LMFDB - Embedded newform 1950.2.i.f.451.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [1950,2,Mod(451,1950)] 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("1950.451"); 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, 0, 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.i (of order $3$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [2,-1,-1,-1,0,-1,3,2,-1,0,3] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(11)] == traces)

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

Self dual:	no
Analytic conductor:	$15.5708283941$
Analytic rank:	$0$
Dimension:	$2$
Coefficient field:	$\Q(\zeta_{6})$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - x + 1 $ x^2 - x + 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 390)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			451.1
Root			$0.500000 + 0.866025i$ of defining polynomial
Character	$\chi$	$=$	1950.451
Dual form			1950.2.i.f.601.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.500000 + 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(-0.500000 - 0.866025i) q^{6} +(1.50000 + 2.59808i) q^{7} +1.00000 q^{8} +(-0.500000 - 0.866025i) q^{9} +(1.50000 - 2.59808i) q^{11} +1.00000 q^{12} +(2.50000 - 2.59808i) q^{13} -3.00000 q^{14} +(-0.500000 + 0.866025i) q^{16} +1.00000 q^{18} +(-1.50000 - 2.59808i) q^{19} -3.00000 q^{21} +(1.50000 + 2.59808i) q^{22} +(-2.00000 + 3.46410i) q^{23} +(-0.500000 + 0.866025i) q^{24} +(1.00000 + 3.46410i) q^{26} +1.00000 q^{27} +(1.50000 - 2.59808i) q^{28} +(2.00000 - 3.46410i) q^{29} +6.00000 q^{31} +(-0.500000 - 0.866025i) q^{32} +(1.50000 + 2.59808i) q^{33} +(-0.500000 + 0.866025i) q^{36} +(4.50000 - 7.79423i) q^{37} +3.00000 q^{38} +(1.00000 + 3.46410i) q^{39} +(5.00000 - 8.66025i) q^{41} +(1.50000 - 2.59808i) q^{42} +(-5.00000 - 8.66025i) q^{43} -3.00000 q^{44} +(-2.00000 - 3.46410i) q^{46} +3.00000 q^{47} +(-0.500000 - 0.866025i) q^{48} +(-1.00000 + 1.73205i) q^{49} +(-3.50000 - 0.866025i) q^{52} -9.00000 q^{53} +(-0.500000 + 0.866025i) q^{54} +(1.50000 + 2.59808i) q^{56} +3.00000 q^{57} +(2.00000 + 3.46410i) q^{58} +(-6.00000 - 10.3923i) q^{59} +(3.00000 + 5.19615i) q^{61} +(-3.00000 + 5.19615i) q^{62} +(1.50000 - 2.59808i) q^{63} +1.00000 q^{64} -3.00000 q^{66} +(-4.00000 + 6.92820i) q^{67} +(-2.00000 - 3.46410i) q^{69} +(7.00000 + 12.1244i) q^{71} +(-0.500000 - 0.866025i) q^{72} +8.00000 q^{73} +(4.50000 + 7.79423i) q^{74} +(-1.50000 + 2.59808i) q^{76} +9.00000 q^{77} +(-3.50000 - 0.866025i) q^{78} +6.00000 q^{79} +(-0.500000 + 0.866025i) q^{81} +(5.00000 + 8.66025i) q^{82} -16.0000 q^{83} +(1.50000 + 2.59808i) q^{84} +10.0000 q^{86} +(2.00000 + 3.46410i) q^{87} +(1.50000 - 2.59808i) q^{88} +(1.50000 - 2.59808i) q^{89} +(10.5000 + 2.59808i) q^{91} +4.00000 q^{92} +(-3.00000 + 5.19615i) q^{93} +(-1.50000 + 2.59808i) q^{94} +1.00000 q^{96} +(4.00000 + 6.92820i) q^{97} +(-1.00000 - 1.73205i) q^{98} -3.00000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q - q^{2} - q^{3} - q^{4} - q^{6} + 3 q^{7} + 2 q^{8} - q^{9} + 3 q^{11} + 2 q^{12} + 5 q^{13} - 6 q^{14} - q^{16} + 2 q^{18} - 3 q^{19} - 6 q^{21} + 3 q^{22} - 4 q^{23} - q^{24} + 2 q^{26} + 2 q^{27}+ \cdots - 6 q^{99}+O(q^{100}) $ 2 * q - q^2 - q^3 - q^4 - q^6 + 3 * q^7 + 2 * q^8 - q^9 + 3 * q^11 + 2 * q^12 + 5 * q^13 - 6 * q^14 - q^16 + 2 * q^18 - 3 * q^19 - 6 * q^21 + 3 * q^22 - 4 * q^23 - q^24 + 2 * q^26 + 2 * q^27 + 3 * q^28 + 4 * q^29 + 12 * q^31 - q^32 + 3 * q^33 - q^36 + 9 * q^37 + 6 * q^38 + 2 * q^39 + 10 * q^41 + 3 * q^42 - 10 * q^43 - 6 * q^44 - 4 * q^46 + 6 * q^47 - q^48 - 2 * q^49 - 7 * q^52 - 18 * q^53 - q^54 + 3 * q^56 + 6 * q^57 + 4 * q^58 - 12 * q^59 + 6 * q^61 - 6 * q^62 + 3 * q^63 + 2 * q^64 - 6 * q^66 - 8 * q^67 - 4 * q^69 + 14 * q^71 - q^72 + 16 * q^73 + 9 * q^74 - 3 * q^76 + 18 * q^77 - 7 * q^78 + 12 * q^79 - q^81 + 10 * q^82 - 32 * q^83 + 3 * q^84 + 20 * q^86 + 4 * q^87 + 3 * q^88 + 3 * q^89 + 21 * q^91 + 8 * q^92 - 6 * q^93 - 3 * q^94 + 2 * q^96 + 8 * q^97 - 2 * q^98 - 6 * q^99

Character values

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

$n$	$301$	$1301$	$1327$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$1$	$1$

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 $

$2$	−0.500000	+	0.866025i	−0.353553	+	0.612372i
$2$	−0.500000	+	0.866025i	−0.353553	+	0.612372i
$3$	−0.500000	+	0.866025i	−0.288675	+	0.500000i
$3$	−0.500000	+	0.866025i	−0.288675	+	0.500000i
$4$	−0.500000	−	0.866025i	−0.250000	−	0.433013i
$5$		0			0
$5$		0			0
$6$	−0.500000	−	0.866025i	−0.204124	−	0.353553i
$7$	1.50000	+	2.59808i	0.566947	+	0.981981i	0.996866	+	0.0791130i	$0.0252088\pi$
$7$	1.50000	+	2.59808i	0.566947	+	0.981981i	−0.429919	+	0.902867i	$0.641458\pi$
$8$	1.00000			0.353553
$9$	−0.500000	−	0.866025i	−0.166667	−	0.288675i
$10$		0			0
$11$	1.50000	−	2.59808i	0.452267	−	0.783349i	−0.546259	−	0.837616i	$-0.683949\pi$
$11$	1.50000	−	2.59808i	0.452267	−	0.783349i	0.998526	+	0.0542666i	$0.0172821\pi$
$12$	1.00000			0.288675
$13$	2.50000	−	2.59808i	0.693375	−	0.720577i
$13$	2.50000	−	2.59808i	0.693375	−	0.720577i
$14$	−3.00000			−0.801784
$15$		0			0
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$17$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$18$	1.00000			0.235702
$19$	−1.50000	−	2.59808i	−0.344124	−	0.596040i	0.641071	−	0.767482i	$-0.278491\pi$
$19$	−1.50000	−	2.59808i	−0.344124	−	0.596040i	−0.985194	+	0.171442i	$0.945157\pi$
$20$		0			0
$21$	−3.00000			−0.654654
$22$	1.50000	+	2.59808i	0.319801	+	0.553912i
$23$	−2.00000	+	3.46410i	−0.417029	+	0.722315i	−0.995639	−	0.0932891i	$-0.970262\pi$
$23$	−2.00000	+	3.46410i	−0.417029	+	0.722315i	0.578610	+	0.815604i	$0.303595\pi$
$24$	−0.500000	+	0.866025i	−0.102062	+	0.176777i
$25$		0			0
$26$	1.00000	+	3.46410i	0.196116	+	0.679366i
$27$	1.00000			0.192450
$28$	1.50000	−	2.59808i	0.283473	−	0.490990i
$29$	2.00000	−	3.46410i	0.371391	−	0.643268i	−0.618389	−	0.785872i	$-0.712214\pi$
$29$	2.00000	−	3.46410i	0.371391	−	0.643268i	0.989780	+	0.142605i	$0.0455477\pi$
$30$		0			0
$31$	6.00000			1.07763			0.538816	−	0.842424i	$-0.318872\pi$
$31$	6.00000			1.07763			0.538816	+	0.842424i	$0.318872\pi$
$32$	−0.500000	−	0.866025i	−0.0883883	−	0.153093i
$33$	1.50000	+	2.59808i	0.261116	+	0.452267i
$34$		0			0
$35$		0			0
$36$	−0.500000	+	0.866025i	−0.0833333	+	0.144338i
$37$	4.50000	−	7.79423i	0.739795	−	1.28136i	−0.212792	−	0.977098i	$-0.568256\pi$
$37$	4.50000	−	7.79423i	0.739795	−	1.28136i	0.952587	−	0.304266i	$-0.0984111\pi$
$38$	3.00000			0.486664
$39$	1.00000	+	3.46410i	0.160128	+	0.554700i
$40$		0			0
$41$	5.00000	−	8.66025i	0.780869	−	1.35250i	−0.150567	−	0.988600i	$-0.548110\pi$
$41$	5.00000	−	8.66025i	0.780869	−	1.35250i	0.931436	−	0.363905i	$-0.118557\pi$
$42$	1.50000	−	2.59808i	0.231455	−	0.400892i
$43$	−5.00000	−	8.66025i	−0.762493	−	1.32068i	−0.941562	−	0.336840i	$-0.890642\pi$
$43$	−5.00000	−	8.66025i	−0.762493	−	1.32068i	0.179069	−	0.983836i	$-0.442691\pi$
$44$	−3.00000			−0.452267
$45$		0			0
$46$	−2.00000	−	3.46410i	−0.294884	−	0.510754i
$47$	3.00000			0.437595			0.218797	−	0.975770i	$-0.429787\pi$
$47$	3.00000			0.437595			0.218797	+	0.975770i	$0.429787\pi$
$48$	−0.500000	−	0.866025i	−0.0721688	−	0.125000i
$49$	−1.00000	+	1.73205i	−0.142857	+	0.247436i
$50$		0			0
$51$		0			0
$52$	−3.50000	−	0.866025i	−0.485363	−	0.120096i
$53$	−9.00000			−1.23625			−0.618123	−	0.786082i	$-0.712106\pi$
$53$	−9.00000			−1.23625			−0.618123	+	0.786082i	$0.712106\pi$
$54$	−0.500000	+	0.866025i	−0.0680414	+	0.117851i
$55$		0			0
$56$	1.50000	+	2.59808i	0.200446	+	0.347183i
$57$	3.00000			0.397360
$58$	2.00000	+	3.46410i	0.262613	+	0.454859i
$59$	−6.00000	−	10.3923i	−0.781133	−	1.35296i	−0.931282	−	0.364299i	$-0.881308\pi$
$59$	−6.00000	−	10.3923i	−0.781133	−	1.35296i	0.150148	−	0.988663i	$-0.452025\pi$
$60$		0			0
$61$	3.00000	+	5.19615i	0.384111	+	0.665299i	0.991645	−	0.128994i	$-0.0411748\pi$
$61$	3.00000	+	5.19615i	0.384111	+	0.665299i	−0.607535	+	0.794293i	$0.707841\pi$
$62$	−3.00000	+	5.19615i	−0.381000	+	0.659912i
$63$	1.50000	−	2.59808i	0.188982	−	0.327327i
$64$	1.00000			0.125000
$65$		0			0
$66$	−3.00000			−0.369274
$67$	−4.00000	+	6.92820i	−0.488678	+	0.846415i	−0.999915	−	0.0130248i	$-0.995854\pi$
$67$	−4.00000	+	6.92820i	−0.488678	+	0.846415i	0.511237	+	0.859440i	$0.329187\pi$
$68$		0			0
$69$	−2.00000	−	3.46410i	−0.240772	−	0.417029i
$70$		0			0
$71$	7.00000	+	12.1244i	0.830747	+	1.43890i	0.897447	+	0.441123i	$0.145420\pi$
$71$	7.00000	+	12.1244i	0.830747	+	1.43890i	−0.0666994	+	0.997773i	$0.521247\pi$
$72$	−0.500000	−	0.866025i	−0.0589256	−	0.102062i
$73$	8.00000			0.936329			0.468165	−	0.883641i	$-0.344915\pi$
$73$	8.00000			0.936329			0.468165	+	0.883641i	$0.344915\pi$
$74$	4.50000	+	7.79423i	0.523114	+	0.906061i
$75$		0			0
$76$	−1.50000	+	2.59808i	−0.172062	+	0.298020i
$77$	9.00000			1.02565
$78$	−3.50000	−	0.866025i	−0.396297	−	0.0980581i
$79$	6.00000			0.675053			0.337526	−	0.941316i	$-0.390410\pi$
$79$	6.00000			0.675053			0.337526	+	0.941316i	$0.390410\pi$
$80$		0			0
$81$	−0.500000	+	0.866025i	−0.0555556	+	0.0962250i
$82$	5.00000	+	8.66025i	0.552158	+	0.956365i
$83$	−16.0000			−1.75623			−0.878114	−	0.478451i	$-0.841198\pi$
$83$	−16.0000			−1.75623			−0.878114	+	0.478451i	$0.841198\pi$
$84$	1.50000	+	2.59808i	0.163663	+	0.283473i
$85$		0			0
$86$	10.0000			1.07833
$87$	2.00000	+	3.46410i	0.214423	+	0.371391i
$88$	1.50000	−	2.59808i	0.159901	−	0.276956i
$89$	1.50000	−	2.59808i	0.159000	−	0.275396i	−0.775509	−	0.631337i	$-0.782506\pi$
$89$	1.50000	−	2.59808i	0.159000	−	0.275396i	0.934508	+	0.355942i	$0.115840\pi$
$90$		0			0
$91$	10.5000	+	2.59808i	1.10070	+	0.272352i
$92$	4.00000			0.417029
$93$	−3.00000	+	5.19615i	−0.311086	+	0.538816i
$94$	−1.50000	+	2.59808i	−0.154713	+	0.267971i
$95$		0			0
$96$	1.00000			0.102062
$97$	4.00000	+	6.92820i	0.406138	+	0.703452i	0.994453	−	0.105180i	$-0.0335417\pi$
$97$	4.00000	+	6.92820i	0.406138	+	0.703452i	−0.588315	+	0.808632i	$0.700208\pi$
$98$	−1.00000	−	1.73205i	−0.101015	−	0.174964i
$99$	−3.00000			−0.301511
$100$		0			0
$101$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$101$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$102$		0			0
$103$	15.0000			1.47799			0.738997	−	0.673709i	$-0.235300\pi$
$103$	15.0000			1.47799			0.738997	+	0.673709i	$0.235300\pi$
$104$	2.50000	−	2.59808i	0.245145	−	0.254762i
$105$		0			0
$106$	4.50000	−	7.79423i	0.437079	−	0.757042i
$107$	1.00000	−	1.73205i	0.0966736	−	0.167444i	−0.813632	−	0.581380i	$-0.802513\pi$
$107$	1.00000	−	1.73205i	0.0966736	−	0.167444i	0.910306	+	0.413936i	$0.135846\pi$
$108$	−0.500000	−	0.866025i	−0.0481125	−	0.0833333i
$109$	−2.00000			−0.191565			−0.0957826	−	0.995402i	$-0.530535\pi$
$109$	−2.00000			−0.191565			−0.0957826	+	0.995402i	$0.530535\pi$
$110$		0			0
$111$	4.50000	+	7.79423i	0.427121	+	0.739795i
$112$	−3.00000			−0.283473
$113$	−4.00000	−	6.92820i	−0.376288	−	0.651751i	0.614231	−	0.789127i	$-0.289466\pi$
$113$	−4.00000	−	6.92820i	−0.376288	−	0.651751i	−0.990519	+	0.137376i	$0.956133\pi$
$114$	−1.50000	+	2.59808i	−0.140488	+	0.243332i
$115$		0			0
$116$	−4.00000			−0.371391
$117$	−3.50000	−	0.866025i	−0.323575	−	0.0800641i
$118$	12.0000			1.10469
$119$		0			0
$120$		0			0
$121$	1.00000	+	1.73205i	0.0909091	+	0.157459i
$122$	−6.00000			−0.543214
$123$	5.00000	+	8.66025i	0.450835	+	0.780869i
$124$	−3.00000	−	5.19615i	−0.269408	−	0.466628i
$125$		0			0
$126$	1.50000	+	2.59808i	0.133631	+	0.231455i
$127$	1.50000	−	2.59808i	0.133103	−	0.230542i	−0.791768	−	0.610822i	$-0.790839\pi$
$127$	1.50000	−	2.59808i	0.133103	−	0.230542i	0.924871	+	0.380280i	$0.124172\pi$
$128$	−0.500000	+	0.866025i	−0.0441942	+	0.0765466i
$129$	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	$0.541837\pi$
$132$	1.50000	−	2.59808i	0.130558	−	0.226134i
$133$	4.50000	−	7.79423i	0.390199	−	0.675845i
$134$	−4.00000	−	6.92820i	−0.345547	−	0.598506i
$135$		0			0
$136$		0			0
$137$	6.00000	+	10.3923i	0.512615	+	0.887875i	0.999893	+	0.0146279i	$0.00465636\pi$
$137$	6.00000	+	10.3923i	0.512615	+	0.887875i	−0.487278	+	0.873247i	$0.662010\pi$
$138$	4.00000			0.340503
$139$	8.50000	+	14.7224i	0.720961	+	1.24874i	0.960615	+	0.277882i	$0.0896325\pi$
$139$	8.50000	+	14.7224i	0.720961	+	1.24874i	−0.239655	+	0.970858i	$0.577034\pi$
$140$		0			0
$141$	−1.50000	+	2.59808i	−0.126323	+	0.218797i
$142$	−14.0000			−1.17485
$143$	−3.00000	−	10.3923i	−0.250873	−	0.869048i
$144$	1.00000			0.0833333
$145$		0			0
$146$	−4.00000	+	6.92820i	−0.331042	+	0.573382i
$147$	−1.00000	−	1.73205i	−0.0824786	−	0.142857i
$148$	−9.00000			−0.739795
$149$	1.00000	+	1.73205i	0.0819232	+	0.141895i	0.904076	−	0.427372i	$-0.140560\pi$
$149$	1.00000	+	1.73205i	0.0819232	+	0.141895i	−0.822153	+	0.569267i	$0.807227\pi$
$150$		0			0
$151$	14.0000			1.13930			0.569652	−	0.821886i	$-0.307078\pi$
$151$	14.0000			1.13930			0.569652	+	0.821886i	$0.307078\pi$
$152$	−1.50000	−	2.59808i	−0.121666	−	0.210732i
$153$		0			0
$154$	−4.50000	+	7.79423i	−0.362620	+	0.628077i
$155$		0			0
$156$	2.50000	−	2.59808i	0.200160	−	0.208013i
$157$	17.0000			1.35675			0.678374	−	0.734717i	$-0.262685\pi$
$157$	17.0000			1.35675			0.678374	+	0.734717i	$0.262685\pi$
$158$	−3.00000	+	5.19615i	−0.238667	+	0.413384i
$159$	4.50000	−	7.79423i	0.356873	−	0.618123i
$160$		0			0
$161$	−12.0000			−0.945732
$162$	−0.500000	−	0.866025i	−0.0392837	−	0.0680414i
$163$	10.0000	+	17.3205i	0.783260	+	1.35665i	0.930033	+	0.367477i	$0.119778\pi$
$163$	10.0000	+	17.3205i	0.783260	+	1.35665i	−0.146772	+	0.989170i	$0.546888\pi$
$164$	−10.0000			−0.780869
$165$		0			0
$166$	8.00000	−	13.8564i	0.620920	−	1.07547i
$167$	4.50000	−	7.79423i	0.348220	−	0.603136i	−0.637713	−	0.770274i	$-0.720119\pi$
$167$	4.50000	−	7.79423i	0.348220	−	0.603136i	0.985933	+	0.167139i	$0.0534527\pi$
$168$	−3.00000			−0.231455
$169$	−0.500000	−	12.9904i	−0.0384615	−	0.999260i
$170$		0			0
$171$	−1.50000	+	2.59808i	−0.114708	+	0.198680i
$172$	−5.00000	+	8.66025i	−0.381246	+	0.660338i
$173$	6.50000	+	11.2583i	0.494186	+	0.855955i	0.999978	−	0.00670064i	$-0.00213290\pi$
$173$	6.50000	+	11.2583i	0.494186	+	0.855955i	−0.505792	+	0.862656i	$0.668800\pi$
$174$	−4.00000			−0.303239
$175$		0			0
$176$	1.50000	+	2.59808i	0.113067	+	0.195837i
$177$	12.0000			0.901975
$178$	1.50000	+	2.59808i	0.112430	+	0.194734i
$179$	−2.00000	+	3.46410i	−0.149487	+	0.258919i	−0.931038	−	0.364922i	$-0.881096\pi$
$179$	−2.00000	+	3.46410i	−0.149487	+	0.258919i	0.781551	+	0.623841i	$0.214429\pi$
$180$		0			0
$181$	−10.0000			−0.743294			−0.371647	−	0.928374i	$-0.621207\pi$
$181$	−10.0000			−0.743294			−0.371647	+	0.928374i	$0.621207\pi$
$182$	−7.50000	+	7.79423i	−0.555937	+	0.577747i
$183$	−6.00000			−0.443533
$184$	−2.00000	+	3.46410i	−0.147442	+	0.255377i
$185$		0			0
$186$	−3.00000	−	5.19615i	−0.219971	−	0.381000i
$187$		0			0
$188$	−1.50000	−	2.59808i	−0.109399	−	0.189484i
$189$	1.50000	+	2.59808i	0.109109	+	0.188982i
$190$		0			0
$191$	3.00000	+	5.19615i	0.217072	+	0.375980i	0.953912	−	0.300088i	$-0.0970159\pi$
$191$	3.00000	+	5.19615i	0.217072	+	0.375980i	−0.736839	+	0.676068i	$0.763683\pi$
$192$	−0.500000	+	0.866025i	−0.0360844	+	0.0625000i
$193$	4.00000	−	6.92820i	0.287926	−	0.498703i	−0.685388	−	0.728178i	$-0.740368\pi$
$193$	4.00000	−	6.92820i	0.287926	−	0.498703i	0.973315	+	0.229475i	$0.0737008\pi$
$194$	−8.00000			−0.574367
$195$		0			0
$196$	2.00000			0.142857
$197$	5.50000	−	9.52628i	0.391859	−	0.678719i	−0.600836	−	0.799372i	$-0.705166\pi$
$197$	5.50000	−	9.52628i	0.391859	−	0.678719i	0.992695	+	0.120653i	$0.0384988\pi$
$198$	1.50000	−	2.59808i	0.106600	−	0.184637i
$199$	5.00000	+	8.66025i	0.354441	+	0.613909i	0.987022	−	0.160585i	$-0.0513380\pi$
$199$	5.00000	+	8.66025i	0.354441	+	0.613909i	−0.632581	+	0.774494i	$0.718005\pi$
$200$		0			0
$201$	−4.00000	−	6.92820i	−0.282138	−	0.488678i
$202$		0			0
$203$	12.0000			0.842235
$204$		0			0
$205$		0			0
$206$	−7.50000	+	12.9904i	−0.522550	+	0.905083i
$207$	4.00000			0.278019
$208$	1.00000	+	3.46410i	0.0693375	+	0.240192i
$209$	−9.00000			−0.622543
$210$		0			0
$211$	−4.50000	+	7.79423i	−0.309793	+	0.536577i	−0.978317	−	0.207114i	$-0.933593\pi$
$211$	−4.50000	+	7.79423i	−0.309793	+	0.536577i	0.668524	+	0.743690i	$0.266926\pi$
$212$	4.50000	+	7.79423i	0.309061	+	0.535310i
$213$	−14.0000			−0.959264
$214$	1.00000	+	1.73205i	0.0683586	+	0.118401i
$215$		0			0
$216$	1.00000			0.0680414
$217$	9.00000	+	15.5885i	0.610960	+	1.05821i
$218$	1.00000	−	1.73205i	0.0677285	−	0.117309i
$219$	−4.00000	+	6.92820i	−0.270295	+	0.468165i
$220$		0			0
$221$		0			0
$222$	−9.00000			−0.604040
$223$	−5.50000	+	9.52628i	−0.368307	+	0.637927i	−0.989301	−	0.145889i	$-0.953396\pi$
$223$	−5.50000	+	9.52628i	−0.368307	+	0.637927i	0.620994	+	0.783815i	$0.286729\pi$
$224$	1.50000	−	2.59808i	0.100223	−	0.173591i
$225$		0			0
$226$	8.00000			0.532152
$227$	−8.00000	−	13.8564i	−0.530979	−	0.919682i	−0.999346	−	0.0361484i	$-0.988491\pi$
$227$	−8.00000	−	13.8564i	−0.530979	−	0.919682i	0.468368	−	0.883534i	$-0.344842\pi$
$228$	−1.50000	−	2.59808i	−0.0993399	−	0.172062i
$229$	−10.0000			−0.660819			−0.330409	−	0.943838i	$-0.607187\pi$
$229$	−10.0000			−0.660819			−0.330409	+	0.943838i	$0.607187\pi$
$230$		0			0
$231$	−4.50000	+	7.79423i	−0.296078	+	0.512823i
$232$	2.00000	−	3.46410i	0.131306	−	0.227429i
$233$	6.00000			0.393073			0.196537	−	0.980497i	$-0.437031\pi$
$233$	6.00000			0.393073			0.196537	+	0.980497i	$0.437031\pi$
$234$	2.50000	−	2.59808i	0.163430	−	0.169842i
$235$		0			0
$236$	−6.00000	+	10.3923i	−0.390567	+	0.676481i
$237$	−3.00000	+	5.19615i	−0.194871	+	0.337526i
$238$		0			0
$239$	−26.0000			−1.68180			−0.840900	−	0.541190i	$-0.817974\pi$
$239$	−26.0000			−1.68180			−0.840900	+	0.541190i	$0.817974\pi$
$240$		0			0
$241$	−3.50000	−	6.06218i	−0.225455	−	0.390499i	0.731001	−	0.682376i	$-0.239053\pi$
$241$	−3.50000	−	6.06218i	−0.225455	−	0.390499i	−0.956456	+	0.291877i	$0.905720\pi$
$242$	−2.00000			−0.128565
$243$	−0.500000	−	0.866025i	−0.0320750	−	0.0555556i
$244$	3.00000	−	5.19615i	0.192055	−	0.332650i
$245$		0			0
$246$	−10.0000			−0.637577
$247$	−10.5000	−	2.59808i	−0.668099	−	0.165312i
$248$	6.00000			0.381000
$249$	8.00000	−	13.8564i	0.506979	−	0.878114i
$250$		0			0
$251$	0.500000	+	0.866025i	0.0315597	+	0.0546630i	0.881374	−	0.472419i	$-0.156619\pi$
$251$	0.500000	+	0.866025i	0.0315597	+	0.0546630i	−0.849814	+	0.527082i	$0.823286\pi$
$252$	−3.00000			−0.188982
$253$	6.00000	+	10.3923i	0.377217	+	0.653359i
$254$	1.50000	+	2.59808i	0.0941184	+	0.163018i
$255$		0			0
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	6.00000	−	10.3923i	0.374270	−	0.648254i	−0.615948	−	0.787787i	$-0.711227\pi$
$257$	6.00000	−	10.3923i	0.374270	−	0.648254i	0.990217	+	0.139533i	$0.0445601\pi$
$258$	−5.00000	+	8.66025i	−0.311286	+	0.539164i
$259$	27.0000			1.67770
$260$		0			0
$261$	−4.00000			−0.247594
$262$	1.50000	−	2.59808i	0.0926703	−	0.160510i
$263$	−15.5000	+	26.8468i	−0.955771	+	1.65544i	−0.223177	+	0.974778i	$0.571643\pi$
$263$	−15.5000	+	26.8468i	−0.955771	+	1.65544i	−0.732594	+	0.680666i	$0.761691\pi$
$264$	1.50000	+	2.59808i	0.0923186	+	0.159901i
$265$		0			0
$266$	4.50000	+	7.79423i	0.275913	+	0.477895i
$267$	1.50000	+	2.59808i	0.0917985	+	0.159000i
$268$	8.00000			0.488678
$269$	2.00000	+	3.46410i	0.121942	+	0.211210i	0.920534	−	0.390664i	$-0.127754\pi$
$269$	2.00000	+	3.46410i	0.121942	+	0.211210i	−0.798591	+	0.601874i	$0.794421\pi$
$270$		0			0
$271$	6.00000	−	10.3923i	0.364474	−	0.631288i	−0.624218	−	0.781251i	$-0.714582\pi$
$271$	6.00000	−	10.3923i	0.364474	−	0.631288i	0.988692	+	0.149963i	$0.0479155\pi$
$272$		0			0
$273$	−7.50000	+	7.79423i	−0.453921	+	0.471728i
$274$	−12.0000			−0.724947
$275$		0			0
$276$	−2.00000	+	3.46410i	−0.120386	+	0.208514i
$277$	−15.5000	−	26.8468i	−0.931305	−	1.61307i	−0.781094	−	0.624413i	$-0.785338\pi$
$277$	−15.5000	−	26.8468i	−0.931305	−	1.61307i	−0.150210	−	0.988654i	$-0.547995\pi$
$278$	−17.0000			−1.01959
$279$	−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	$0.852700\pi$
$282$	−1.50000	−	2.59808i	−0.0893237	−	0.154713i
$283$	3.00000	−	5.19615i	0.178331	−	0.308879i	−0.762978	−	0.646425i	$-0.776263\pi$
$283$	3.00000	−	5.19615i	0.178331	−	0.308879i	0.941309	+	0.337546i	$0.109597\pi$
$284$	7.00000	−	12.1244i	0.415374	−	0.719448i
$285$		0			0
$286$	10.5000	+	2.59808i	0.620878	+	0.153627i
$287$	30.0000			1.77084
$288$	−0.500000	+	0.866025i	−0.0294628	+	0.0510310i
$289$	8.50000	−	14.7224i	0.500000	−	0.866025i
$290$		0			0
$291$	−8.00000			−0.468968
$292$	−4.00000	−	6.92820i	−0.234082	−	0.405442i
$293$	−0.500000	−	0.866025i	−0.0292103	−	0.0505937i	0.851051	−	0.525084i	$-0.175966\pi$
$293$	−0.500000	−	0.866025i	−0.0292103	−	0.0505937i	−0.880261	+	0.474490i	$0.842633\pi$
$294$	2.00000			0.116642
$295$		0			0
$296$	4.50000	−	7.79423i	0.261557	−	0.453030i
$297$	1.50000	−	2.59808i	0.0870388	−	0.150756i
$298$	−2.00000			−0.115857
$299$	4.00000	+	13.8564i	0.231326	+	0.801337i
$300$		0			0
$301$	15.0000	−	25.9808i	0.864586	−	1.49751i
$302$	−7.00000	+	12.1244i	−0.402805	+	0.697678i
$303$		0			0
$304$	3.00000			0.172062
$305$		0			0
$306$		0			0
$307$	−26.0000			−1.48390			−0.741949	−	0.670456i	$-0.766098\pi$
$307$	−26.0000			−1.48390			−0.741949	+	0.670456i	$0.766098\pi$
$308$	−4.50000	−	7.79423i	−0.256411	−	0.444117i
$309$	−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	$0.536177\pi$
$312$	1.00000	+	3.46410i	0.0566139	+	0.196116i
$313$	−26.0000			−1.46961			−0.734803	−	0.678280i	$-0.762726\pi$
$313$	−26.0000			−1.46961			−0.734803	+	0.678280i	$0.762726\pi$
$314$	−8.50000	+	14.7224i	−0.479683	+	0.830835i
$315$		0			0
$316$	−3.00000	−	5.19615i	−0.168763	−	0.292306i
$317$	−17.0000			−0.954815			−0.477408	−	0.878682i	$-0.658423\pi$
$317$	−17.0000			−0.954815			−0.477408	+	0.878682i	$0.658423\pi$
$318$	4.50000	+	7.79423i	0.252347	+	0.437079i
$319$	−6.00000	−	10.3923i	−0.335936	−	0.581857i
$320$		0			0
$321$	1.00000	+	1.73205i	0.0558146	+	0.0966736i
$322$	6.00000	−	10.3923i	0.334367	−	0.579141i
$323$		0			0
$324$	1.00000			0.0555556
$325$		0			0
$326$	−20.0000			−1.10770
$327$	1.00000	−	1.73205i	0.0553001	−	0.0957826i
$328$	5.00000	−	8.66025i	0.276079	−	0.478183i
$329$	4.50000	+	7.79423i	0.248093	+	0.429710i
$330$		0			0
$331$	14.0000	+	24.2487i	0.769510	+	1.33283i	0.937829	+	0.347097i	$0.112833\pi$
$331$	14.0000	+	24.2487i	0.769510	+	1.33283i	−0.168320	+	0.985732i	$0.553834\pi$
$332$	8.00000	+	13.8564i	0.439057	+	0.760469i
$333$	−9.00000			−0.493197
$334$	4.50000	+	7.79423i	0.246229	+	0.426481i
$335$		0			0
$336$	1.50000	−	2.59808i	0.0818317	−	0.141737i
$337$	−6.00000			−0.326841			−0.163420	−	0.986557i	$-0.552253\pi$
$337$	−6.00000			−0.326841			−0.163420	+	0.986557i	$0.552253\pi$
$338$	11.5000	+	6.06218i	0.625518	+	0.329739i
$339$	8.00000			0.434500
$340$		0			0
$341$	9.00000	−	15.5885i	0.487377	−	0.844162i
$342$	−1.50000	−	2.59808i	−0.0811107	−	0.140488i
$343$	15.0000			0.809924
$344$	−5.00000	−	8.66025i	−0.269582	−	0.466930i
$345$		0			0
$346$	−13.0000			−0.698884
$347$	−12.0000	−	20.7846i	−0.644194	−	1.11578i	−0.984487	−	0.175457i	$-0.943860\pi$
$347$	−12.0000	−	20.7846i	−0.644194	−	1.11578i	0.340293	−	0.940319i	$-0.389474\pi$
$348$	2.00000	−	3.46410i	0.107211	−	0.185695i
$349$	−8.00000	+	13.8564i	−0.428230	+	0.741716i	−0.996716	−	0.0809766i	$-0.974196\pi$
$349$	−8.00000	+	13.8564i	−0.428230	+	0.741716i	0.568486	+	0.822693i	$0.307529\pi$
$350$		0			0
$351$	2.50000	−	2.59808i	0.133440	−	0.138675i
$352$	−3.00000			−0.159901
$353$	−4.00000	+	6.92820i	−0.212899	+	0.368751i	−0.952620	−	0.304162i	$-0.901624\pi$
$353$	−4.00000	+	6.92820i	−0.212899	+	0.368751i	0.739722	+	0.672913i	$0.234957\pi$
$354$	−6.00000	+	10.3923i	−0.318896	+	0.552345i
$355$		0			0
$356$	−3.00000			−0.159000
$357$		0			0
$358$	−2.00000	−	3.46410i	−0.105703	−	0.183083i
$359$	30.0000			1.58334			0.791670	−	0.610949i	$-0.209212\pi$
$359$	30.0000			1.58334			0.791670	+	0.610949i	$0.209212\pi$
$360$		0			0
$361$	5.00000	−	8.66025i	0.263158	−	0.455803i
$362$	5.00000	−	8.66025i	0.262794	−	0.455173i
$363$	−2.00000			−0.104973
$364$	−3.00000	−	10.3923i	−0.157243	−	0.544705i
$365$		0			0
$366$	3.00000	−	5.19615i	0.156813	−	0.271607i
$367$	4.00000	−	6.92820i	0.208798	−	0.361649i	−0.742538	−	0.669804i	$-0.766378\pi$
$367$	4.00000	−	6.92820i	0.208798	−	0.361649i	0.951336	+	0.308155i	$0.0997115\pi$
$368$	−2.00000	−	3.46410i	−0.104257	−	0.180579i
$369$	−10.0000			−0.520579
$370$		0			0
$371$	−13.5000	−	23.3827i	−0.700885	−	1.21397i
$372$	6.00000			0.311086
$373$	−13.0000	−	22.5167i	−0.673114	−	1.16587i	−0.977016	−	0.213165i	$-0.931623\pi$
$373$	−13.0000	−	22.5167i	−0.673114	−	1.16587i	0.303902	−	0.952703i	$-0.401711\pi$
$374$		0			0
$375$		0			0
$376$	3.00000			0.154713
$377$	−4.00000	−	13.8564i	−0.206010	−	0.713641i
$378$	−3.00000			−0.154303
$379$	16.5000	−	28.5788i	0.847548	−	1.46800i	−0.0358418	−	0.999357i	$-0.511411\pi$
$379$	16.5000	−	28.5788i	0.847548	−	1.46800i	0.883390	−	0.468639i	$-0.155255\pi$
$380$		0			0
$381$	1.50000	+	2.59808i	0.0768473	+	0.133103i
$382$	−6.00000			−0.306987
$383$	2.00000	+	3.46410i	0.102195	+	0.177007i	0.912589	−	0.408879i	$-0.134080\pi$
$383$	2.00000	+	3.46410i	0.102195	+	0.177007i	−0.810394	+	0.585886i	$0.800747\pi$
$384$	−0.500000	−	0.866025i	−0.0255155	−	0.0441942i
$385$		0			0
$386$	4.00000	+	6.92820i	0.203595	+	0.352636i
$387$	−5.00000	+	8.66025i	−0.254164	+	0.440225i
$388$	4.00000	−	6.92820i	0.203069	−	0.351726i
$389$	24.0000			1.21685			0.608424	−	0.793612i	$-0.291802\pi$
$389$	24.0000			1.21685			0.608424	+	0.793612i	$0.291802\pi$
$390$		0			0
$391$		0			0
$392$	−1.00000	+	1.73205i	−0.0505076	+	0.0874818i
$393$	1.50000	−	2.59808i	0.0756650	−	0.131056i
$394$	5.50000	+	9.52628i	0.277086	+	0.479927i
$395$		0			0
$396$	1.50000	+	2.59808i	0.0753778	+	0.130558i
$397$	−11.5000	−	19.9186i	−0.577168	−	0.999685i	−0.995802	−	0.0915300i	$-0.970824\pi$
$397$	−11.5000	−	19.9186i	−0.577168	−	0.999685i	0.418634	−	0.908155i	$-0.362509\pi$
$398$	−10.0000			−0.501255
$399$	4.50000	+	7.79423i	0.225282	+	0.390199i
$400$		0			0
$401$	13.5000	−	23.3827i	0.674158	−	1.16768i	−0.302556	−	0.953131i	$-0.597840\pi$
$401$	13.5000	−	23.3827i	0.674158	−	1.16768i	0.976714	−	0.214544i	$-0.0688266\pi$
$402$	8.00000			0.399004
$403$	15.0000	−	15.5885i	0.747203	−	0.776516i
$404$		0			0
$405$		0			0
$406$	−6.00000	+	10.3923i	−0.297775	+	0.515761i
$407$	−13.5000	−	23.3827i	−0.669170	−	1.15904i
$408$		0			0
$409$	3.50000	+	6.06218i	0.173064	+	0.299755i	0.939490	−	0.342578i	$-0.111300\pi$
$409$	3.50000	+	6.06218i	0.173064	+	0.299755i	−0.766426	+	0.642333i	$0.777967\pi$
$410$		0			0
$411$	−12.0000			−0.591916
$412$	−7.50000	−	12.9904i	−0.369498	−	0.639990i
$413$	18.0000	−	31.1769i	0.885722	−	1.53412i
$414$	−2.00000	+	3.46410i	−0.0982946	+	0.170251i
$415$		0			0
$416$	−3.50000	−	0.866025i	−0.171602	−	0.0424604i
$417$	−17.0000			−0.832494
$418$	4.50000	−	7.79423i	0.220102	−	0.381228i
$419$	6.00000	−	10.3923i	0.293119	−	0.507697i	−0.681426	−	0.731887i	$-0.738640\pi$
$419$	6.00000	−	10.3923i	0.293119	−	0.507697i	0.974546	+	0.224189i	$0.0719734\pi$
$420$		0			0
$421$	−28.0000			−1.36464			−0.682318	−	0.731055i	$-0.739028\pi$
$421$	−28.0000			−1.36464			−0.682318	+	0.731055i	$0.739028\pi$
$422$	−4.50000	−	7.79423i	−0.219057	−	0.379417i
$423$	−1.50000	−	2.59808i	−0.0729325	−	0.126323i
$424$	−9.00000			−0.437079
$425$		0			0
$426$	7.00000	−	12.1244i	0.339151	−	0.587427i
$427$	−9.00000	+	15.5885i	−0.435541	+	0.754378i
$428$	−2.00000			−0.0966736
$429$	10.5000	+	2.59808i	0.506945	+	0.125436i
$430$		0			0
$431$	6.00000	−	10.3923i	0.289010	−	0.500580i	−0.684564	−	0.728953i	$-0.740007\pi$
$431$	6.00000	−	10.3923i	0.289010	−	0.500580i	0.973574	+	0.228373i	$0.0733406\pi$
$432$	−0.500000	+	0.866025i	−0.0240563	+	0.0416667i
$433$	−8.00000	−	13.8564i	−0.384455	−	0.665896i	0.607238	−	0.794520i	$-0.292277\pi$
$433$	−8.00000	−	13.8564i	−0.384455	−	0.665896i	−0.991693	+	0.128624i	$0.958944\pi$
$434$	−18.0000			−0.864028
$435$		0			0
$436$	1.00000	+	1.73205i	0.0478913	+	0.0829502i
$437$	12.0000			0.574038
$438$	−4.00000	−	6.92820i	−0.191127	−	0.331042i
$439$	15.0000	−	25.9808i	0.715911	−	1.23999i	−0.246696	−	0.969093i	$-0.579345\pi$
$439$	15.0000	−	25.9808i	0.715911	−	1.23999i	0.962607	−	0.270901i	$-0.0873217\pi$
$440$		0			0
$441$	2.00000			0.0952381
$442$		0			0
$443$	10.0000			0.475114			0.237557	−	0.971374i	$-0.423653\pi$
$443$	10.0000			0.475114			0.237557	+	0.971374i	$0.423653\pi$
$444$	4.50000	−	7.79423i	0.213561	−	0.369898i
$445$		0			0
$446$	−5.50000	−	9.52628i	−0.260433	−	0.451082i
$447$	−2.00000			−0.0945968
$448$	1.50000	+	2.59808i	0.0708683	+	0.122748i
$449$	17.5000	+	30.3109i	0.825876	+	1.43046i	0.901248	+	0.433304i	$0.142652\pi$
$449$	17.5000	+	30.3109i	0.825876	+	1.43046i	−0.0753719	+	0.997155i	$0.524014\pi$
$450$		0			0
$451$	−15.0000	−	25.9808i	−0.706322	−	1.22339i
$452$	−4.00000	+	6.92820i	−0.188144	+	0.325875i
$453$	−7.00000	+	12.1244i	−0.328889	+	0.569652i
$454$	16.0000			0.750917
$455$		0			0
$456$	3.00000			0.140488
$457$	−21.0000	+	36.3731i	−0.982339	+	1.70146i	−0.329125	+	0.944286i	$0.606754\pi$
$457$	−21.0000	+	36.3731i	−0.982339	+	1.70146i	−0.653213	+	0.757174i	$0.726579\pi$
$458$	5.00000	−	8.66025i	0.233635	−	0.404667i
$459$		0			0
$460$		0			0
$461$	16.0000	+	27.7128i	0.745194	+	1.29071i	0.950104	+	0.311933i	$0.100977\pi$
$461$	16.0000	+	27.7128i	0.745194	+	1.29071i	−0.204910	+	0.978781i	$0.565690\pi$
$462$	−4.50000	−	7.79423i	−0.209359	−	0.362620i
$463$	24.0000			1.11537			0.557687	−	0.830051i	$-0.311689\pi$
$463$	24.0000			1.11537			0.557687	+	0.830051i	$0.311689\pi$
$464$	2.00000	+	3.46410i	0.0928477	+	0.160817i
$465$		0			0
$466$	−3.00000	+	5.19615i	−0.138972	+	0.240707i
$467$	−8.00000			−0.370196			−0.185098	−	0.982720i	$-0.559260\pi$
$467$	−8.00000			−0.370196			−0.185098	+	0.982720i	$0.559260\pi$
$468$	1.00000	+	3.46410i	0.0462250	+	0.160128i
$469$	−24.0000			−1.10822
$470$		0			0
$471$	−8.50000	+	14.7224i	−0.391659	+	0.678374i
$472$	−6.00000	−	10.3923i	−0.276172	−	0.478345i
$473$	−30.0000			−1.37940
$474$	−3.00000	−	5.19615i	−0.137795	−	0.238667i
$475$		0			0
$476$		0			0
$477$	4.50000	+	7.79423i	0.206041	+	0.356873i
$478$	13.0000	−	22.5167i	0.594606	−	1.02989i
$479$	−6.00000	+	10.3923i	−0.274147	+	0.474837i	−0.969920	−	0.243426i	$-0.921729\pi$
$479$	−6.00000	+	10.3923i	−0.274147	+	0.474837i	0.695773	+	0.718262i	$0.255062\pi$
$480$		0			0
$481$	−9.00000	−	31.1769i	−0.410365	−	1.42154i
$482$	7.00000			0.318841
$483$	6.00000	−	10.3923i	0.273009	−	0.472866i
$484$	1.00000	−	1.73205i	0.0454545	−	0.0787296i
$485$		0			0
$486$	1.00000			0.0453609
$487$	14.5000	+	25.1147i	0.657058	+	1.13806i	0.981374	+	0.192109i	$0.0615326\pi$
$487$	14.5000	+	25.1147i	0.657058	+	1.13806i	−0.324316	+	0.945949i	$0.605134\pi$
$488$	3.00000	+	5.19615i	0.135804	+	0.235219i
$489$	−20.0000			−0.904431
$490$		0			0
$491$	−2.50000	+	4.33013i	−0.112823	+	0.195416i	−0.916908	−	0.399100i	$-0.869323\pi$
$491$	−2.50000	+	4.33013i	−0.112823	+	0.195416i	0.804084	+	0.594515i	$0.202656\pi$
$492$	5.00000	−	8.66025i	0.225417	−	0.390434i
$493$		0			0
$494$	7.50000	−	7.79423i	0.337441	−	0.350679i
$495$		0			0
$496$	−3.00000	+	5.19615i	−0.134704	+	0.233314i
$497$	−21.0000	+	36.3731i	−0.941979	+	1.63156i
$498$	8.00000	+	13.8564i	0.358489	+	0.620920i
$499$	20.0000			0.895323			0.447661	−	0.894203i	$-0.352257\pi$
$499$	20.0000			0.895323			0.447661	+	0.894203i	$0.352257\pi$
$500$		0			0
$501$	4.50000	+	7.79423i	0.201045	+	0.348220i
$502$	−1.00000			−0.0446322
$503$	10.5000	+	18.1865i	0.468172	+	0.810897i	0.999338	−	0.0363700i	$-0.0115795\pi$
$503$	10.5000	+	18.1865i	0.468172	+	0.810897i	−0.531167	+	0.847267i	$0.678246\pi$
$504$	1.50000	−	2.59808i	0.0668153	−	0.115728i
$505$		0			0
$506$	−12.0000			−0.533465
$507$	11.5000	+	6.06218i	0.510733	+	0.269231i
$508$	−3.00000			−0.133103
$509$	−5.00000	+	8.66025i	−0.221621	+	0.383859i	−0.955300	−	0.295637i	$-0.904468\pi$
$509$	−5.00000	+	8.66025i	−0.221621	+	0.383859i	0.733679	+	0.679496i	$0.237801\pi$
$510$		0			0
$511$	12.0000	+	20.7846i	0.530849	+	0.919457i
$512$	1.00000			0.0441942
$513$	−1.50000	−	2.59808i	−0.0662266	−	0.114708i
$514$	6.00000	+	10.3923i	0.264649	+	0.458385i
$515$		0			0
$516$	−5.00000	−	8.66025i	−0.220113	−	0.381246i
$517$	4.50000	−	7.79423i	0.197910	−	0.342790i
$518$	−13.5000	+	23.3827i	−0.593156	+	1.02738i
$519$	−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	$0.778097\pi$
$522$	2.00000	−	3.46410i	0.0875376	−	0.151620i
$523$	11.0000	−	19.0526i	0.480996	−	0.833110i	−0.518766	−	0.854916i	$-0.673608\pi$
$523$	11.0000	−	19.0526i	0.480996	−	0.833110i	0.999762	+	0.0218062i	$0.00694167\pi$
$524$	1.50000	+	2.59808i	0.0655278	+	0.113497i
$525$		0			0
$526$	−15.5000	−	26.8468i	−0.675832	−	1.17058i
$527$		0			0
$528$	−3.00000			−0.130558
$529$	3.50000	+	6.06218i	0.152174	+	0.263573i
$530$		0			0
$531$	−6.00000	+	10.3923i	−0.260378	+	0.450988i
$532$	−9.00000			−0.390199
$533$	−10.0000	−	34.6410i	−0.433148	−	1.50047i
$534$	−3.00000			−0.129823
$535$		0			0
$536$	−4.00000	+	6.92820i	−0.172774	+	0.299253i
$537$	−2.00000	−	3.46410i	−0.0863064	−	0.149487i
$538$	−4.00000			−0.172452
$539$	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	$0.656803\pi$
$542$	6.00000	+	10.3923i	0.257722	+	0.446388i
$543$	5.00000	−	8.66025i	0.214571	−	0.371647i
$544$		0			0
$545$		0			0
$546$	−3.00000	−	10.3923i	−0.128388	−	0.444750i
$547$	−22.0000			−0.940652			−0.470326	−	0.882493i	$-0.655864\pi$
$547$	−22.0000			−0.940652			−0.470326	+	0.882493i	$0.655864\pi$
$548$	6.00000	−	10.3923i	0.256307	−	0.443937i
$549$	3.00000	−	5.19615i	0.128037	−	0.221766i
$550$		0			0
$551$	−12.0000			−0.511217
$552$	−2.00000	−	3.46410i	−0.0851257	−	0.147442i
$553$	9.00000	+	15.5885i	0.382719	+	0.662889i
$554$	31.0000			1.31706
$555$		0			0
$556$	8.50000	−	14.7224i	0.360480	−	0.624370i
$557$	−4.50000	+	7.79423i	−0.190671	+	0.330252i	−0.945473	−	0.325701i	$-0.894400\pi$
$557$	−4.50000	+	7.79423i	−0.190671	+	0.330252i	0.754802	+	0.655953i	$0.227733\pi$
$558$	6.00000			0.254000
$559$	−35.0000	−	8.66025i	−1.48034	−	0.366290i
$560$		0			0
$561$		0			0
$562$	15.0000	−	25.9808i	0.632737	−	1.09593i
$563$	10.0000	+	17.3205i	0.421450	+	0.729972i	0.996082	−	0.0884397i	$-0.0281881\pi$
$563$	10.0000	+	17.3205i	0.421450	+	0.729972i	−0.574632	+	0.818412i	$0.694855\pi$
$564$	3.00000			0.126323
$565$		0			0
$566$	3.00000	+	5.19615i	0.126099	+	0.218411i
$567$	−3.00000			−0.125988
$568$	7.00000	+	12.1244i	0.293713	+	0.508727i
$569$	19.5000	−	33.7750i	0.817483	−	1.41592i	−0.0900490	−	0.995937i	$-0.528702\pi$
$569$	19.5000	−	33.7750i	0.817483	−	1.41592i	0.907532	−	0.419984i	$-0.137964\pi$
$570$		0			0
$571$	23.0000			0.962520			0.481260	−	0.876578i	$-0.340179\pi$
$571$	23.0000			0.962520			0.481260	+	0.876578i	$0.340179\pi$
$572$	−7.50000	+	7.79423i	−0.313591	+	0.325893i
$573$	−6.00000			−0.250654
$574$	−15.0000	+	25.9808i	−0.626088	+	1.08442i
$575$		0			0
$576$	−0.500000	−	0.866025i	−0.0208333	−	0.0360844i
$577$	38.0000			1.58196			0.790980	−	0.611842i	$-0.209571\pi$
$577$	38.0000			1.58196			0.790980	+	0.611842i	$0.209571\pi$
$578$	8.50000	+	14.7224i	0.353553	+	0.612372i
$579$	4.00000	+	6.92820i	0.166234	+	0.287926i
$580$		0			0
$581$	−24.0000	−	41.5692i	−0.995688	−	1.72458i
$582$	4.00000	−	6.92820i	0.165805	−	0.287183i
$583$	−13.5000	+	23.3827i	−0.559113	+	0.968412i
$584$	8.00000			0.331042
$585$		0			0
$586$	1.00000			0.0413096
$587$	9.00000	−	15.5885i	0.371470	−	0.643404i	−0.618322	−	0.785925i	$-0.712187\pi$
$587$	9.00000	−	15.5885i	0.371470	−	0.643404i	0.989792	+	0.142520i	$0.0455206\pi$
$588$	−1.00000	+	1.73205i	−0.0412393	+	0.0714286i
$589$	−9.00000	−	15.5885i	−0.370839	−	0.642311i
$590$		0			0
$591$	5.50000	+	9.52628i	0.226240	+	0.391859i
$592$	4.50000	+	7.79423i	0.184949	+	0.320341i
$593$	−36.0000			−1.47834			−0.739171	−	0.673517i	$-0.764783\pi$
$593$	−36.0000			−1.47834			−0.739171	+	0.673517i	$0.764783\pi$
$594$	1.50000	+	2.59808i	0.0615457	+	0.106600i
$595$		0			0
$596$	1.00000	−	1.73205i	0.0409616	−	0.0709476i
$597$	−10.0000			−0.409273
$598$	−14.0000	−	3.46410i	−0.572503	−	0.141658i
$599$	−30.0000			−1.22577			−0.612883	−	0.790173i	$-0.709990\pi$
$599$	−30.0000			−1.22577			−0.612883	+	0.790173i	$0.709990\pi$
$600$		0			0
$601$	−10.5000	+	18.1865i	−0.428304	+	0.741844i	−0.996723	−	0.0808953i	$-0.974222\pi$
$601$	−10.5000	+	18.1865i	−0.428304	+	0.741844i	0.568419	+	0.822739i	$0.307555\pi$
$602$	15.0000	+	25.9808i	0.611354	+	1.05890i
$603$	8.00000			0.325785
$604$	−7.00000	−	12.1244i	−0.284826	−	0.493333i
$605$		0			0
$606$		0			0
$607$	13.5000	+	23.3827i	0.547948	+	0.949074i	0.998415	+	0.0562808i	$0.0179242\pi$
$607$	13.5000	+	23.3827i	0.547948	+	0.949074i	−0.450467	+	0.892793i	$0.648742\pi$
$608$	−1.50000	+	2.59808i	−0.0608330	+	0.105366i
$609$	−6.00000	+	10.3923i	−0.243132	+	0.421117i
$610$		0			0
$611$	7.50000	−	7.79423i	0.303418	−	0.315321i
$612$		0			0
$613$	−3.50000	+	6.06218i	−0.141364	+	0.244849i	−0.928010	−	0.372554i	$-0.878482\pi$
$613$	−3.50000	+	6.06218i	−0.141364	+	0.244849i	0.786647	+	0.617403i	$0.211815\pi$
$614$	13.0000	−	22.5167i	0.524637	−	0.908698i
$615$		0			0
$616$	9.00000			0.362620
$617$	−15.0000	−	25.9808i	−0.603877	−	1.04595i	−0.992228	−	0.124434i	$-0.960288\pi$
$617$	−15.0000	−	25.9808i	−0.603877	−	1.04595i	0.388351	−	0.921512i	$-0.373045\pi$
$618$	−7.50000	−	12.9904i	−0.301694	−	0.522550i
$619$	−23.0000			−0.924448			−0.462224	−	0.886763i	$-0.652948\pi$
$619$	−23.0000			−0.924448			−0.462224	+	0.886763i	$0.652948\pi$
$620$		0			0
$621$	−2.00000	+	3.46410i	−0.0802572	+	0.139010i
$622$	2.00000	−	3.46410i	0.0801927	−	0.138898i
$623$	9.00000			0.360577
$624$	−3.50000	−	0.866025i	−0.140112	−	0.0346688i
$625$		0			0
$626$	13.0000	−	22.5167i	0.519584	−	0.899947i
$627$	4.50000	−	7.79423i	0.179713	−	0.311272i
$628$	−8.50000	−	14.7224i	−0.339187	−	0.587489i
$629$		0			0
$630$		0			0
$631$	−6.00000	−	10.3923i	−0.238856	−	0.413711i	0.721530	−	0.692383i	$-0.243439\pi$
$631$	−6.00000	−	10.3923i	−0.238856	−	0.413711i	−0.960386	+	0.278672i	$0.910106\pi$
$632$	6.00000			0.238667
$633$	−4.50000	−	7.79423i	−0.178859	−	0.309793i
$634$	8.50000	−	14.7224i	0.337578	−	0.584702i
$635$		0			0
$636$	−9.00000			−0.356873
$637$	2.00000	+	6.92820i	0.0792429	+	0.274505i
$638$	12.0000			0.475085
$639$	7.00000	−	12.1244i	0.276916	−	0.479632i
$640$		0			0
$641$	−17.5000	−	30.3109i	−0.691208	−	1.19721i	−0.971442	−	0.237276i	$-0.923745\pi$
$641$	−17.5000	−	30.3109i	−0.691208	−	1.19721i	0.280234	−	0.959932i	$-0.409588\pi$
$642$	−2.00000			−0.0789337
$643$	14.0000	+	24.2487i	0.552106	+	0.956276i	0.998122	+	0.0612510i	$0.0195090\pi$
$643$	14.0000	+	24.2487i	0.552106	+	0.956276i	−0.446016	+	0.895025i	$0.647158\pi$
$644$	6.00000	+	10.3923i	0.236433	+	0.409514i
$645$		0			0
$646$		0			0
$647$	−22.5000	+	38.9711i	−0.884566	+	1.53211i	−0.0383563	+	0.999264i	$0.512212\pi$
$647$	−22.5000	+	38.9711i	−0.884566	+	1.53211i	−0.846210	+	0.532850i	$0.821121\pi$
$648$	−0.500000	+	0.866025i	−0.0196419	+	0.0340207i
$649$	−36.0000			−1.41312
$650$		0			0
$651$	−18.0000			−0.705476
$652$	10.0000	−	17.3205i	0.391630	−	0.678323i
$653$	1.50000	−	2.59808i	0.0586995	−	0.101671i	−0.835182	−	0.549973i	$-0.814638\pi$
$653$	1.50000	−	2.59808i	0.0586995	−	0.101671i	0.893882	+	0.448303i	$0.147971\pi$
$654$	1.00000	+	1.73205i	0.0391031	+	0.0677285i
$655$		0			0
$656$	5.00000	+	8.66025i	0.195217	+	0.338126i
$657$	−4.00000	−	6.92820i	−0.156055	−	0.270295i
$658$	−9.00000			−0.350857
$659$	−2.00000	−	3.46410i	−0.0779089	−	0.134942i	0.824439	−	0.565951i	$-0.191491\pi$
$659$	−2.00000	−	3.46410i	−0.0779089	−	0.134942i	−0.902348	+	0.431009i	$0.858158\pi$
$660$		0			0
$661$	−15.0000	+	25.9808i	−0.583432	+	1.01053i	0.411636	+	0.911348i	$0.364957\pi$
$661$	−15.0000	+	25.9808i	−0.583432	+	1.01053i	−0.995069	+	0.0991864i	$0.968376\pi$
$662$	−28.0000			−1.08825
$663$		0			0
$664$	−16.0000			−0.620920
$665$		0			0
$666$	4.50000	−	7.79423i	0.174371	−	0.302020i
$667$	8.00000	+	13.8564i	0.309761	+	0.536522i
$668$	−9.00000			−0.348220
$669$	−5.50000	−	9.52628i	−0.212642	−	0.368307i
$670$		0			0
$671$	18.0000			0.694882
$672$	1.50000	+	2.59808i	0.0578638	+	0.100223i
$673$	24.0000	−	41.5692i	0.925132	−	1.60238i	0.133783	−	0.991011i	$-0.457287\pi$
$673$	24.0000	−	41.5692i	0.925132	−	1.60238i	0.791349	−	0.611365i	$-0.209379\pi$
$674$	3.00000	−	5.19615i	0.115556	−	0.200148i
$675$		0			0
$676$	−11.0000	+	6.92820i	−0.423077	+	0.266469i
$677$	6.00000			0.230599			0.115299	−	0.993331i	$-0.463217\pi$
$677$	6.00000			0.230599			0.115299	+	0.993331i	$0.463217\pi$
$678$	−4.00000	+	6.92820i	−0.153619	+	0.266076i
$679$	−12.0000	+	20.7846i	−0.460518	+	0.797640i
$680$		0			0
$681$	16.0000			0.613121
$682$	9.00000	+	15.5885i	0.344628	+	0.596913i
$683$	15.0000	+	25.9808i	0.573959	+	0.994126i	0.996154	+	0.0876211i	$0.0279265\pi$
$683$	15.0000	+	25.9808i	0.573959	+	0.994126i	−0.422195	+	0.906505i	$0.638740\pi$
$684$	3.00000			0.114708
$685$		0			0
$686$	−7.50000	+	12.9904i	−0.286351	+	0.495975i
$687$	5.00000	−	8.66025i	0.190762	−	0.330409i
$688$	10.0000			0.381246
$689$	−22.5000	+	23.3827i	−0.857182	+	0.890809i
$690$		0			0
$691$	3.50000	−	6.06218i	0.133146	−	0.230616i	−0.791742	−	0.610856i	$-0.790825\pi$
$691$	3.50000	−	6.06218i	0.133146	−	0.230616i	0.924888	+	0.380240i	$0.124159\pi$
$692$	6.50000	−	11.2583i	0.247093	−	0.427977i
$693$	−4.50000	−	7.79423i	−0.170941	−	0.296078i
$694$	24.0000			0.911028
$695$		0			0
$696$	2.00000	+	3.46410i	0.0758098	+	0.131306i
$697$		0			0
$698$	−8.00000	−	13.8564i	−0.302804	−	0.524473i
$699$	−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	$0.350270\pi$
$702$	1.00000	+	3.46410i	0.0377426	+	0.130744i
$703$	−27.0000			−1.01832
$704$	1.50000	−	2.59808i	0.0565334	−	0.0979187i
$705$		0			0
$706$	−4.00000	−	6.92820i	−0.150542	−	0.260746i
$707$		0			0
$708$	−6.00000	−	10.3923i	−0.225494	−	0.390567i
$709$	20.0000	+	34.6410i	0.751116	+	1.30097i	0.947282	+	0.320400i	$0.103817\pi$
$709$	20.0000	+	34.6410i	0.751116	+	1.30097i	−0.196167	+	0.980571i	$0.562849\pi$
$710$		0			0
$711$	−3.00000	−	5.19615i	−0.112509	−	0.194871i
$712$	1.50000	−	2.59808i	0.0562149	−	0.0973670i
$713$	−12.0000	+	20.7846i	−0.449404	+	0.778390i
$714$		0			0
$715$		0			0
$716$	4.00000			0.149487
$717$	13.0000	−	22.5167i	0.485494	−	0.840900i
$718$	−15.0000	+	25.9808i	−0.559795	+	0.969593i
$719$	18.0000	+	31.1769i	0.671287	+	1.16270i	0.977539	+	0.210752i	$0.0675914\pi$
$719$	18.0000	+	31.1769i	0.671287	+	1.16270i	−0.306253	+	0.951950i	$0.599075\pi$
$720$		0			0
$721$	22.5000	+	38.9711i	0.837944	+	1.45136i
$722$	5.00000	+	8.66025i	0.186081	+	0.322301i
$723$	7.00000			0.260333
$724$	5.00000	+	8.66025i	0.185824	+	0.321856i
$725$		0			0
$726$	1.00000	−	1.73205i	0.0371135	−	0.0642824i
$727$	3.00000			0.111264			0.0556319	−	0.998451i	$-0.482283\pi$
$727$	3.00000			0.111264			0.0556319	+	0.998451i	$0.482283\pi$
$728$	10.5000	+	2.59808i	0.389156	+	0.0962911i
$729$	1.00000			0.0370370
$730$		0			0
$731$		0			0
$732$	3.00000	+	5.19615i	0.110883	+	0.192055i
$733$	−53.0000			−1.95760			−0.978800	−	0.204819i	$-0.934339\pi$
$733$	−53.0000			−1.95760			−0.978800	+	0.204819i	$0.934339\pi$
$734$	4.00000	+	6.92820i	0.147643	+	0.255725i
$735$		0			0
$736$	4.00000			0.147442
$737$	12.0000	+	20.7846i	0.442026	+	0.765611i
$738$	5.00000	−	8.66025i	0.184053	−	0.318788i
$739$	−5.50000	+	9.52628i	−0.202321	+	0.350430i	−0.949276	−	0.314445i	$-0.898182\pi$
$739$	−5.50000	+	9.52628i	−0.202321	+	0.350430i	0.746955	+	0.664875i	$0.231515\pi$
$740$		0			0
$741$	7.50000	−	7.79423i	0.275519	−	0.286328i
$742$	27.0000			0.991201
$743$	24.0000	−	41.5692i	0.880475	−	1.52503i	0.0296605	−	0.999560i	$-0.490557\pi$
$743$	24.0000	−	41.5692i	0.880475	−	1.52503i	0.850814	−	0.525467i	$-0.176109\pi$
$744$	−3.00000	+	5.19615i	−0.109985	+	0.190500i
$745$		0			0
$746$	26.0000			0.951928
$747$	8.00000	+	13.8564i	0.292705	+	0.506979i
$748$		0			0
$749$	6.00000			0.219235
$750$		0			0
$751$	12.0000	−	20.7846i	0.437886	−	0.758441i	−0.559640	−	0.828736i	$-0.689061\pi$
$751$	12.0000	−	20.7846i	0.437886	−	0.758441i	0.997526	+	0.0702946i	$0.0223939\pi$
$752$	−1.50000	+	2.59808i	−0.0546994	+	0.0947421i
$753$	−1.00000			−0.0364420
$754$	14.0000	+	3.46410i	0.509850	+	0.126155i
$755$		0			0
$756$	1.50000	−	2.59808i	0.0545545	−	0.0944911i
$757$	8.50000	−	14.7224i	0.308938	−	0.535096i	−0.669193	−	0.743089i	$-0.733360\pi$
$757$	8.50000	−	14.7224i	0.308938	−	0.535096i	0.978130	+	0.207993i	$0.0666932\pi$
$758$	16.5000	+	28.5788i	0.599307	+	1.03803i
$759$	−12.0000			−0.435572
$760$		0			0
$761$	15.5000	+	26.8468i	0.561875	+	0.973195i	0.997333	+	0.0729864i	$0.0232530\pi$
$761$	15.5000	+	26.8468i	0.561875	+	0.973195i	−0.435458	+	0.900209i	$0.643414\pi$
$762$	−3.00000			−0.108679
$763$	−3.00000	−	5.19615i	−0.108607	−	0.188113i
$764$	3.00000	−	5.19615i	0.108536	−	0.187990i
$765$		0			0
$766$	−4.00000			−0.144526
$767$	−42.0000	−	10.3923i	−1.51653	−	0.375244i
$768$	1.00000			0.0360844
$769$	−23.0000	+	39.8372i	−0.829401	+	1.43657i	0.0691074	+	0.997609i	$0.477985\pi$
$769$	−23.0000	+	39.8372i	−0.829401	+	1.43657i	−0.898509	+	0.438956i	$0.855348\pi$
$770$		0			0
$771$	6.00000	+	10.3923i	0.216085	+	0.374270i
$772$	−8.00000			−0.287926
$773$	−3.50000	−	6.06218i	−0.125886	−	0.218041i	0.796193	−	0.605043i	$-0.206844\pi$
$773$	−3.50000	−	6.06218i	−0.125886	−	0.218041i	−0.922079	+	0.387002i	$0.873511\pi$
$774$	−5.00000	−	8.66025i	−0.179721	−	0.311286i
$775$		0			0
$776$	4.00000	+	6.92820i	0.143592	+	0.248708i
$777$	−13.5000	+	23.3827i	−0.484310	+	0.838849i
$778$	−12.0000	+	20.7846i	−0.430221	+	0.745164i
$779$	−30.0000			−1.07486
$780$		0			0
$781$	42.0000			1.50288
$782$		0			0
$783$	2.00000	−	3.46410i	0.0714742	−	0.123797i
$784$	−1.00000	−	1.73205i	−0.0357143	−	0.0618590i
$785$		0			0
$786$	1.50000	+	2.59808i	0.0535032	+	0.0926703i
$787$	−18.0000	−	31.1769i	−0.641631	−	1.11134i	−0.985069	−	0.172162i	$-0.944925\pi$
$787$	−18.0000	−	31.1769i	−0.641631	−	1.11134i	0.343438	−	0.939175i	$-0.388408\pi$
$788$	−11.0000			−0.391859
$789$	−15.5000	−	26.8468i	−0.551815	−	0.955771i
$790$		0			0
$791$	12.0000	−	20.7846i	0.426671	−	0.739016i
$792$	−3.00000			−0.106600
$793$	21.0000	+	5.19615i	0.745732	+	0.184521i
$794$	23.0000			0.816239
$795$		0			0
$796$	5.00000	−	8.66025i	0.177220	−	0.306955i
$797$	−21.0000	−	36.3731i	−0.743858	−	1.28840i	−0.950726	−	0.310031i	$-0.899660\pi$
$797$	−21.0000	−	36.3731i	−0.743858	−	1.28840i	0.206868	−	0.978369i	$-0.433673\pi$
$798$	−9.00000			−0.318597
$799$		0			0
$800$		0			0
$801$	−3.00000			−0.106000
$802$	13.5000	+	23.3827i	0.476702	+	0.825671i
$803$	12.0000	−	20.7846i	0.423471	−	0.733473i
$804$	−4.00000	+	6.92820i	−0.141069	+	0.244339i
$805$		0			0
$806$	6.00000	+	20.7846i	0.211341	+	0.732107i
$807$	−4.00000			−0.140807
$808$		0			0
$809$	5.00000	−	8.66025i	0.175791	−	0.304478i	−0.764644	−	0.644453i	$-0.777085\pi$
$809$	5.00000	−	8.66025i	0.175791	−	0.304478i	0.940435	+	0.339975i	$0.110418\pi$
$810$		0			0
$811$	−31.0000			−1.08856			−0.544279	−	0.838905i	$-0.683197\pi$
$811$	−31.0000			−1.08856			−0.544279	+	0.838905i	$0.683197\pi$
$812$	−6.00000	−	10.3923i	−0.210559	−	0.364698i
$813$	6.00000	+	10.3923i	0.210429	+	0.364474i
$814$	27.0000			0.946350
$815$		0			0
$816$		0			0
$817$	−15.0000	+	25.9808i	−0.524784	+	0.908952i
$818$	−7.00000			−0.244749
$819$	−3.00000	−	10.3923i	−0.104828	−	0.363137i
$820$		0			0
$821$	−25.0000	+	43.3013i	−0.872506	+	1.51122i	−0.0131101	+	0.999914i	$0.504173\pi$
$821$	−25.0000	+	43.3013i	−0.872506	+	1.51122i	−0.859396	+	0.511311i	$0.829160\pi$
$822$	6.00000	−	10.3923i	0.209274	−	0.362473i
$823$	−5.50000	−	9.52628i	−0.191718	−	0.332065i	0.754102	−	0.656758i	$-0.228073\pi$
$823$	−5.50000	−	9.52628i	−0.191718	−	0.332065i	−0.945820	+	0.324692i	$0.894739\pi$
$824$	15.0000			0.522550
$825$		0			0
$826$	18.0000	+	31.1769i	0.626300	+	1.08478i
$827$	18.0000			0.625921			0.312961	−	0.949766i	$-0.398679\pi$
$827$	18.0000			0.625921			0.312961	+	0.949766i	$0.398679\pi$
$828$	−2.00000	−	3.46410i	−0.0695048	−	0.120386i
$829$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$829$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$830$		0			0
$831$	31.0000			1.07538
$832$	2.50000	−	2.59808i	0.0866719	−	0.0900721i
$833$		0			0
$834$	8.50000	−	14.7224i	0.294331	−	0.509796i
$835$		0			0
$836$	4.50000	+	7.79423i	0.155636	+	0.269569i
$837$	6.00000			0.207390
$838$	6.00000	+	10.3923i	0.207267	+	0.358996i
$839$	3.00000	+	5.19615i	0.103572	+	0.179391i	0.913154	−	0.407615i	$-0.133640\pi$
$839$	3.00000	+	5.19615i	0.103572	+	0.179391i	−0.809582	+	0.587007i	$0.800306\pi$
$840$		0			0
$841$	6.50000	+	11.2583i	0.224138	+	0.388218i
$842$	14.0000	−	24.2487i	0.482472	−	0.835666i
$843$	15.0000	−	25.9808i	0.516627	−	0.894825i
$844$	9.00000			0.309793
$845$		0			0
$846$	3.00000			0.103142
$847$	−3.00000	+	5.19615i	−0.103081	+	0.178542i
$848$	4.50000	−	7.79423i	0.154531	−	0.267655i
$849$	3.00000	+	5.19615i	0.102960	+	0.178331i
$850$		0			0
$851$	18.0000	+	31.1769i	0.617032	+	1.06873i
$852$	7.00000	+	12.1244i	0.239816	+	0.415374i
$853$	26.0000			0.890223			0.445112	−	0.895475i	$-0.353164\pi$
$853$	26.0000			0.890223			0.445112	+	0.895475i	$0.353164\pi$
$854$	−9.00000	−	15.5885i	−0.307974	−	0.533426i
$855$		0			0
$856$	1.00000	−	1.73205i	0.0341793	−	0.0592003i
$857$	50.0000			1.70797			0.853984	−	0.520300i	$-0.174180\pi$
$857$	50.0000			1.70797			0.853984	+	0.520300i	$0.174180\pi$
$858$	−7.50000	+	7.79423i	−0.256046	+	0.266091i
$859$	−5.00000			−0.170598			−0.0852989	−	0.996355i	$-0.527185\pi$
$859$	−5.00000			−0.170598			−0.0852989	+	0.996355i	$0.527185\pi$
$860$		0			0
$861$	−15.0000	+	25.9808i	−0.511199	+	0.885422i
$862$	6.00000	+	10.3923i	0.204361	+	0.353963i
$863$	24.0000			0.816970			0.408485	−	0.912765i	$-0.366057\pi$
$863$	24.0000			0.816970			0.408485	+	0.912765i	$0.366057\pi$
$864$	−0.500000	−	0.866025i	−0.0170103	−	0.0294628i
$865$		0			0
$866$	16.0000			0.543702
$867$	8.50000	+	14.7224i	0.288675	+	0.500000i
$868$	9.00000	−	15.5885i	0.305480	−	0.529107i
$869$	9.00000	−	15.5885i	0.305304	−	0.528802i
$870$		0			0
$871$	8.00000	+	27.7128i	0.271070	+	0.939013i
$872$	−2.00000			−0.0677285
$873$	4.00000	−	6.92820i	0.135379	−	0.234484i
$874$	−6.00000	+	10.3923i	−0.202953	+	0.351525i
$875$		0			0
$876$	8.00000			0.270295
$877$	−19.0000	−	32.9090i	−0.641584	−	1.11126i	−0.985079	−	0.172102i	$-0.944944\pi$
$877$	−19.0000	−	32.9090i	−0.641584	−	1.11126i	0.343495	−	0.939155i	$-0.388389\pi$
$878$	15.0000	+	25.9808i	0.506225	+	0.876808i
$879$	1.00000			0.0337292
$880$		0			0
$881$	11.5000	−	19.9186i	0.387445	−	0.671074i	−0.604660	−	0.796484i	$-0.706691\pi$
$881$	11.5000	−	19.9186i	0.387445	−	0.671074i	0.992105	+	0.125409i	$0.0400244\pi$
$882$	−1.00000	+	1.73205i	−0.0336718	+	0.0583212i
$883$	−22.0000			−0.740359			−0.370179	−	0.928960i	$-0.620704\pi$
$883$	−22.0000			−0.740359			−0.370179	+	0.928960i	$0.620704\pi$
$884$		0			0
$885$		0			0
$886$	−5.00000	+	8.66025i	−0.167978	+	0.290947i
$887$	4.50000	−	7.79423i	0.151095	−	0.261705i	−0.780535	−	0.625112i	$-0.785053\pi$
$887$	4.50000	−	7.79423i	0.151095	−	0.261705i	0.931630	+	0.363407i	$0.118387\pi$
$888$	4.50000	+	7.79423i	0.151010	+	0.261557i
$889$	9.00000			0.301850
$890$		0			0
$891$	1.50000	+	2.59808i	0.0502519	+	0.0870388i
$892$	11.0000			0.368307
$893$	−4.50000	−	7.79423i	−0.150587	−	0.260824i
$894$	1.00000	−	1.73205i	0.0334450	−	0.0579284i
$895$		0			0
$896$	−3.00000			−0.100223
$897$	−14.0000	−	3.46410i	−0.467446	−	0.115663i
$898$	−35.0000			−1.16797
$899$	12.0000	−	20.7846i	0.400222	−	0.693206i
$900$		0			0
$901$		0			0
$902$	30.0000			0.998891
$903$	15.0000	+	25.9808i	0.499169	+	0.864586i
$904$	−4.00000	−	6.92820i	−0.133038	−	0.230429i
$905$		0			0
$906$	−7.00000	−	12.1244i	−0.232559	−	0.402805i
$907$	−7.00000	+	12.1244i	−0.232431	+	0.402583i	−0.958523	−	0.285015i	$-0.908001\pi$
$907$	−7.00000	+	12.1244i	−0.232431	+	0.402583i	0.726092	+	0.687598i	$0.241335\pi$
$908$	−8.00000	+	13.8564i	−0.265489	+	0.459841i
$909$		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	$0.346471\pi$
$912$	−1.50000	+	2.59808i	−0.0496700	+	0.0860309i
$913$	−24.0000	+	41.5692i	−0.794284	+	1.37574i
$914$	−21.0000	−	36.3731i	−0.694618	−	1.20311i
$915$		0			0
$916$	5.00000	+	8.66025i	0.165205	+	0.286143i
$917$	−4.50000	−	7.79423i	−0.148603	−	0.257388i
$918$		0			0
$919$	−7.00000	−	12.1244i	−0.230909	−	0.399946i	0.727167	−	0.686461i	$-0.240837\pi$
$919$	−7.00000	−	12.1244i	−0.230909	−	0.399946i	−0.958076	+	0.286515i	$0.907503\pi$
$920$		0			0
$921$	13.0000	−	22.5167i	0.428365	−	0.741949i
$922$	−32.0000			−1.05386
$923$	49.0000	+	12.1244i	1.61285	+	0.399078i
$924$	9.00000			0.296078
$925$		0			0
$926$	−12.0000	+	20.7846i	−0.394344	+	0.683025i
$927$	−7.50000	−	12.9904i	−0.246332	−	0.426660i
$928$	−4.00000			−0.131306
$929$	−1.00000	−	1.73205i	−0.0328089	−	0.0568267i	0.849155	−	0.528144i	$-0.177112\pi$
$929$	−1.00000	−	1.73205i	−0.0328089	−	0.0568267i	−0.881964	+	0.471317i	$0.843779\pi$
$930$		0			0
$931$	6.00000			0.196642
$932$	−3.00000	−	5.19615i	−0.0982683	−	0.170206i
$933$	2.00000	−	3.46410i	0.0654771	−	0.113410i
$934$	4.00000	−	6.92820i	0.130884	−	0.226698i
$935$		0			0
$936$	−3.50000	−	0.866025i	−0.114401	−	0.0283069i
$937$	−14.0000			−0.457360			−0.228680	−	0.973502i	$-0.573441\pi$
$937$	−14.0000			−0.457360			−0.228680	+	0.973502i	$0.573441\pi$
$938$	12.0000	−	20.7846i	0.391814	−	0.678642i
$939$	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	$0.674659\pi$
$942$	−8.50000	−	14.7224i	−0.276945	−	0.479683i
$943$	20.0000	+	34.6410i	0.651290	+	1.12807i
$944$	12.0000			0.390567
$945$		0			0
$946$	15.0000	−	25.9808i	0.487692	−	0.844707i
$947$	9.00000	−	15.5885i	0.292461	−	0.506557i	−0.681930	−	0.731417i	$-0.738859\pi$
$947$	9.00000	−	15.5885i	0.292461	−	0.506557i	0.974391	+	0.224860i	$0.0721926\pi$
$948$	6.00000			0.194871
$949$	20.0000	−	20.7846i	0.649227	−	0.674697i
$950$		0			0
$951$	8.50000	−	14.7224i	0.275631	−	0.477408i
$952$		0			0
$953$	17.0000	+	29.4449i	0.550684	+	0.953813i	0.998225	+	0.0595495i	$0.0189664\pi$
$953$	17.0000	+	29.4449i	0.550684	+	0.953813i	−0.447541	+	0.894263i	$0.647700\pi$
$954$	−9.00000			−0.291386
$955$		0			0
$956$	13.0000	+	22.5167i	0.420450	+	0.728241i
$957$	12.0000			0.387905
$958$	−6.00000	−	10.3923i	−0.193851	−	0.335760i
$959$	−18.0000	+	31.1769i	−0.581250	+	1.00676i
$960$		0			0
$961$	5.00000			0.161290
$962$	31.5000	+	7.79423i	1.01560	+	0.251296i
$963$	−2.00000			−0.0644491
$964$	−3.50000	+	6.06218i	−0.112727	+	0.195250i
$965$		0			0
$966$	6.00000	+	10.3923i	0.193047	+	0.334367i
$967$	−25.0000			−0.803946			−0.401973	−	0.915652i	$-0.631675\pi$
$967$	−25.0000			−0.803946			−0.401973	+	0.915652i	$0.631675\pi$
$968$	1.00000	+	1.73205i	0.0321412	+	0.0556702i
$969$		0			0
$970$		0			0
$971$	−7.50000	−	12.9904i	−0.240686	−	0.416881i	0.720224	−	0.693742i	$-0.244039\pi$
$971$	−7.50000	−	12.9904i	−0.240686	−	0.416881i	−0.960910	+	0.276861i	$0.910706\pi$
$972$	−0.500000	+	0.866025i	−0.0160375	+	0.0277778i
$973$	−25.5000	+	44.1673i	−0.817492	+	1.41594i
$974$	−29.0000			−0.929220
$975$		0			0
$976$	−6.00000			−0.192055
$977$	−22.0000	+	38.1051i	−0.703842	+	1.21909i	0.263265	+	0.964723i	$0.415201\pi$
$977$	−22.0000	+	38.1051i	−0.703842	+	1.21909i	−0.967108	+	0.254367i	$0.918133\pi$
$978$	10.0000	−	17.3205i	0.319765	−	0.553849i
$979$	−4.50000	−	7.79423i	−0.143821	−	0.249105i
$980$		0			0
$981$	1.00000	+	1.73205i	0.0319275	+	0.0553001i
$982$	−2.50000	−	4.33013i	−0.0797782	−	0.138180i
$983$	−55.0000			−1.75423			−0.877114	−	0.480283i	$-0.840534\pi$
$983$	−55.0000			−1.75423			−0.877114	+	0.480283i	$0.840534\pi$
$984$	5.00000	+	8.66025i	0.159394	+	0.276079i
$985$		0			0
$986$		0			0
$987$	−9.00000			−0.286473
$988$	3.00000	+	10.3923i	0.0954427	+	0.330623i
$989$	40.0000			1.27193
$990$		0			0
$991$	−29.0000	+	50.2295i	−0.921215	+	1.59559i	−0.123678	+	0.992322i	$0.539469\pi$
$991$	−29.0000	+	50.2295i	−0.921215	+	1.59559i	−0.797537	+	0.603269i	$0.793864\pi$
$992$	−3.00000	−	5.19615i	−0.0952501	−	0.164978i
$993$	−28.0000			−0.888553
$994$	−21.0000	−	36.3731i	−0.666080	−	1.15368i
$995$		0			0
$996$	−16.0000			−0.506979
$997$	23.5000	+	40.7032i	0.744252	+	1.28908i	0.950543	+	0.310592i	$0.100527\pi$
$997$	23.5000	+	40.7032i	0.744252	+	1.28908i	−0.206291	+	0.978491i	$0.566139\pi$
$998$	−10.0000	+	17.3205i	−0.316544	+	0.548271i
$999$	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.i.f.451.1		2
5.2	odd	4		1950.2.z.d.1699.1		4
5.3	odd	4		1950.2.z.d.1699.2		4
5.4	even	2		390.2.i.e.61.1	✓	2
13.3	even	3	inner	1950.2.i.f.601.1		2
15.14	odd	2		1170.2.i.c.451.1		2
65.3	odd	12		1950.2.z.d.1849.1		4
65.4	even	6		5070.2.a.r.1.1		1
65.9	even	6		5070.2.a.b.1.1		1
65.19	odd	12		5070.2.b.b.1351.2		2
65.29	even	6		390.2.i.e.211.1	yes	2
65.42	odd	12		1950.2.z.d.1849.2		4
65.59	odd	12		5070.2.b.b.1351.1		2
195.29	odd	6		1170.2.i.c.991.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
390.2.i.e.61.1	✓	2	5.4	even	2
390.2.i.e.211.1	yes	2	65.29	even	6
1170.2.i.c.451.1		2	15.14	odd	2
1170.2.i.c.991.1		2	195.29	odd	6
1950.2.i.f.451.1		2	1.1	even	1	trivial
1950.2.i.f.601.1		2	13.3	even	3	inner
1950.2.z.d.1699.1		4	5.2	odd	4
1950.2.z.d.1699.2		4	5.3	odd	4
1950.2.z.d.1849.1		4	65.3	odd	12
1950.2.z.d.1849.2		4	65.42	odd	12
5070.2.a.b.1.1		1	65.9	even	6
5070.2.a.r.1.1		1	65.4	even	6
5070.2.b.b.1351.1		2	65.59	odd	12
5070.2.b.b.1351.2		2	65.19	odd	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.i (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.500000 + 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(-0.500000 - 0.866025i) q^{6} +(1.50000 + 2.59808i) q^{7} +1.00000 q^{8} +(-0.500000 - 0.866025i) q^{9} +(1.50000 - 2.59808i) q^{11} +1.00000 q^{12} +(2.50000 - 2.59808i) q^{13} -3.00000 q^{14} +(-0.500000 + 0.866025i) q^{16} +1.00000 q^{18} +(-1.50000 - 2.59808i) q^{19} -3.00000 q^{21} +(1.50000 + 2.59808i) q^{22} +(-2.00000 + 3.46410i) q^{23} +(-0.500000 + 0.866025i) q^{24} +(1.00000 + 3.46410i) q^{26} +1.00000 q^{27} +(1.50000 - 2.59808i) q^{28} +(2.00000 - 3.46410i) q^{29} +6.00000 q^{31} +(-0.500000 - 0.866025i) q^{32} +(1.50000 + 2.59808i) q^{33} +(-0.500000 + 0.866025i) q^{36} +(4.50000 - 7.79423i) q^{37} +3.00000 q^{38} +(1.00000 + 3.46410i) q^{39} +(5.00000 - 8.66025i) q^{41} +(1.50000 - 2.59808i) q^{42} +(-5.00000 - 8.66025i) q^{43} -3.00000 q^{44} +(-2.00000 - 3.46410i) q^{46} +3.00000 q^{47} +(-0.500000 - 0.866025i) q^{48} +(-1.00000 + 1.73205i) q^{49} +(-3.50000 - 0.866025i) q^{52} -9.00000 q^{53} +(-0.500000 + 0.866025i) q^{54} +(1.50000 + 2.59808i) q^{56} +3.00000 q^{57} +(2.00000 + 3.46410i) q^{58} +(-6.00000 - 10.3923i) q^{59} +(3.00000 + 5.19615i) q^{61} +(-3.00000 + 5.19615i) q^{62} +(1.50000 - 2.59808i) q^{63} +1.00000 q^{64} -3.00000 q^{66} +(-4.00000 + 6.92820i) q^{67} +(-2.00000 - 3.46410i) q^{69} +(7.00000 + 12.1244i) q^{71} +(-0.500000 - 0.866025i) q^{72} +8.00000 q^{73} +(4.50000 + 7.79423i) q^{74} +(-1.50000 + 2.59808i) q^{76} +9.00000 q^{77} +(-3.50000 - 0.866025i) q^{78} +6.00000 q^{79} +(-0.500000 + 0.866025i) q^{81} +(5.00000 + 8.66025i) q^{82} -16.0000 q^{83} +(1.50000 + 2.59808i) q^{84} +10.0000 q^{86} +(2.00000 + 3.46410i) q^{87} +(1.50000 - 2.59808i) q^{88} +(1.50000 - 2.59808i) q^{89} +(10.5000 + 2.59808i) q^{91} +4.00000 q^{92} +(-3.00000 + 5.19615i) q^{93} +(-1.50000 + 2.59808i) q^{94} +1.00000 q^{96} +(4.00000 + 6.92820i) q^{97} +(-1.00000 - 1.73205i) q^{98} -3.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - q^{2} - q^{3} - q^{4} - q^{6} + 3 q^{7} + 2 q^{8} - q^{9} + 3 q^{11} + 2 q^{12} + 5 q^{13} - 6 q^{14} - q^{16} + 2 q^{18} - 3 q^{19} - 6 q^{21} + 3 q^{22} - 4 q^{23} - q^{24} + 2 q^{26} + 2 q^{27}+ \cdots - 6 q^{99}+O(q^{100}) \) 2 * q - q^2 - q^3 - q^4 - q^6 + 3 * q^7 + 2 * q^8 - q^9 + 3 * q^11 + 2 * q^12 + 5 * q^13 - 6 * q^14 - q^16 + 2 * q^18 - 3 * q^19 - 6 * q^21 + 3 * q^22 - 4 * q^23 - q^24 + 2 * q^26 + 2 * q^27 + 3 * q^28 + 4 * q^29 + 12 * q^31 - q^32 + 3 * q^33 - q^36 + 9 * q^37 + 6 * q^38 + 2 * q^39 + 10 * q^41 + 3 * q^42 - 10 * q^43 - 6 * q^44 - 4 * q^46 + 6 * q^47 - q^48 - 2 * q^49 - 7 * q^52 - 18 * q^53 - q^54 + 3 * q^56 + 6 * q^57 + 4 * q^58 - 12 * q^59 + 6 * q^61 - 6 * q^62 + 3 * q^63 + 2 * q^64 - 6 * q^66 - 8 * q^67 - 4 * q^69 + 14 * q^71 - q^72 + 16 * q^73 + 9 * q^74 - 3 * q^76 + 18 * q^77 - 7 * q^78 + 12 * q^79 - q^81 + 10 * q^82 - 32 * q^83 + 3 * q^84 + 20 * q^86 + 4 * q^87 + 3 * q^88 + 3 * q^89 + 21 * q^91 + 8 * q^92 - 6 * q^93 - 3 * q^94 + 2 * q^96 + 8 * q^97 - 2 * q^98 - 6 * q^99

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