50000	+	9.52628i	−0.277086	+	0.479927i
$395$		0			0
$396$	1.50000	−	2.59808i	0.0753778	−	0.130558i
$397$	19.9186	+	11.5000i	0.999685	+	0.577168i	0.908155	−	0.418634i	$-0.137491\pi$
$397$	19.9186	+	11.5000i	0.999685	+	0.577168i	0.0915300	+	0.995802i	$0.470824\pi$
$398$		−	10.0000i		−	0.501255i
$399$	−4.50000	+	7.79423i	−0.225282	+	0.390199i
$400$		0			0
$401$	13.5000	+	23.3827i	0.674158	+	1.16768i	0.976714	+	0.214544i	$0.0688266\pi$
$401$	13.5000	+	23.3827i	0.674158	+	1.16768i	−0.302556	+	0.953131i	$0.597840\pi$
$402$		−	8.00000i		−	0.399004i
$403$	−15.5885	+	15.0000i	−0.776516	+	0.747203i
$404$		0			0
$405$		0			0
$406$	−6.00000	−	10.3923i	−0.297775	−	0.515761i
$407$	23.3827	+	13.5000i	1.15904	+	0.669170i
$408$		0			0
$409$	−3.50000	+	6.06218i	−0.173064	+	0.299755i	−0.939490	−	0.342578i	$-0.888700\pi$
$409$	−3.50000	+	6.06218i	−0.173064	+	0.299755i	0.766426	+	0.642333i	$0.222033\pi$
$410$		0			0
$411$	−12.0000			−0.591916
$412$	12.9904	+	7.50000i	0.639990	+	0.369498i
$413$	−31.1769	+	18.0000i	−1.53412	+	0.885722i
$414$	2.00000	+	3.46410i	0.0982946	+	0.170251i
$415$		0			0
$416$	−3.50000	+	0.866025i	−0.171602	+	0.0424604i
$417$			17.0000i			0.832494i
$418$	−7.79423	+	4.50000i	−0.381228	+	0.220102i
$419$	−6.00000	−	10.3923i	−0.293119	−	0.507697i	0.681426	−	0.731887i	$-0.261360\pi$
$419$	−6.00000	−	10.3923i	−0.293119	−	0.507697i	−0.974546	+	0.224189i	$0.928027\pi$
$420$		0			0
$421$	−28.0000			−1.36464			−0.682318	−	0.731055i	$-0.739028\pi$
$421$	−28.0000			−1.36464			−0.682318	+	0.731055i	$0.739028\pi$
$422$	7.79423	+	4.50000i	0.379417	+	0.219057i
$423$	−2.59808	−	1.50000i	−0.126323	−	0.0729325i
$424$	9.00000			0.437079
$425$		0			0
$426$	7.00000	+	12.1244i	0.339151	+	0.587427i
$427$	−15.5885	+	9.00000i	−0.754378	+	0.435541i
$428$		−	2.00000i		−	0.0966736i
$429$	−10.5000	+	2.59808i	−0.506945	+	0.125436i
$430$		0			0
$431$	6.00000	+	10.3923i	0.289010	+	0.500580i	0.973574	−	0.228373i	$-0.0733406\pi$
$431$	6.00000	+	10.3923i	0.289010	+	0.500580i	−0.684564	+	0.728953i	$0.740007\pi$
$432$	−0.866025	+	0.500000i	−0.0416667	+	0.0240563i
$433$	−13.8564	−	8.00000i	−0.665896	−	0.384455i	0.128624	−	0.991693i	$-0.458944\pi$
$433$	−13.8564	−	8.00000i	−0.665896	−	0.384455i	−0.794520	+	0.607238i	$0.792277\pi$
$434$	18.0000			0.864028
$435$		0			0
$436$	1.00000	−	1.73205i	0.0478913	−	0.0829502i
$437$		−	12.0000i		−	0.574038i
$438$	−6.92820	−	4.00000i	−0.331042	−	0.191127i
$439$	−15.0000	−	25.9808i	−0.715911	−	1.23999i	−0.962607	−	0.270901i	$-0.912678\pi$
$439$	−15.0000	−	25.9808i	−0.715911	−	1.23999i	0.246696	−	0.969093i	$-0.420655\pi$
$440$		0			0
$441$	2.00000			0.0952381
$442$		0			0
$443$			10.0000i			0.475114i	0.971374	+	0.237557i	$0.0763467\pi$
$443$			10.0000i			0.475114i	−0.971374	+	0.237557i	$0.923653\pi$
$444$	−4.50000	−	7.79423i	−0.213561	−	0.369898i
$445$		0			0
$446$	−5.50000	+	9.52628i	−0.260433	+	0.451082i
$447$			2.00000i			0.0945968i
$448$	2.59808	+	1.50000i	0.122748	+	0.0708683i
$449$	−17.5000	+	30.3109i	−0.825876	+	1.43046i	0.0753719	+	0.997155i	$0.475986\pi$
$449$	−17.5000	+	30.3109i	−0.825876	+	1.43046i	−0.901248	+	0.433304i	$0.857348\pi$
$450$		0			0
$451$	−15.0000	+	25.9808i	−0.706322	+	1.22339i
$452$	−6.92820	+	4.00000i	−0.325875	+	0.188144i
$453$	12.1244	−	7.00000i	0.569652	−	0.328889i
$454$	−16.0000			−0.750917
$455$		0			0
$456$	3.00000			0.140488
$457$	−36.3731	+	21.0000i	−1.70146	+	0.982339i	−0.757174	+	0.653213i	$0.773421\pi$
$457$	−36.3731	+	21.0000i	−1.70146	+	0.982339i	−0.944286	+	0.329125i	$0.893246\pi$
$458$	−8.66025	+	5.00000i	−0.404667	+	0.233635i
$459$		0			0
$460$		0			0
$461$	16.0000	−	27.7128i	0.745194	−	1.29071i	−0.204910	−	0.978781i	$-0.565690\pi$
$461$	16.0000	−	27.7128i	0.745194	−	1.29071i	0.950104	−	0.311933i	$-0.100977\pi$
$462$	7.79423	+	4.50000i	0.362620	+	0.209359i
$463$			24.0000i			1.11537i	0.830051	+	0.557687i	$0.188311\pi$
$463$			24.0000i			1.11537i	−0.830051	+	0.557687i	$0.811689\pi$
$464$	−2.00000	+	3.46410i	−0.0928477	+	0.160817i
$465$		0			0
$466$	−3.00000	−	5.19615i	−0.138972	−	0.240707i
$467$			8.00000i			0.370196i	0.982720	+	0.185098i	$0.0592602\pi$
$467$			8.00000i			0.370196i	−0.982720	+	0.185098i	$0.940740\pi$
$468$	3.46410	+	1.00000i	0.160128	+	0.0462250i
$469$	24.0000			1.10822
$470$		0			0
$471$	−8.50000	−	14.7224i	−0.391659	−	0.678374i
$472$	10.3923	+	6.00000i	0.478345	+	0.276172i
$473$		−	30.0000i		−	1.37940i
$474$	3.00000	−	5.19615i	0.137795	−	0.238667i
$475$		0			0
$476$		0			0
$477$	−7.79423	−	4.50000i	−0.356873	−	0.206041i
$478$	−22.5167	+	13.0000i	−1.02989	+	0.594606i
$479$	6.00000	+	10.3923i	0.274147	+	0.474837i	0.969920	−	0.243426i	$-0.0782712\pi$
$479$	6.00000	+	10.3923i	0.274147	+	0.474837i	−0.695773	+	0.718262i	$0.744938\pi$
$480$		0			0
$481$	−9.00000	+	31.1769i	−0.410365	+	1.42154i
$482$		−	7.00000i		−	0.318841i
$483$	−10.3923	+	6.00000i	−0.472866	+	0.273009i
$484$	−1.00000	−	1.73205i	−0.0454545	−	0.0787296i
$485$		0			0
$486$	1.00000			0.0453609
$487$	−25.1147	−	14.5000i	−1.13806	−	0.657058i	−0.192109	−	0.981374i	$-0.561533\pi$
$487$	−25.1147	−	14.5000i	−1.13806	−	0.657058i	−0.945949	+	0.324316i	$0.894866\pi$
$488$	5.19615	+	3.00000i	0.235219	+	0.135804i
$489$	20.0000			0.904431
$490$		0			0
$491$	−2.50000	−	4.33013i	−0.112823	−	0.195416i	0.804084	−	0.594515i	$-0.202656\pi$
$491$	−2.50000	−	4.33013i	−0.112823	−	0.195416i	−0.916908	+	0.399100i	$0.869323\pi$
$492$	8.66025	−	5.00000i	0.390434	−	0.225417i
$493$		0			0
$494$	−7.50000	−	7.79423i	−0.337441	−	0.350679i
$495$		0			0
$496$	−3.00000	−	5.19615i	−0.134704	−	0.233314i
$497$	−36.3731	+	21.0000i	−1.63156	+	0.941979i
$498$	13.8564	+	8.00000i	0.620920	+	0.358489i
$499$	−20.0000			−0.895323			−0.447661	−	0.894203i	$-0.647743\pi$
$499$	−20.0000			−0.895323			−0.447661	+	0.894203i	$0.647743\pi$
$500$		0			0
$501$	4.50000	−	7.79423i	0.201045	−	0.348220i
$502$			1.00000i			0.0446322i
$503$	18.1865	+	10.5000i	0.810897	+	0.468172i	0.847267	−	0.531167i	$-0.178246\pi$
$503$	18.1865	+	10.5000i	0.810897	+	0.468172i	−0.0363700	+	0.999338i	$0.511579\pi$
$504$	−1.50000	−	2.59808i	−0.0668153	−	0.115728i
$505$		0			0
$506$	−12.0000			−0.533465
$507$	−6.06218	−	11.5000i	−0.269231	−	0.510733i
$508$		−	3.00000i		−	0.133103i
$509$	5.00000	+	8.66025i	0.221621	+	0.383859i	0.955300	−	0.295637i	$-0.0955319\pi$
$509$	5.00000	+	8.66025i	0.221621	+	0.383859i	−0.733679	+	0.679496i	$0.762199\pi$
$510$		0			0
$511$	12.0000	−	20.7846i	0.530849	−	0.919457i
$512$		−	1.00000i		−	0.0441942i
$513$	−2.59808	−	1.50000i	−0.114708	−	0.0662266i
$514$	−6.00000	+	10.3923i	−0.264649	+	0.458385i
$515$		0			0
$516$	−5.00000	+	8.66025i	−0.220113	+	0.381246i
$517$	7.79423	−	4.50000i	0.342790	−	0.197910i
$518$	23.3827	−	13.5000i	1.02738	−	0.593156i
$519$	13.0000			0.570637
$520$		0			0
$521$	−35.0000			−1.53338			−0.766689	−	0.642019i	$-0.778097\pi$
$521$	−35.0000			−1.53338			−0.766689	+	0.642019i	$0.778097\pi$
$522$	3.46410	−	2.00000i	0.151620	−	0.0875376i
$523$	−19.0526	+	11.0000i	−0.833110	+	0.480996i	−0.854916	−	0.518766i	$-0.826392\pi$
$523$	−19.0526	+	11.0000i	−0.833110	+	0.480996i	0.0218062	+	0.999762i	$0.493058\pi$
$524$	−1.50000	+	2.59808i	−0.0655278	+	0.113497i
$525$		0			0
$526$	−15.5000	+	26.8468i	−0.675832	+	1.17058i
$527$		0			0
$528$		−	3.00000i		−	0.130558i
$529$	−3.50000	+	6.06218i	−0.152174	+	0.263573i
$530$		0			0
$531$	−6.00000	−	10.3923i	−0.260378	−	0.450988i
$532$			9.00000i			0.390199i
$533$	−34.6410	−	10.0000i	−1.50047	−	0.433148i
$534$	3.00000			0.129823
$535$		0			0
$536$	−4.00000	−	6.92820i	−0.172774	−	0.299253i
$537$	3.46410	+	2.00000i	0.149487	+	0.0863064i
$538$		−	4.00000i		−	0.172452i
$539$	−3.00000	+	5.19615i	−0.129219	+	0.223814i
$540$		0			0
$541$	−22.0000			−0.945854			−0.472927	−	0.881102i	$-0.656803\pi$
$541$	−22.0000			−0.945854			−0.472927	+	0.881102i	$0.656803\pi$
$542$	−10.3923	−	6.00000i	−0.446388	−	0.257722i
$543$	−8.66025	+	5.00000i	−0.371647	+	0.214571i
$544$		0			0
$545$		0			0
$546$	−3.00000	+	10.3923i	−0.128388	+	0.444750i
$547$			22.0000i			0.940652i	0.882493	+	0.470326i	$0.155864\pi$
$547$			22.0000i			0.940652i	−0.882493	+	0.470326i	$0.844136\pi$
$548$	−10.3923	+	6.00000i	−0.443937	+	0.256307i
$549$	−3.00000	−	5.19615i	−0.128037	−	0.221766i
$550$		0			0
$551$	−12.0000			−0.511217
$552$	3.46410	+	2.00000i	0.147442	+	0.0851257i
$553$	15.5885	+	9.00000i	0.662889	+	0.382719i
$554$	−31.0000			−1.31706
$555$		0			0
$556$	8.50000	+	14.7224i	0.360480	+	0.624370i
$557$	−7.79423	+	4.50000i	−0.330252	+	0.190671i	−0.655953	−	0.754802i	$-0.727733\pi$
$557$	−7.79423	+	4.50000i	−0.330252	+	0.190671i	0.325701	+	0.945473i	$0.394400\pi$
$558$			6.00000i			0.254000i
$559$	35.0000	−	8.66025i	1.48034	−	0.366290i
$560$		0			0
$561$		0			0
$562$	25.9808	−	15.0000i	1.09593	−	0.632737i
$563$	17.3205	+	10.0000i	0.729972	+	0.421450i	0.818412	−	0.574632i	$-0.194855\pi$
$563$	17.3205	+	10.0000i	0.729972	+	0.421450i	−0.0884397	+	0.996082i	$0.528188\pi$
$564$	−3.00000			−0.126323
$565$		0			0
$566$	3.00000	−	5.19615i	0.126099	−	0.218411i
$567$			3.00000i			0.125988i
$568$	12.1244	+	7.00000i	0.508727	+	0.293713i
$569$	−19.5000	−	33.7750i	−0.817483	−	1.41592i	−0.907532	−	0.419984i	$-0.862036\pi$
$569$	−19.5000	−	33.7750i	−0.817483	−	1.41592i	0.0900490	−	0.995937i	$-0.471298\pi$
$570$		0			0
$571$	23.0000			0.962520			0.481260	−	0.876578i	$-0.340179\pi$
$571$	23.0000			0.962520			0.481260	+	0.876578i	$0.340179\pi$
$572$	−7.79423	+	7.50000i	−0.325893	+	0.313591i
$573$		−	6.00000i		−	0.250654i
$574$	15.0000	+	25.9808i	0.626088	+	1.08442i
$575$		0			0
$576$	−0.500000	+	0.866025i	−0.0208333	+	0.0360844i
$577$		−	38.0000i		−	1.58196i	−0.611842	−	0.790980i	$-0.709571\pi$
$577$		−	38.0000i		−	1.58196i	0.611842	−	0.790980i	$-0.290429\pi$
$578$	14.7224	+	8.50000i	0.612372	+	0.353553i
$579$	−4.00000	+	6.92820i	−0.166234	+	0.287926i
$580$		0			0
$581$	−24.0000	+	41.5692i	−0.995688	+	1.72458i
$582$	6.92820	−	4.00000i	0.287183	−	0.165805i
$583$	23.3827	−	13.5000i	0.968412	−	0.559113i
$584$	−8.00000			−0.331042
$585$		0			0
$586$	1.00000			0.0413096
$587$	15.5885	−	9.00000i	0.643404	−	0.371470i	−0.142520	−	0.989792i	$-0.545521\pi$
$587$	15.5885	−	9.00000i	0.643404	−	0.371470i	0.785925	+	0.618322i	$0.212187\pi$
$588$	1.73205	−	1.00000i	0.0714286	−	0.0412393i
$589$	9.00000	−	15.5885i	0.370839	−	0.642311i
$590$		0			0
$591$	5.50000	−	9.52628i	0.226240	−	0.391859i
$592$	−7.79423	−	4.50000i	−0.320341	−	0.184949i
$593$		−	36.0000i		−	1.47834i	−0.673517	−	0.739171i	$-0.735217\pi$
$593$		−	36.0000i		−	1.47834i	0.673517	−	0.739171i	$-0.264783\pi$
$594$	−1.50000	+	2.59808i	−0.0615457	+	0.106600i
$595$		0			0
$596$	1.00000	+	1.73205i	0.0409616	+	0.0709476i
$597$			10.0000i			0.409273i
$598$	−3.46410	−	14.0000i	−0.141658	−	0.572503i
$599$	30.0000			1.22577			0.612883	−	0.790173i	$-0.290010\pi$
$599$	30.0000			1.22577			0.612883	+	0.790173i	$0.290010\pi$
$600$		0			0
$601$	−10.5000	−	18.1865i	−0.428304	−	0.741844i	0.568419	−	0.822739i	$-0.307555\pi$
$601$	−10.5000	−	18.1865i	−0.428304	−	0.741844i	−0.996723	+	0.0808953i	$0.974222\pi$
$602$	−25.9808	−	15.0000i	−1.05890	−	0.611354i
$603$			8.00000i			0.325785i
$604$	7.00000	−	12.1244i	0.284826	−	0.493333i
$605$		0			0
$606$		0			0
$607$	−23.3827	−	13.5000i	−0.949074	−	0.547948i	−0.0562808	−	0.998415i	$-0.517924\pi$
$607$	−23.3827	−	13.5000i	−0.949074	−	0.547948i	−0.892793	+	0.450467i	$0.851258\pi$
$608$	2.59808	−	1.50000i	0.105366	−	0.0608330i
$609$	6.00000	+	10.3923i	0.243132	+	0.421117i
$610$		0			0
$611$	7.50000	+	7.79423i	0.303418	+	0.315321i
$612$		0			0
$613$	6.06218	−	3.50000i	0.244849	−	0.141364i	−0.372554	−	0.928010i	$-0.621518\pi$
$613$	6.06218	−	3.50000i	0.244849	−	0.141364i	0.617403	+	0.786647i	$0.288185\pi$
$614$	−13.0000	−	22.5167i	−0.524637	−	0.908698i
$615$		0			0
$616$	9.00000			0.362620
$617$	25.9808	+	15.0000i	1.04595	+	0.603877i	0.921512	−	0.388351i	$-0.126955\pi$
$617$	25.9808	+	15.0000i	1.04595	+	0.603877i	0.124434	+	0.992228i	$0.460288\pi$
$618$	−12.9904	−	7.50000i	−0.522550	−	0.301694i
$619$	23.0000			0.924448			0.462224	−	0.886763i	$-0.347052\pi$
$619$	23.0000			0.924448			0.462224	+	0.886763i	$0.347052\pi$
$620$		0			0
$621$	−2.00000	−	3.46410i	−0.0802572	−	0.139010i
$622$	3.46410	−	2.00000i	0.138898	−	0.0801927i
$623$			9.00000i			0.360577i
$624$	3.50000	−	0.866025i	0.140112	−	0.0346688i
$625$		0			0
$626$	13.0000	+	22.5167i	0.519584	+	0.899947i
$627$	7.79423	−	4.50000i	0.311272	−	0.179713i
$628$	−14.7224	−	8.50000i	−0.587489	−	0.339187i
$629$		0			0
$630$		0			0
$631$	−6.00000	+	10.3923i	−0.238856	+	0.413711i	−0.960386	−	0.278672i	$-0.910106\pi$
$631$	−6.00000	+	10.3923i	−0.238856	+	0.413711i	0.721530	+	0.692383i	$0.243439\pi$
$632$		−	6.00000i		−	0.238667i
$633$	−7.79423	−	4.50000i	−0.309793	−	0.178859i
$634$	−8.50000	−	14.7224i	−0.337578	−	0.584702i
$635$		0			0
$636$	−9.00000			−0.356873
$637$	−6.92820	−	2.00000i	−0.274505	−	0.0792429i
$638$			12.0000i			0.475085i
$639$	−7.00000	−	12.1244i	−0.276916	−	0.479632i
$640$		0			0
$641$	−17.5000	+	30.3109i	−0.691208	+	1.19721i	0.280234	+	0.959932i	$0.409588\pi$
$641$	−17.5000	+	30.3109i	−0.691208	+	1.19721i	−0.971442	+	0.237276i	$0.923745\pi$
$642$			2.00000i			0.0789337i
$643$	24.2487	+	14.0000i	0.956276	+	0.552106i	0.895025	−	0.446016i	$-0.147158\pi$
$643$	24.2487	+	14.0000i	0.956276	+	0.552106i	0.0612510	+	0.998122i	$0.480491\pi$
$644$	−6.00000	+	10.3923i	−0.236433	+	0.409514i
$645$		0			0
$646$		0			0
$647$	−38.9711	+	22.5000i	−1.53211	+	0.884566i	−0.532850	+	0.846210i	$0.678879\pi$
$647$	−38.9711	+	22.5000i	−1.53211	+	0.884566i	−0.999264	+	0.0383563i	$0.987788\pi$
$648$	0.866025	−	0.500000i	0.0340207	−	0.0196419i
$649$	36.0000			1.41312
$650$		0			0
$651$	−18.0000			−0.705476
$652$	17.3205	−	10.0000i	0.678323	−	0.391630i
$653$	−2.59808	+	1.50000i	−0.101671	+	0.0586995i	−0.549973	−	0.835182i	$-0.685362\pi$
$653$	−2.59808	+	1.50000i	−0.101671	+	0.0586995i	0.448303	+	0.893882i	$0.352029\pi$
$654$	−1.00000	+	1.73205i	−0.0391031	+	0.0677285i
$655$		0			0
$656$	5.00000	−	8.66025i	0.195217	−	0.338126i
$657$	6.92820	+	4.00000i	0.270295	+	0.156055i
$658$		−	9.00000i		−	0.350857i
$659$	2.00000	−	3.46410i	0.0779089	−	0.134942i	−0.824439	−	0.565951i	$-0.808509\pi$
$659$	2.00000	−	3.46410i	0.0779089	−	0.134942i	0.902348	+	0.431009i	$0.141842\pi$
$660$		0			0
$661$	−15.0000	−	25.9808i	−0.583432	−	1.01053i	−0.995069	−	0.0991864i	$-0.968376\pi$
$661$	−15.0000	−	25.9808i	−0.583432	−	1.01053i	0.411636	−	0.911348i	$-0.364957\pi$
$662$			28.0000i			1.08825i
$663$		0			0
$664$	16.0000			0.620920
$665$		0			0
$666$	4.50000	+	7.79423i	0.174371	+	0.302020i
$667$	−13.8564	−	8.00000i	−0.536522	−	0.309761i
$668$		−	9.00000i		−	0.348220i
$669$	5.50000	−	9.52628i	0.212642	−	0.368307i
$670$		0			0
$671$	18.0000			0.694882
$672$	−2.59808	−	1.50000i	−0.100223	−	0.0578638i
$673$	−41.5692	+	24.0000i	−1.60238	+	0.925132i	−0.611365	+	0.791349i	$0.709379\pi$
$673$	−41.5692	+	24.0000i	−1.60238	+	0.925132i	−0.991011	+	0.133783i	$0.957287\pi$
$674$	−3.00000	−	5.19615i	−0.115556	−	0.200148i
$675$		0			0
$676$	−11.0000	−	6.92820i	−0.423077	−	0.266469i
$677$		−	6.00000i		−	0.230599i	−0.993331	−	0.115299i	$-0.963217\pi$
$677$		−	6.00000i		−	0.230599i	0.993331	−	0.115299i	$-0.0367827\pi$
$678$	6.92820	−	4.00000i	0.266076	−	0.153619i
$679$	12.0000	+	20.7846i	0.460518	+	0.797640i
$680$		0			0
$681$	16.0000			0.613121
$682$	−15.5885	−	9.00000i	−0.596913	−	0.344628i
$683$	25.9808	+	15.0000i	0.994126	+	0.573959i	0.906505	−	0.422195i	$-0.138740\pi$
$683$	25.9808	+	15.0000i	0.994126	+	0.573959i	0.0876211	+	0.996154i	$0.472074\pi$
$684$	−3.00000			−0.114708
$685$		0			0
$686$	−7.50000	−	12.9904i	−0.286351	−	0.495975i
$687$	8.66025	−	5.00000i	0.330409	−	0.190762i
$688$			10.0000i			0.381246i
$689$	22.5000	+	23.3827i	0.857182	+	0.890809i
$690$		0			0
$691$	3.50000	+	6.06218i	0.133146	+	0.230616i	0.924888	−	0.380240i	$-0.124159\pi$
$691$	3.50000	+	6.06218i	0.133146	+	0.230616i	−0.791742	+	0.610856i	$0.790825\pi$
$692$	11.2583	−	6.50000i	0.427977	−	0.247093i
$693$	−7.79423	−	4.50000i	−0.296078	−	0.170941i
$694$	−24.0000			−0.911028
$695$		0			0
$696$	2.00000	−	3.46410i	0.0758098	−	0.131306i
$697$		0			0
$698$	−13.8564	−	8.00000i	−0.524473	−	0.302804i
$699$	3.00000	+	5.19615i	0.113470	+	0.196537i
$700$		0			0
$701$	24.0000			0.906467			0.453234	−	0.891392i	$-0.350270\pi$
$701$	24.0000			0.906467			0.453234	+	0.891392i	$0.350270\pi$
$702$	−3.46410	−	1.00000i	−0.130744	−	0.0377426i
$703$		−	27.0000i		−	1.01832i
$704$	−1.50000	−	2.59808i	−0.0565334	−	0.0979187i
$705$		0			0
$706$	−4.00000	+	6.92820i	−0.150542	+	0.260746i
$707$		0			0
$708$	−10.3923	−	6.00000i	−0.390567	−	0.225494i
$709$	−20.0000	+	34.6410i	−0.751116	+	1.30097i	0.196167	+	0.980571i	$0.437151\pi$
$709$	−20.0000	+	34.6410i	−0.751116	+	1.30097i	−0.947282	+	0.320400i	$0.896183\pi$
$710$		0			0
$711$	−3.00000	+	5.19615i	−0.112509	+	0.194871i
$712$	2.59808	−	1.50000i	0.0973670	−	0.0562149i
$713$	20.7846	−	12.0000i	0.778390	−	0.449404i
$714$		0			0
$715$		0			0
$716$	4.00000			0.149487
$717$	22.5167	−	13.0000i	0.840900	−	0.485494i
$718$	25.9808	−	15.0000i	0.969593	−	0.559795i
$719$	−18.0000	+	31.1769i	−0.671287	+	1.16270i	0.306253	+	0.951950i	$0.400925\pi$
$719$	−18.0000	+	31.1769i	−0.671287	+	1.16270i	−0.977539	+	0.210752i	$0.932409\pi$
$720$		0			0
$721$	22.5000	−	38.9711i	0.837944	−	1.45136i
$722$	−8.66025	−	5.00000i	−0.322301	−	0.186081i
$723$			7.00000i			0.260333i
$724$	−5.00000	+	8.66025i	−0.185824	+	0.321856i
$725$		0			0
$726$	1.00000	+	1.73205i	0.0371135	+	0.0642824i
$727$		−	3.00000i		−	0.111264i	−0.998451	−	0.0556319i	$-0.982283\pi$
$727$		−	3.00000i		−	0.111264i	0.998451	−	0.0556319i	$-0.0177173\pi$
$728$	2.59808	+	10.5000i	0.0962911	+	0.389156i
$729$	−1.00000			−0.0370370
$730$		0			0
$731$		0			0
$732$	−5.19615	−	3.00000i	−0.192055	−	0.110883i
$733$		−	53.0000i		−	1.95760i	−0.204819	−	0.978800i	$-0.565661\pi$
$733$		−	53.0000i		−	1.95760i	0.204819	−	0.978800i	$-0.434339\pi$
$734$	−4.00000	+	6.92820i	−0.147643	+	0.255725i
$735$		0			0
$736$	4.00000			0.147442
$737$	−20.7846	−	12.0000i	−0.765611	−	0.442026i
$738$	−8.66025	+	5.00000i	−0.318788	+	0.184053i
$739$	5.50000	+	9.52628i	0.202321	+	0.350430i	0.949276	−	0.314445i	$-0.101818\pi$
$739$	5.50000	+	9.52628i	0.202321	+	0.350430i	−0.746955	+	0.664875i	$0.768485\pi$
$740$		0			0
$741$	7.50000	+	7.79423i	0.275519	+	0.286328i
$742$		−	27.0000i		−	0.991201i
$743$	−41.5692	+	24.0000i	−1.52503	+	0.880475i	−0.525467	+	0.850814i	$0.676109\pi$
$743$	−41.5692	+	24.0000i	−1.52503	+	0.880475i	−0.999560	+	0.0296605i	$0.990557\pi$
$744$	3.00000	+	5.19615i	0.109985	+	0.190500i
$745$		0			0
$746$	26.0000			0.951928
$747$	−13.8564	−	8.00000i	−0.506979	−	0.292705i
$748$		0			0
$749$	−6.00000			−0.219235
$750$		0			0
$751$	12.0000	+	20.7846i	0.437886	+	0.758441i	0.997526	−	0.0702946i	$-0.0223939\pi$
$751$	12.0000	+	20.7846i	0.437886	+	0.758441i	−0.559640	+	0.828736i	$0.689061\pi$
$752$	−2.59808	+	1.50000i	−0.0947421	+	0.0546994i
$753$		−	1.00000i		−	0.0364420i
$754$	−14.0000	+	3.46410i	−0.509850	+	0.126155i
$755$		0			0
$756$	1.50000	+	2.59808i	0.0545545	+	0.0944911i
$757$	14.7224	−	8.50000i	0.535096	−	0.308938i	−0.207993	−	0.978130i	$-0.566693\pi$
$757$	14.7224	−	8.50000i	0.535096	−	0.308938i	0.743089	+	0.669193i	$0.233360\pi$
$758$	28.5788	+	16.5000i	1.03803	+	0.599307i
$759$	12.0000			0.435572
$760$		0			0
$761$	15.5000	−	26.8468i	0.561875	−	0.973195i	−0.435458	−	0.900209i	$-0.643414\pi$
$761$	15.5000	−	26.8468i	0.561875	−	0.973195i	0.997333	−	0.0729864i	$-0.0232530\pi$
$762$			3.00000i			0.108679i
$763$	−5.19615	−	3.00000i	−0.188113	−	0.108607i
$764$	−3.00000	−	5.19615i	−0.108536	−	0.187990i
$765$		0			0
$766$	−4.00000			−0.144526
$767$	10.3923	+	42.0000i	0.375244	+	1.51653i
$768$			1.00000i			0.0360844i
$769$	23.0000	+	39.8372i	0.829401	+	1.43657i	0.898509	+	0.438956i	$0.144652\pi$
$769$	23.0000	+	39.8372i	0.829401	+	1.43657i	−0.0691074	+	0.997609i	$0.522015\pi$
$770$		0			0
$771$	6.00000	−	10.3923i	0.216085	−	0.374270i
$772$			8.00000i			0.287926i
$773$	−6.06218	−	3.50000i	−0.218041	−	0.125886i	0.387002	−	0.922079i	$-0.373511\pi$
$773$	−6.06218	−	3.50000i	−0.218041	−	0.125886i	−0.605043	+	0.796193i	$0.706844\pi$
$774$	5.00000	−	8.66025i	0.179721	−	0.311286i
$775$		0			0
$776$	4.00000	−	6.92820i	0.143592	−	0.248708i
$777$	−23.3827	+	13.5000i	−0.838849	+	0.484310i
$778$	20.7846	−	12.0000i	0.745164	−	0.430221i
$779$	30.0000			1.07486
$780$		0			0
$781$	42.0000			1.50288
$782$		0			0
$783$	−3.46410	+	2.00000i	−0.123797	+	0.0714742i
$784$	1.00000	−	1.73205i	0.0357143	−	0.0618590i
$785$		0			0
$786$	1.50000	−	2.59808i	0.0535032	−	0.0926703i
$787$	31.1769	+	18.0000i	1.11134	+	0.641631i	0.939175	−	0.343438i	$-0.111592\pi$
$787$	31.1769	+	18.0000i	1.11134	+	0.641631i	0.172162	+	0.985069i	$0.444925\pi$
$788$		−	11.0000i		−	0.391859i
$789$	15.5000	−	26.8468i	0.551815	−	0.955771i
$790$		0			0
$791$	12.0000	+	20.7846i	0.426671	+	0.739016i
$792$			3.00000i			0.106600i
$793$	5.19615	+	21.0000i	0.184521	+	0.745732i
$794$	−23.0000			−0.816239
$795$		0			0
$796$	5.00000	+	8.66025i	0.177220	+	0.306955i
$797$	36.3731	+	21.0000i	1.28840	+	0.743858i	0.978369	−	0.206868i	$-0.0663271\pi$
$797$	36.3731	+	21.0000i	1.28840	+	0.743858i	0.310031	+	0.950726i	$0.399660\pi$
$798$		−	9.00000i		−	0.318597i
$799$		0			0
$800$		0			0
$801$	−3.00000			−0.106000
$802$	−23.3827	−	13.5000i	−0.825671	−	0.476702i
$803$	−20.7846	+	12.0000i	−0.733473	+	0.423471i
$804$	4.00000	+	6.92820i	0.141069	+	0.244339i
$805$		0			0
$806$	6.00000	−	20.7846i	0.211341	−	0.732107i
$807$			4.00000i			0.140807i
$808$		0			0
$809$	−5.00000	−	8.66025i	−0.175791	−	0.304478i	0.764644	−	0.644453i	$-0.222915\pi$
$809$	−5.00000	−	8.66025i	−0.175791	−	0.304478i	−0.940435	+	0.339975i	$0.889582\pi$
$810$		0			0
$811$	−31.0000			−1.08856			−0.544279	−	0.838905i	$-0.683197\pi$
$811$	−31.0000			−1.08856			−0.544279	+	0.838905i	$0.683197\pi$
$812$	10.3923	+	6.00000i	0.364698	+	0.210559i
$813$	10.3923	+	6.00000i	0.364474	+	0.210429i
$814$	−27.0000			−0.946350
$815$		0			0
$816$		0			0
$817$	−25.9808	+	15.0000i	−0.908952	+	0.524784i
$818$		−	7.00000i		−	0.244749i
$819$	3.00000	−	10.3923i	0.104828	−	0.363137i
$820$		0			0
$821$	−25.0000	−	43.3013i	−0.872506	−	1.51122i	−0.859396	−	0.511311i	$-0.829160\pi$
$821$	−25.0000	−	43.3013i	−0.872506	−	1.51122i	−0.0131101	−	0.999914i	$-0.504173\pi$
$822$	10.3923	−	6.00000i	0.362473	−	0.209274i
$823$	−9.52628	−	5.50000i	−0.332065	−	0.191718i	0.324692	−	0.945820i	$-0.394739\pi$
$823$	−9.52628	−	5.50000i	−0.332065	−	0.191718i	−0.656758	+	0.754102i	$0.728073\pi$
$824$	−15.0000			−0.522550
$825$		0			0
$826$	18.0000	−	31.1769i	0.626300	−	1.08478i
$827$		−	18.0000i		−	0.625921i	−0.949766	−	0.312961i	$-0.898679\pi$
$827$		−	18.0000i		−	0.625921i	0.949766	−	0.312961i	$-0.101321\pi$
$828$	−3.46410	−	2.00000i	−0.120386	−	0.0695048i
$829$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$829$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$830$		0			0
$831$	31.0000			1.07538
$832$	2.59808	−	2.50000i	0.0900721	−	0.0866719i
$833$		0			0
$834$	−8.50000	−	14.7224i	−0.294331	−	0.509796i
$835$		0			0
$836$	4.50000	−	7.79423i	0.155636	−	0.269569i
$837$		−	6.00000i		−	0.207390i
$838$	10.3923	+	6.00000i	0.358996	+	0.207267i
$839$	−3.00000	+	5.19615i	−0.103572	+	0.179391i	−0.913154	−	0.407615i	$-0.866360\pi$
$839$	−3.00000	+	5.19615i	−0.103572	+	0.179391i	0.809582	+	0.587007i	$0.199694\pi$
$840$		0			0
$841$	6.50000	−	11.2583i	0.224138	−	0.388218i
$842$	24.2487	−	14.0000i	0.835666	−	0.482472i
$843$	−25.9808	+	15.0000i	−0.894825	+	0.516627i
$844$	−9.00000			−0.309793
$845$		0			0
$846$	3.00000			0.103142
$847$	−5.19615	+	3.00000i	−0.178542	+	0.103081i
$848$	−7.79423	+	4.50000i	−0.267655	+	0.154531i
$849$	−3.00000	+	5.19615i	−0.102960	+	0.178331i
$850$		0			0
$851$	18.0000	−	31.1769i	0.617032	−	1.06873i
$852$	−12.1244	−	7.00000i	−0.415374	−	0.239816i
$853$			26.0000i			0.890223i	0.895475	+	0.445112i	$0.146836\pi$
$853$			26.0000i			0.890223i	−0.895475	+	0.445112i	$0.853164\pi$
$854$	9.00000	−	15.5885i	0.307974	−	0.533426i
$855$		0			0
$856$	1.00000	+	1.73205i	0.0341793	+	0.0592003i
$857$		−	50.0000i		−	1.70797i	−0.520300	−	0.853984i	$-0.674180\pi$
$857$		−	50.0000i		−	1.70797i	0.520300	−	0.853984i	$-0.325820\pi$
$858$	7.79423	−	7.50000i	0.266091	−	0.256046i
$859$	5.00000			0.170598			0.0852989	−	0.996355i	$-0.472815\pi$
$859$	5.00000			0.170598			0.0852989	+	0.996355i	$0.472815\pi$
$860$		0			0
$861$	−15.0000	−	25.9808i	−0.511199	−	0.885422i
$862$	−10.3923	−	6.00000i	−0.353963	−	0.204361i
$863$			24.0000i			0.816970i	0.912765	+	0.408485i	$0.133943\pi$
$863$			24.0000i			0.816970i	−0.912765	+	0.408485i	$0.866057\pi$
$864$	0.500000	−	0.866025i	0.0170103	−	0.0294628i
$865$		0			0
$866$	16.0000			0.543702
$867$	−14.7224	−	8.50000i	−0.500000	−	0.288675i
$868$	−15.5885	+	9.00000i	−0.529107	+	0.305480i
$869$	−9.00000	−	15.5885i	−0.305304	−	0.528802i
$870$		0			0
$871$	8.00000	−	27.7128i	0.271070	−	0.939013i
$872$			2.00000i			0.0677285i
$873$	−6.92820	+	4.00000i	−0.234484	+	0.135379i
$874$	6.00000	+	10.3923i	0.202953	+	0.351525i
$875$		0			0
$876$	8.00000			0.270295
$877$	32.9090	+	19.0000i	1.11126	+	0.641584i	0.939155	−	0.343495i	$-0.111611\pi$
$877$	32.9090	+	19.0000i	1.11126	+	0.641584i	0.172102	+	0.985079i	$0.444944\pi$
$878$	25.9808	+	15.0000i	0.876808	+	0.506225i
$879$	−1.00000			−0.0337292
$880$		0			0
$881$	11.5000	+	19.9186i	0.387445	+	0.671074i	0.992105	−	0.125409i	$-0.0400244\pi$
$881$	11.5000	+	19.9186i	0.387445	+	0.671074i	−0.604660	+	0.796484i	$0.706691\pi$
$882$	−1.73205	+	1.00000i	−0.0583212	+	0.0336718i
$883$		−	22.0000i		−	0.740359i	−0.928960	−	0.370179i	$-0.879296\pi$
$883$		−	22.0000i		−	0.740359i	0.928960	−	0.370179i	$-0.120704\pi$
$884$		0			0
$885$		0			0
$886$	−5.00000	−	8.66025i	−0.167978	−	0.290947i
$887$	7.79423	−	4.50000i	0.261705	−	0.151095i	−0.363407	−	0.931630i	$-0.618387\pi$
$887$	7.79423	−	4.50000i	0.261705	−	0.151095i	0.625112	+	0.780535i	$0.285053\pi$
$888$	7.79423	+	4.50000i	0.261557	+	0.151010i
$889$	−9.00000			−0.301850
$890$		0			0
$891$	1.50000	−	2.59808i	0.0502519	−	0.0870388i
$892$		−	11.0000i		−	0.368307i
$893$	−7.79423	−	4.50000i	−0.260824	−	0.150587i
$894$	−1.00000	−	1.73205i	−0.0334450	−	0.0579284i
$895$		0			0
$896$	−3.00000			−0.100223
$897$	3.46410	+	14.0000i	0.115663	+	0.467446i
$898$		−	35.0000i		−	1.16797i
$899$	−12.0000	−	20.7846i	−0.400222	−	0.693206i
$900$		0			0
$901$		0			0
$902$		−	30.0000i		−	0.998891i
$903$	25.9808	+	15.0000i	0.864586	+	0.499169i
$904$	4.00000	−	6.92820i	0.133038	−	0.230429i
$905$		0			0
$906$	−7.00000	+	12.1244i	−0.232559	+	0.402805i
$907$	−12.1244	+	7.00000i	−0.402583	+	0.232431i	−0.687598	−	0.726092i	$-0.741335\pi$
$907$	−12.1244	+	7.00000i	−0.402583	+	0.232431i	0.285015	+	0.958523i	$0.408001\pi$
$908$	13.8564	−	8.00000i	0.459841	−	0.265489i
$909$		0			0
$910$		0			0
$911$	28.0000			0.927681			0.463841	−	0.885919i	$-0.346471\pi$
$911$	28.0000			0.927681			0.463841	+	0.885919i	$0.346471\pi$
$912$	−2.59808	+	1.50000i	−0.0860309	+	0.0496700i
$913$	41.5692	−	24.0000i	1.37574	−	0.794284i
$914$	21.0000	−	36.3731i	0.694618	−	1.20311i
$915$		0			0
$916$	5.00000	−	8.66025i	0.165205	−	0.286143i
$917$	7.79423	+	4.50000i	0.257388	+	0.148603i
$918$		0			0
$919$	7.00000	−	12.1244i	0.230909	−	0.399946i	−0.727167	−	0.686461i	$-0.759163\pi$
$919$	7.00000	−	12.1244i	0.230909	−	0.399946i	0.958076	+	0.286515i	$0.0924968\pi$
$920$		0			0
$921$	13.0000	+	22.5167i	0.428365	+	0.741949i
$922$			32.0000i			1.05386i
$923$	12.1244	+	49.0000i	0.399078	+	1.61285i
$924$	−9.00000			−0.296078
$925$		0			0
$926$	−12.0000	−	20.7846i	−0.394344	−	0.683025i
$927$	12.9904	+	7.50000i	0.426660	+	0.246332i
$928$		−	4.00000i		−	0.131306i
$929$	1.00000	−	1.73205i	0.0328089	−	0.0568267i	−0.849155	−	0.528144i	$-0.822888\pi$
$929$	1.00000	−	1.73205i	0.0328089	−	0.0568267i	0.881964	+	0.471317i	$0.156221\pi$
$930$		0			0
$931$	6.00000			0.196642
$932$	5.19615	+	3.00000i	0.170206	+	0.0982683i
$933$	−3.46410	+	2.00000i	−0.113410	+	0.0654771i
$934$	−4.00000	−	6.92820i	−0.130884	−	0.226698i
$935$		0			0
$936$	−3.50000	+	0.866025i	−0.114401	+	0.0283069i
$937$			14.0000i			0.457360i	0.973502	+	0.228680i	$0.0734410\pi$
$937$			14.0000i			0.457360i	−0.973502	+	0.228680i	$0.926559\pi$
$938$	−20.7846	+	12.0000i	−0.678642	+	0.391814i
$939$	−13.0000	−	22.5167i	−0.424239	−	0.734803i
$940$		0			0
$941$	−32.0000			−1.04317			−0.521585	−	0.853199i	$-0.674659\pi$
$941$	−32.0000			−1.04317			−0.521585	+	0.853199i	$0.674659\pi$
$942$	14.7224	+	8.50000i	0.479683	+	0.276945i
$943$	34.6410	+	20.0000i	1.12807	+	0.651290i
$944$	−12.0000			−0.390567
$945$		0			0
$946$	15.0000	+	25.9808i	0.487692	+	0.844707i
$947$	15.5885	−	9.00000i	0.506557	−	0.292461i	−0.224860	−	0.974391i	$-0.572193\pi$
$947$	15.5885	−	9.00000i	0.506557	−	0.292461i	0.731417	+	0.681930i	$0.238859\pi$
$948$			6.00000i			0.194871i
$949$	−20.0000	−	20.7846i	−0.649227	−	0.674697i
$950$		0			0
$951$	8.50000	+	14.7224i	0.275631	+	0.477408i
$952$		0			0
$953$	29.4449	+	17.0000i	0.953813	+	0.550684i	0.894263	−	0.447541i	$-0.147700\pi$
$953$	29.4449	+	17.0000i	0.953813	+	0.550684i	0.0595495	+	0.998225i	$0.481034\pi$
$954$	9.00000			0.291386
$955$		0			0
$956$	13.0000	−	22.5167i	0.420450	−	0.728241i
$957$		−	12.0000i		−	0.387905i
$958$	−10.3923	−	6.00000i	−0.335760	−	0.193851i
$959$	18.0000	+	31.1769i	0.581250	+	1.00676i
$960$		0			0
$961$	5.00000			0.161290
$962$	−7.79423	−	31.5000i	−0.251296	−	1.01560i
$963$		−	2.00000i		−	0.0644491i
$964$	3.50000	+	6.06218i	0.112727	+	0.195250i
$965$		0			0
$966$	6.00000	−	10.3923i	0.193047	−	0.334367i
$967$			25.0000i			0.803946i	0.915652	+	0.401973i	$0.131675\pi$
$967$			25.0000i			0.803946i	−0.915652	+	0.401973i	$0.868325\pi$
$968$	1.73205	+	1.00000i	0.0556702	+	0.0321412i
$969$		0			0
$970$		0			0
$971$	−7.50000	+	12.9904i	−0.240686	+	0.416881i	−0.960910	−	0.276861i	$-0.910706\pi$
$971$	−7.50000	+	12.9904i	−0.240686	+	0.416881i	0.720224	+	0.693742i	$0.244039\pi$
$972$	−0.866025	+	0.500000i	−0.0277778	+	0.0160375i
$973$	44.1673	−	25.5000i	1.41594	−	0.817492i
$974$	29.0000			0.929220
$975$		0			0
$976$	−6.00000			−0.192055
$977$	−38.1051	+	22.0000i	−1.21909	+	0.703842i	−0.964723	−	0.263265i	$-0.915201\pi$
$977$	−38.1051	+	22.0000i	−1.21909	+	0.703842i	−0.254367	+	0.967108i	$0.581867\pi$
$978$	−17.3205	+	10.0000i	−0.553849	+	0.319765i
$979$	4.50000	−	7.79423i	0.143821	−	0.249105i
$980$		0			0
$981$	1.00000	−	1.73205i	0.0319275	−	0.0553001i
$982$	4.33013	+	2.50000i	0.138180	+	0.0797782i
$983$		−	55.0000i		−	1.75423i	−0.480283	−	0.877114i	$-0.659466\pi$
$983$		−	55.0000i		−	1.75423i	0.480283	−	0.877114i	$-0.340534\pi$
$984$	−5.00000	+	8.66025i	−0.159394	+	0.276079i
$985$		0			0
$986$		0			0
$987$			9.00000i			0.286473i
$988$	10.3923	+	3.00000i	0.330623	+	0.0954427i
$989$	−40.0000			−1.27193
$990$		0			0
$991$	−29.0000	−	50.2295i	−0.921215	−	1.59559i	−0.797537	−	0.603269i	$-0.793864\pi$
$991$	−29.0000	−	50.2295i	−0.921215	−	1.59559i	−0.123678	−	0.992322i	$-0.539469\pi$
$992$	5.19615	+	3.00000i	0.164978	+	0.0952501i
$993$		−	28.0000i		−	0.888553i
$994$	21.0000	−	36.3731i	0.666080	−	1.15368i
$995$		0			0
$996$	−16.0000			−0.506979
$997$	−40.7032	−	23.5000i	−1.28908	−	0.744252i	−0.310592	−	0.950543i	$-0.600527\pi$
$997$	−40.7032	−	23.5000i	−1.28908	−	0.744252i	−0.978491	+	0.206291i	$0.933861\pi$
$998$	17.3205	−	10.0000i	0.548271	−	0.316544i
$999$	−4.50000	−	7.79423i	−0.142374	−	0.246598i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1950.2.z.d.1849.1		4
5.2	odd	4		1950.2.i.f.601.1		2
5.3	odd	4		390.2.i.e.211.1	yes	2
5.4	even	2	inner	1950.2.z.d.1849.2		4
13.9	even	3	inner	1950.2.z.d.1699.2		4
15.8	even	4		1170.2.i.c.991.1		2
65.3	odd	12		5070.2.a.b.1.1		1
65.9	even	6	inner	1950.2.z.d.1699.1		4
65.22	odd	12		1950.2.i.f.451.1		2
65.23	odd	12		5070.2.a.r.1.1		1
65.28	even	12		5070.2.b.b.1351.2		2
65.48	odd	12		390.2.i.e.61.1	✓	2
65.63	even	12		5070.2.b.b.1351.1		2
195.113	even	12		1170.2.i.c.451.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
390.2.i.e.61.1	✓	2	65.48	odd	12
390.2.i.e.211.1	yes	2	5.3	odd	4
1170.2.i.c.451.1		2	195.113	even	12
1170.2.i.c.991.1		2	15.8	even	4
1950.2.i.f.451.1		2	65.22	odd	12
1950.2.i.f.601.1		2	5.2	odd	4
1950.2.z.d.1699.1		4	65.9	even	6	inner
1950.2.z.d.1699.2		4	13.9	even	3	inner
1950.2.z.d.1849.1		4	1.1	even	1	trivial
1950.2.z.d.1849.2		4	5.4	even	2	inner
5070.2.a.b.1.1		1	65.3	odd	12
5070.2.a.r.1.1		1	65.23	odd	12
5070.2.b.b.1351.1		2	65.63	even	12
5070.2.b.b.1351.2		2	65.28	even	12

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:	\( N \)	\(=\)	\( 1950 = 2 \cdot 3 \cdot 5^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1950.z (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.866025 + 0.500000i) q^{2} +(0.866025 - 0.500000i) q^{3} +(0.500000 - 0.866025i) q^{4} +(-0.500000 + 0.866025i) q^{6} +(-2.59808 - 1.50000i) q^{7} +1.00000i q^{8} +(0.500000 - 0.866025i) q^{9} +(1.50000 + 2.59808i) q^{11} -1.00000i q^{12} +(-2.59808 + 2.50000i) q^{13} +3.00000 q^{14} +(-0.500000 - 0.866025i) q^{16} +1.00000i q^{18} +(1.50000 - 2.59808i) q^{19} -3.00000 q^{21} +(-2.59808 - 1.50000i) q^{22} +(3.46410 - 2.00000i) q^{23} +(0.500000 + 0.866025i) q^{24} +(1.00000 - 3.46410i) q^{26} -1.00000i q^{27} +(-2.59808 + 1.50000i) q^{28} +(-2.00000 - 3.46410i) q^{29} +6.00000 q^{31} +(0.866025 + 0.500000i) q^{32} +(2.59808 + 1.50000i) q^{33} +(-0.500000 - 0.866025i) q^{36} +(7.79423 - 4.50000i) q^{37} +3.00000i q^{38} +(-1.00000 + 3.46410i) q^{39} +(5.00000 + 8.66025i) q^{41} +(2.59808 - 1.50000i) q^{42} +(-8.66025 - 5.00000i) q^{43} +3.00000 q^{44} +(-2.00000 + 3.46410i) q^{46} -3.00000i q^{47} +(-0.866025 - 0.500000i) q^{48} +(1.00000 + 1.73205i) q^{49} +(0.866025 + 3.50000i) q^{52} -9.00000i q^{53} +(0.500000 + 0.866025i) q^{54} +(1.50000 - 2.59808i) q^{56} -3.00000i q^{57} +(3.46410 + 2.00000i) q^{58} +(6.00000 - 10.3923i) q^{59} +(3.00000 - 5.19615i) q^{61} +(-5.19615 + 3.00000i) q^{62} +(-2.59808 + 1.50000i) q^{63} -1.00000 q^{64} -3.00000 q^{66} +(-6.92820 + 4.00000i) q^{67} +(2.00000 - 3.46410i) q^{69} +(7.00000 - 12.1244i) q^{71} +(0.866025 + 0.500000i) q^{72} +8.00000i q^{73} +(-4.50000 + 7.79423i) q^{74} +(-1.50000 - 2.59808i) q^{76} -9.00000i q^{77} +(-0.866025 - 3.50000i) q^{78} -6.00000 q^{79} +(-0.500000 - 0.866025i) q^{81} +(-8.66025 - 5.00000i) q^{82} -16.0000i q^{83} +(-1.50000 + 2.59808i) q^{84} +10.0000 q^{86} +(-3.46410 - 2.00000i) q^{87} +(-2.59808 + 1.50000i) q^{88} +(-1.50000 - 2.59808i) q^{89} +(10.5000 - 2.59808i) q^{91} -4.00000i q^{92} +(5.19615 - 3.00000i) q^{93} +(1.50000 + 2.59808i) q^{94} +1.00000 q^{96} +(-6.92820 - 4.00000i) q^{97} +(-1.73205 - 1.00000i) q^{98} +3.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 2 q^{4} - 2 q^{6} + 2 q^{9} + 6 q^{11} + 12 q^{14} - 2 q^{16} + 6 q^{19} - 12 q^{21} + 2 q^{24} + 4 q^{26} - 8 q^{29} + 24 q^{31} - 2 q^{36} - 4 q^{39} + 20 q^{41} + 12 q^{44} - 8 q^{46} + 4 q^{49}+ \cdots + 12 q^{99}+O(q^{100}) \) 4 * q + 2 * q^4 - 2 * q^6 + 2 * q^9 + 6 * q^11 + 12 * q^14 - 2 * q^16 + 6 * q^19 - 12 * q^21 + 2 * q^24 + 4 * q^26 - 8 * q^29 + 24 * q^31 - 2 * q^36 - 4 * q^39 + 20 * q^41 + 12 * q^44 - 8 * q^46 + 4 * q^49 + 2 * q^54 + 6 * q^56 + 24 * q^59 + 12 * q^61 - 4 * q^64 - 12 * q^66 + 8 * q^69 + 28 * q^71 - 18 * q^74 - 6 * q^76 - 24 * q^79 - 2 * q^81 - 6 * q^84 + 40 * q^86 - 6 * q^89 + 42 * q^91 + 6 * q^94 + 4 * q^96 + 12 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more