LMFDB - Embedded newform 1950.2.z.a.1699.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1950,2,Mod(1699,1950)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

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")

//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);

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: f = N[0] # Warning: the index may be different

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:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			1699.1
Root			$-0.866025 + 0.500000i$ of defining polynomial
Character	$\chi$	$=$	1950.1699
Dual form			1950.2.z.a.1849.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.866025 - 0.500000i) q^{2} +(0.866025 + 0.500000i) q^{3} +(0.500000 + 0.866025i) q^{4} +(-0.500000 - 0.866025i) q^{6} -1.00000i q^{8} +(0.500000 + 0.866025i) q^{9} +O(q^{10})$	\(q+(-0.866025 - 0.500000i) q^{2} +(0.866025 + 0.500000i) q^{3} +(0.500000 + 0.866025i) q^{4} +(-0.500000 - 0.866025i) q^{6} -1.00000i q^{8} +(0.500000 + 0.866025i) q^{9} +(-1.50000 + 2.59808i) q^{11} +1.00000i q^{12} +(-2.59808 - 2.50000i) q^{13} +(-0.500000 + 0.866025i) q^{16} +(5.19615 - 3.00000i) q^{17} -1.00000i q^{18} +(-3.00000 - 5.19615i) q^{19} +(2.59808 - 1.50000i) q^{22} +(-4.33013 - 2.50000i) q^{23} +(0.500000 - 0.866025i) q^{24} +(1.00000 + 3.46410i) q^{26} +1.00000i q^{27} +(1.00000 - 1.73205i) q^{29} -6.00000 q^{31} +(0.866025 - 0.500000i) q^{32} +(-2.59808 + 1.50000i) q^{33} -6.00000 q^{34} +(-0.500000 + 0.866025i) q^{36} +(7.79423 + 4.50000i) q^{37} +6.00000i q^{38} +(-1.00000 - 3.46410i) q^{39} +(5.00000 - 8.66025i) q^{41} +(6.92820 - 4.00000i) q^{43} -3.00000 q^{44} +(2.50000 + 4.33013i) q^{46} -12.0000i q^{47} +(-0.866025 + 0.500000i) q^{48} +(-3.50000 + 6.06218i) q^{49} +6.00000 q^{51} +(0.866025 - 3.50000i) q^{52} -12.0000i q^{53} +(0.500000 - 0.866025i) q^{54} -6.00000i q^{57} +(-1.73205 + 1.00000i) q^{58} +(7.50000 + 12.9904i) q^{61} +(5.19615 + 3.00000i) q^{62} -1.00000 q^{64} +3.00000 q^{66} +(3.46410 + 2.00000i) q^{67} +(5.19615 + 3.00000i) q^{68} +(-2.50000 - 4.33013i) q^{69} +(-3.50000 - 6.06218i) q^{71} +(0.866025 - 0.500000i) q^{72} +1.00000i q^{73} +(-4.50000 - 7.79423i) q^{74} +(3.00000 - 5.19615i) q^{76} +(-0.866025 + 3.50000i) q^{78} -6.00000 q^{79} +(-0.500000 + 0.866025i) q^{81} +(-8.66025 + 5.00000i) q^{82} -5.00000i q^{83} -8.00000 q^{86} +(1.73205 - 1.00000i) q^{87} +(2.59808 + 1.50000i) q^{88} +(-3.00000 + 5.19615i) q^{89} -5.00000i q^{92} +(-5.19615 - 3.00000i) q^{93} +(-6.00000 + 10.3923i) q^{94} +1.00000 q^{96} +(-4.33013 + 2.50000i) q^{97} +(6.06218 - 3.50000i) q^{98} -3.00000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 2 q^{4} - 2 q^{6} + 2 q^{9}+O(q^{10}) $ 4 * q + 2 * q^4 - 2 * q^6 + 2 * q^9	$ 4 q + 2 q^{4} - 2 q^{6} + 2 q^{9} - 6 q^{11} - 2 q^{16} - 12 q^{19} + 2 q^{24} + 4 q^{26} + 4 q^{29} - 24 q^{31} - 24 q^{34} - 2 q^{36} - 4 q^{39} + 20 q^{41} - 12 q^{44} + 10 q^{46} - 14 q^{49} + 24 q^{51} + 2 q^{54} + 30 q^{61} - 4 q^{64} + 12 q^{66} - 10 q^{69} - 14 q^{71} - 18 q^{74} + 12 q^{76} - 24 q^{79} - 2 q^{81} - 32 q^{86} - 12 q^{89} - 24 q^{94} + 4 q^{96} - 12 q^{99}+O(q^{100}) $ 4 * q + 2 * q^4 - 2 * q^6 + 2 * q^9 - 6 * q^11 - 2 * q^16 - 12 * q^19 + 2 * q^24 + 4 * q^26 + 4 * q^29 - 24 * q^31 - 24 * q^34 - 2 * q^36 - 4 * q^39 + 20 * q^41 - 12 * q^44 + 10 * q^46 - 14 * q^49 + 24 * q^51 + 2 * q^54 + 30 * q^61 - 4 * q^64 + 12 * q^66 - 10 * q^69 - 14 * q^71 - 18 * q^74 + 12 * q^76 - 24 * q^79 - 2 * q^81 - 32 * q^86 - 12 * q^89 - 24 * q^94 + 4 * q^96 - 12 * q^99

Display 100 coefficients 10 coefficients

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 $

$2$	−0.866025	−	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
$7$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$7$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$8$		−	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	$-0.982718\pi$
$11$	−1.50000	+	2.59808i	−0.452267	+	0.783349i	0.546259	+	0.837616i	$0.316051\pi$
$12$			1.00000i			0.288675i
$13$	−2.59808	−	2.50000i	−0.720577	−	0.693375i
$13$	−2.59808	−	2.50000i	−0.720577	−	0.693375i
$14$		0			0
$15$		0			0
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$	5.19615	−	3.00000i	1.26025	−	0.727607i	0.287129	−	0.957892i	$-0.407299\pi$
$17$	5.19615	−	3.00000i	1.26025	−	0.727607i	0.973123	+	0.230285i	$0.0739659\pi$
$18$		−	1.00000i		−	0.235702i
$19$	−3.00000	−	5.19615i	−0.688247	−	1.19208i	−0.972404	−	0.233301i	$-0.925047\pi$
$19$	−3.00000	−	5.19615i	−0.688247	−	1.19208i	0.284157	−	0.958778i	$-0.408286\pi$
$20$		0			0
$21$		0			0
$22$	2.59808	−	1.50000i	0.553912	−	0.319801i
$23$	−4.33013	−	2.50000i	−0.902894	−	0.521286i	−0.0247559	−	0.999694i	$-0.507881\pi$
$23$	−4.33013	−	2.50000i	−0.902894	−	0.521286i	−0.878138	+	0.478407i	$0.841214\pi$
$24$	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
$28$		0			0
$29$	1.00000	−	1.73205i	0.185695	−	0.321634i	−0.758115	−	0.652121i	$-0.773880\pi$
$29$	1.00000	−	1.73205i	0.185695	−	0.321634i	0.943811	+	0.330487i	$0.107213\pi$
$30$		0			0
$31$	−6.00000			−1.07763			−0.538816	−	0.842424i	$-0.681128\pi$
$31$	−6.00000			−1.07763			−0.538816	+	0.842424i	$0.681128\pi$
$32$	0.866025	−	0.500000i	0.153093	−	0.0883883i
$33$	−2.59808	+	1.50000i	−0.452267	+	0.261116i
$34$	−6.00000			−1.02899
$35$		0			0
$36$	−0.500000	+	0.866025i	−0.0833333	+	0.144338i
$37$	7.79423	+	4.50000i	1.28136	+	0.739795i	0.977098	−	0.212792i	$-0.0682556\pi$
$37$	7.79423	+	4.50000i	1.28136	+	0.739795i	0.304266	+	0.952587i	$0.401589\pi$
$38$			6.00000i			0.973329i
$39$	−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	$-0.118557\pi$
$42$		0			0
$43$	6.92820	−	4.00000i	1.05654	−	0.609994i	0.132068	−	0.991241i	$-0.457838\pi$
$43$	6.92820	−	4.00000i	1.05654	−	0.609994i	0.924473	+	0.381246i	$0.124505\pi$
$44$	−3.00000			−0.452267
$45$		0			0
$46$	2.50000	+	4.33013i	0.368605	+	0.638442i
$47$		−	12.0000i		−	1.75038i	−0.483779	−	0.875190i	$-0.660736\pi$
$47$		−	12.0000i		−	1.75038i	0.483779	−	0.875190i	$-0.339264\pi$
$48$	−0.866025	+	0.500000i	−0.125000	+	0.0721688i
$49$	−3.50000	+	6.06218i	−0.500000	+	0.866025i
$50$		0			0
$51$	6.00000			0.840168
$52$	0.866025	−	3.50000i	0.120096	−	0.485363i
$53$		−	12.0000i		−	1.64833i	−0.566352	−	0.824163i	$-0.691646\pi$
$53$		−	12.0000i		−	1.64833i	0.566352	−	0.824163i	$-0.308354\pi$
$54$	0.500000	−	0.866025i	0.0680414	−	0.117851i
$55$		0			0
$56$		0			0
$57$		−	6.00000i		−	0.794719i
$58$	−1.73205	+	1.00000i	−0.227429	+	0.131306i
$59$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$59$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$60$		0			0
$61$	7.50000	+	12.9904i	0.960277	+	1.66325i	0.721803	+	0.692099i	$0.243314\pi$
$61$	7.50000	+	12.9904i	0.960277	+	1.66325i	0.238474	+	0.971149i	$0.423353\pi$
$62$	5.19615	+	3.00000i	0.659912	+	0.381000i
$63$		0			0
$64$	−1.00000			−0.125000
$65$		0			0
$66$	3.00000			0.369274
$67$	3.46410	+	2.00000i	0.423207	+	0.244339i	0.696449	−	0.717607i	$-0.254762\pi$
$67$	3.46410	+	2.00000i	0.423207	+	0.244339i	−0.273241	+	0.961946i	$0.588096\pi$
$68$	5.19615	+	3.00000i	0.630126	+	0.363803i
$69$	−2.50000	−	4.33013i	−0.300965	−	0.521286i
$70$		0			0
$71$	−3.50000	−	6.06218i	−0.415374	−	0.719448i	0.580094	−	0.814550i	$-0.303016\pi$
$71$	−3.50000	−	6.06218i	−0.415374	−	0.719448i	−0.995468	+	0.0951014i	$0.969682\pi$
$72$	0.866025	−	0.500000i	0.102062	−	0.0589256i
$73$			1.00000i			0.117041i	0.998286	+	0.0585206i	$0.0186383\pi$
$73$			1.00000i			0.117041i	−0.998286	+	0.0585206i	$0.981362\pi$
$74$	−4.50000	−	7.79423i	−0.523114	−	0.906061i
$75$		0			0
$76$	3.00000	−	5.19615i	0.344124	−	0.596040i
$77$		0			0
$78$	−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
$83$		−	5.00000i		−	0.548821i	−0.961613	−	0.274411i	$-0.911517\pi$
$83$		−	5.00000i		−	0.548821i	0.961613	−	0.274411i	$-0.0884828\pi$
$84$		0			0
$85$		0			0
$86$	−8.00000			−0.862662
$87$	1.73205	−	1.00000i	0.185695	−	0.107211i
$88$	2.59808	+	1.50000i	0.276956	+	0.159901i
$89$	−3.00000	+	5.19615i	−0.317999	+	0.550791i	−0.980071	−	0.198650i	$-0.936344\pi$
$89$	−3.00000	+	5.19615i	−0.317999	+	0.550791i	0.662071	+	0.749441i	$0.269678\pi$
$90$		0			0
$91$		0			0
$92$		−	5.00000i		−	0.521286i
$93$	−5.19615	−	3.00000i	−0.538816	−	0.311086i
$94$	−6.00000	+	10.3923i	−0.618853	+	1.07188i
$95$		0			0
$96$	1.00000			0.102062
$97$	−4.33013	+	2.50000i	−0.439658	+	0.253837i	−0.703452	−	0.710742i	$-0.748359\pi$
$97$	−4.33013	+	2.50000i	−0.439658	+	0.253837i	0.263795	+	0.964579i	$0.415026\pi$
$98$	6.06218	−	3.50000i	0.612372	−	0.353553i
$99$	−3.00000			−0.301511
$100$		0			0
$101$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$101$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$102$	−5.19615	−	3.00000i	−0.514496	−	0.297044i
$103$		−	12.0000i		−	1.18240i	−0.806527	−	0.591198i	$-0.798655\pi$
$103$		−	12.0000i		−	1.18240i	0.806527	−	0.591198i	$-0.201345\pi$
$104$	−2.50000	+	2.59808i	−0.245145	+	0.254762i
$105$		0			0
$106$	−6.00000	+	10.3923i	−0.582772	+	1.00939i
$107$	6.92820	+	4.00000i	0.669775	+	0.386695i	0.795991	−	0.605308i	$-0.206950\pi$
$107$	6.92820	+	4.00000i	0.669775	+	0.386695i	−0.126217	+	0.992003i	$0.540283\pi$
$108$	−0.866025	+	0.500000i	−0.0833333	+	0.0481125i
$109$	5.00000			0.478913			0.239457	−	0.970907i	$-0.423031\pi$
$109$	5.00000			0.478913			0.239457	+	0.970907i	$0.423031\pi$
$110$		0			0
$111$	4.50000	+	7.79423i	0.427121	+	0.739795i
$112$		0			0
$113$	3.46410	−	2.00000i	0.325875	−	0.188144i	−0.328133	−	0.944632i	$-0.606419\pi$
$113$	3.46410	−	2.00000i	0.325875	−	0.188144i	0.654008	+	0.756487i	$0.273086\pi$
$114$	−3.00000	+	5.19615i	−0.280976	+	0.486664i
$115$		0			0
$116$	2.00000			0.185695
$117$	0.866025	−	3.50000i	0.0800641	−	0.323575i
$118$		0			0
$119$		0			0
$120$		0			0
$121$	1.00000	+	1.73205i	0.0909091	+	0.157459i
$122$		−	15.0000i		−	1.35804i
$123$	8.66025	−	5.00000i	0.780869	−	0.450835i
$124$	−3.00000	−	5.19615i	−0.269408	−	0.466628i
$125$		0			0
$126$		0			0
$127$	15.5885	+	9.00000i	1.38325	+	0.798621i	0.992543	−	0.121894i	$-0.0388966\pi$
$127$	15.5885	+	9.00000i	1.38325	+	0.798621i	0.390709	+	0.920514i	$0.372230\pi$
$128$	0.866025	+	0.500000i	0.0765466	+	0.0441942i
$129$	8.00000			0.704361
$130$		0			0
$131$	12.0000			1.04844			0.524222	−	0.851581i	$-0.324356\pi$
$131$	12.0000			1.04844			0.524222	+	0.851581i	$0.324356\pi$
$132$	−2.59808	−	1.50000i	−0.226134	−	0.130558i
$133$		0			0
$134$	−2.00000	−	3.46410i	−0.172774	−	0.299253i
$135$		0			0
$136$	−3.00000	−	5.19615i	−0.257248	−	0.445566i
$137$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$137$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$138$			5.00000i			0.425628i
$139$	−10.0000	−	17.3205i	−0.848189	−	1.46911i	−0.882823	−	0.469706i	$-0.844360\pi$
$139$	−10.0000	−	17.3205i	−0.848189	−	1.46911i	0.0346338	−	0.999400i	$-0.488974\pi$
$140$		0			0
$141$	6.00000	−	10.3923i	0.505291	−	0.875190i
$142$			7.00000i			0.587427i
$143$	10.3923	−	3.00000i	0.869048	−	0.250873i
$144$	−1.00000			−0.0833333
$145$		0			0
$146$	0.500000	−	0.866025i	0.0413803	−	0.0716728i
$147$	−6.06218	+	3.50000i	−0.500000	+	0.288675i
$148$			9.00000i			0.739795i
$149$	−7.00000	−	12.1244i	−0.573462	−	0.993266i	−0.996207	−	0.0870170i	$-0.972267\pi$
$149$	−7.00000	−	12.1244i	−0.573462	−	0.993266i	0.422744	−	0.906249i	$-0.361067\pi$
$150$		0			0
$151$	2.00000			0.162758			0.0813788	−	0.996683i	$-0.474068\pi$
$151$	2.00000			0.162758			0.0813788	+	0.996683i	$0.474068\pi$
$152$	−5.19615	+	3.00000i	−0.421464	+	0.243332i
$153$	5.19615	+	3.00000i	0.420084	+	0.242536i
$154$		0			0
$155$		0			0
$156$	2.50000	−	2.59808i	0.200160	−	0.208013i
$157$		−	13.0000i		−	1.03751i	−0.854922	−	0.518756i	$-0.826395\pi$
$157$		−	13.0000i		−	1.03751i	0.854922	−	0.518756i	$-0.173605\pi$
$158$	5.19615	+	3.00000i	0.413384	+	0.238667i
$159$	6.00000	−	10.3923i	0.475831	−	0.824163i
$160$		0			0
$161$		0			0
$162$	0.866025	−	0.500000i	0.0680414	−	0.0392837i
$163$	1.73205	−	1.00000i	0.135665	−	0.0783260i	−0.430632	−	0.902528i	$-0.641709\pi$
$163$	1.73205	−	1.00000i	0.135665	−	0.0783260i	0.566296	+	0.824202i	$0.308376\pi$
$164$	10.0000			0.780869
$165$		0			0
$166$	−2.50000	+	4.33013i	−0.194038	+	0.336083i
$167$	−18.1865	−	10.5000i	−1.40732	−	0.812514i	−0.412188	−	0.911099i	$-0.635235\pi$
$167$	−18.1865	−	10.5000i	−1.40732	−	0.812514i	−0.995129	+	0.0985846i	$0.968568\pi$
$168$		0			0
$169$	0.500000	+	12.9904i	0.0384615	+	0.999260i
$170$		0			0
$171$	3.00000	−	5.19615i	0.229416	−	0.397360i
$172$	6.92820	+	4.00000i	0.528271	+	0.304997i
$173$	−6.92820	+	4.00000i	−0.526742	+	0.304114i	−0.739689	−	0.672949i	$-0.765027\pi$
$173$	−6.92820	+	4.00000i	−0.526742	+	0.304114i	0.212947	+	0.977064i	$0.431694\pi$
$174$	−2.00000			−0.151620
$175$		0			0
$176$	−1.50000	−	2.59808i	−0.113067	−	0.195837i
$177$		0			0
$178$	5.19615	−	3.00000i	0.389468	−	0.224860i
$179$	3.50000	−	6.06218i	0.261602	−	0.453108i	−0.705066	−	0.709142i	$-0.749082\pi$
$179$	3.50000	−	6.06218i	0.261602	−	0.453108i	0.966668	+	0.256034i	$0.0824158\pi$
$180$		0			0
$181$	−1.00000			−0.0743294			−0.0371647	−	0.999309i	$-0.511833\pi$
$181$	−1.00000			−0.0743294			−0.0371647	+	0.999309i	$0.511833\pi$
$182$		0			0
$183$			15.0000i			1.10883i
$184$	−2.50000	+	4.33013i	−0.184302	+	0.319221i
$185$		0			0
$186$	3.00000	+	5.19615i	0.219971	+	0.381000i
$187$			18.0000i			1.31629i
$188$	10.3923	−	6.00000i	0.757937	−	0.437595i
$189$		0			0
$190$		0			0
$191$	1.50000	+	2.59808i	0.108536	+	0.187990i	0.915177	−	0.403051i	$-0.132050\pi$
$191$	1.50000	+	2.59808i	0.108536	+	0.187990i	−0.806641	+	0.591041i	$0.798717\pi$
$192$	−0.866025	−	0.500000i	−0.0625000	−	0.0360844i
$193$	−9.52628	−	5.50000i	−0.685717	−	0.395899i	0.116289	−	0.993215i	$-0.462900\pi$
$193$	−9.52628	−	5.50000i	−0.685717	−	0.395899i	−0.802005	+	0.597317i	$0.796234\pi$
$194$	5.00000			0.358979
$195$		0			0
$196$	−7.00000			−0.500000
$197$	−8.66025	−	5.00000i	−0.617018	−	0.356235i	0.158689	−	0.987329i	$-0.449273\pi$
$197$	−8.66025	−	5.00000i	−0.617018	−	0.356235i	−0.775707	+	0.631093i	$0.782606\pi$
$198$	2.59808	+	1.50000i	0.184637	+	0.106600i
$199$	−2.00000	−	3.46410i	−0.141776	−	0.245564i	0.786389	−	0.617731i	$-0.211948\pi$
$199$	−2.00000	−	3.46410i	−0.141776	−	0.245564i	−0.928166	+	0.372168i	$0.878615\pi$
$200$		0			0
$201$	2.00000	+	3.46410i	0.141069	+	0.244339i
$202$		0			0
$203$		0			0
$204$	3.00000	+	5.19615i	0.210042	+	0.363803i
$205$		0			0
$206$	−6.00000	+	10.3923i	−0.418040	+	0.724066i
$207$		−	5.00000i		−	0.347524i
$208$	3.46410	−	1.00000i	0.240192	−	0.0693375i
$209$	18.0000			1.24509
$210$		0			0
$211$	6.00000	−	10.3923i	0.413057	−	0.715436i	−0.582165	−	0.813070i	$-0.697794\pi$
$211$	6.00000	−	10.3923i	0.413057	−	0.715436i	0.995222	+	0.0976347i	$0.0311277\pi$
$212$	10.3923	−	6.00000i	0.713746	−	0.412082i
$213$		−	7.00000i		−	0.479632i
$214$	−4.00000	−	6.92820i	−0.273434	−	0.473602i
$215$		0			0
$216$	1.00000			0.0680414
$217$		0			0
$218$	−4.33013	−	2.50000i	−0.293273	−	0.169321i
$219$	−0.500000	+	0.866025i	−0.0337869	+	0.0585206i
$220$		0			0
$221$	−21.0000	−	5.19615i	−1.41261	−	0.349531i
$222$		−	9.00000i		−	0.604040i
$223$	−13.8564	−	8.00000i	−0.927894	−	0.535720i	−0.0417488	−	0.999128i	$-0.513293\pi$
$223$	−13.8564	−	8.00000i	−0.927894	−	0.535720i	−0.886145	+	0.463409i	$0.846626\pi$
$224$		0			0
$225$		0			0
$226$	−4.00000			−0.266076
$227$	−19.9186	+	11.5000i	−1.32204	+	0.763282i	−0.984054	−	0.177868i	$-0.943080\pi$
$227$	−19.9186	+	11.5000i	−1.32204	+	0.763282i	−0.337989	+	0.941150i	$0.609747\pi$
$228$	5.19615	−	3.00000i	0.344124	−	0.198680i
$229$	−23.0000			−1.51988			−0.759941	−	0.649992i	$-0.774772\pi$
$229$	−23.0000			−1.51988			−0.759941	+	0.649992i	$0.774772\pi$
$230$		0			0
$231$		0			0
$232$	−1.73205	−	1.00000i	−0.113715	−	0.0656532i
$233$		0			0		1.00000			$0$
$233$		0			0		−1.00000			$\pi$
$234$	−2.50000	+	2.59808i	−0.163430	+	0.169842i
$235$		0			0
$236$		0			0
$237$	−5.19615	−	3.00000i	−0.337526	−	0.194871i
$238$		0			0
$239$	11.0000			0.711531			0.355765	−	0.934575i	$-0.384220\pi$
$239$	11.0000			0.711531			0.355765	+	0.934575i	$0.384220\pi$
$240$		0			0
$241$	1.00000	+	1.73205i	0.0644157	+	0.111571i	0.896435	−	0.443176i	$-0.146148\pi$
$241$	1.00000	+	1.73205i	0.0644157	+	0.111571i	−0.832019	+	0.554747i	$0.812815\pi$
$242$		−	2.00000i		−	0.128565i
$243$	−0.866025	+	0.500000i	−0.0555556	+	0.0320750i
$244$	−7.50000	+	12.9904i	−0.480138	+	0.831624i
$245$		0			0
$246$	−10.0000			−0.637577
$247$	−5.19615	+	21.0000i	−0.330623	+	1.33620i
$248$			6.00000i			0.381000i
$249$	2.50000	−	4.33013i	0.158431	−	0.274411i
$250$		0			0
$251$	−11.5000	−	19.9186i	−0.725874	−	1.25725i	−0.958613	−	0.284711i	$-0.908102\pi$
$251$	−11.5000	−	19.9186i	−0.725874	−	1.25725i	0.232740	−	0.972539i	$-0.425231\pi$
$252$		0			0
$253$	12.9904	−	7.50000i	0.816698	−	0.471521i
$254$	−9.00000	−	15.5885i	−0.564710	−	0.978107i
$255$		0			0
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$257$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$258$	−6.92820	−	4.00000i	−0.431331	−	0.249029i
$259$		0			0
$260$		0			0
$261$	2.00000			0.123797
$262$	−10.3923	−	6.00000i	−0.642039	−	0.370681i
$263$	11.2583	+	6.50000i	0.694218	+	0.400807i	0.805190	−	0.593016i	$-0.202063\pi$
$263$	11.2583	+	6.50000i	0.694218	+	0.400807i	−0.110972	+	0.993824i	$0.535396\pi$
$264$	1.50000	+	2.59808i	0.0923186	+	0.159901i
$265$		0			0
$266$		0			0
$267$	−5.19615	+	3.00000i	−0.317999	+	0.183597i
$268$			4.00000i			0.244339i
$269$	16.0000	+	27.7128i	0.975537	+	1.68968i	0.678151	+	0.734923i	$0.262782\pi$
$269$	16.0000	+	27.7128i	0.975537	+	1.68968i	0.297386	+	0.954757i	$0.403885\pi$
$270$		0			0
$271$	−9.00000	+	15.5885i	−0.546711	+	0.946931i	0.451786	+	0.892126i	$0.350787\pi$
$271$	−9.00000	+	15.5885i	−0.546711	+	0.946931i	−0.998497	+	0.0548050i	$0.982546\pi$
$272$			6.00000i			0.363803i
$273$		0			0
$274$		0			0
$275$		0			0
$276$	2.50000	−	4.33013i	0.150482	−	0.260643i
$277$	11.2583	−	6.50000i	0.676448	−	0.390547i	−0.122068	−	0.992522i	$-0.538953\pi$
$277$	11.2583	−	6.50000i	0.676448	−	0.390547i	0.798515	+	0.601975i	$0.205619\pi$
$278$			20.0000i			1.19952i
$279$	−3.00000	−	5.19615i	−0.179605	−	0.311086i
$280$		0			0
$281$	30.0000			1.78965			0.894825	−	0.446417i	$-0.147300\pi$
$281$	30.0000			1.78965			0.894825	+	0.446417i	$0.147300\pi$
$282$	−10.3923	+	6.00000i	−0.618853	+	0.357295i
$283$	−20.7846	−	12.0000i	−1.23552	−	0.713326i	−0.267342	−	0.963602i	$-0.586145\pi$
$283$	−20.7846	−	12.0000i	−1.23552	−	0.713326i	−0.968175	+	0.250276i	$0.919479\pi$
$284$	3.50000	−	6.06218i	0.207687	−	0.359724i
$285$		0			0
$286$	−10.5000	−	2.59808i	−0.620878	−	0.153627i
$287$		0			0
$288$	0.866025	+	0.500000i	0.0510310	+	0.0294628i
$289$	9.50000	−	16.4545i	0.558824	−	0.967911i
$290$		0			0
$291$	−5.00000			−0.293105
$292$	−0.866025	+	0.500000i	−0.0506803	+	0.0292603i
$293$	−24.2487	+	14.0000i	−1.41662	+	0.817889i	−0.996001	−	0.0893462i	$-0.971522\pi$
$293$	−24.2487	+	14.0000i	−1.41662	+	0.817889i	−0.420624	+	0.907235i	$0.638189\pi$
$294$	7.00000			0.408248
$295$		0			0
$296$	4.50000	−	7.79423i	0.261557	−	0.453030i
$297$	−2.59808	−	1.50000i	−0.150756	−	0.0870388i
$298$			14.0000i			0.810998i
$299$	5.00000	+	17.3205i	0.289157	+	1.00167i
$300$		0			0
$301$		0			0
$302$	−1.73205	−	1.00000i	−0.0996683	−	0.0575435i
$303$		0			0
$304$	6.00000			0.344124
$305$		0			0
$306$	−3.00000	−	5.19615i	−0.171499	−	0.297044i
$307$			16.0000i			0.913168i	0.889680	+	0.456584i	$0.150927\pi$
$307$			16.0000i			0.913168i	−0.889680	+	0.456584i	$0.849073\pi$
$308$		0			0
$309$	6.00000	−	10.3923i	0.341328	−	0.591198i
$310$		0			0
$311$	5.00000			0.283524			0.141762	−	0.989901i	$-0.454723\pi$
$311$	5.00000			0.283524			0.141762	+	0.989901i	$0.454723\pi$
$312$	−3.46410	+	1.00000i	−0.196116	+	0.0566139i
$313$		−	1.00000i		−	0.0565233i	−0.999601	−	0.0282617i	$-0.991003\pi$
$313$		−	1.00000i		−	0.0565233i	0.999601	−	0.0282617i	$-0.00899717\pi$
$314$	−6.50000	+	11.2583i	−0.366816	+	0.635344i
$315$		0			0
$316$	−3.00000	−	5.19615i	−0.168763	−	0.292306i
$317$		−	32.0000i		−	1.79730i	−0.438667	−	0.898650i	$-0.644549\pi$
$317$		−	32.0000i		−	1.79730i	0.438667	−	0.898650i	$-0.355451\pi$
$318$	−10.3923	+	6.00000i	−0.582772	+	0.336463i
$319$	3.00000	+	5.19615i	0.167968	+	0.290929i
$320$		0			0
$321$	4.00000	+	6.92820i	0.223258	+	0.386695i
$322$		0			0
$323$	−31.1769	−	18.0000i	−1.73473	−	1.00155i
$324$	−1.00000			−0.0555556
$325$		0			0
$326$	−2.00000			−0.110770
$327$	4.33013	+	2.50000i	0.239457	+	0.138250i
$328$	−8.66025	−	5.00000i	−0.478183	−	0.276079i
$329$		0			0
$330$		0			0
$331$	−13.0000	−	22.5167i	−0.714545	−	1.23763i	−0.963135	−	0.269019i	$-0.913301\pi$
$331$	−13.0000	−	22.5167i	−0.714545	−	1.23763i	0.248590	−	0.968609i	$-0.420033\pi$
$332$	4.33013	−	2.50000i	0.237647	−	0.137205i
$333$			9.00000i			0.493197i
$334$	10.5000	+	18.1865i	0.574534	+	0.995123i
$335$		0			0
$336$		0			0
$337$			30.0000i			1.63420i	0.576493	+	0.817102i	$0.304421\pi$
$337$			30.0000i			1.63420i	−0.576493	+	0.817102i	$0.695579\pi$
$338$	6.06218	−	11.5000i	0.329739	−	0.625518i
$339$	4.00000			0.217250
$340$		0			0
$341$	9.00000	−	15.5885i	0.487377	−	0.844162i
$342$	−5.19615	+	3.00000i	−0.280976	+	0.162221i
$343$		0			0
$344$	−4.00000	−	6.92820i	−0.215666	−	0.373544i
$345$		0			0
$346$	8.00000			0.430083
$347$	23.3827	−	13.5000i	1.25525	−	0.724718i	0.283101	−	0.959090i	$-0.408637\pi$
$347$	23.3827	−	13.5000i	1.25525	−	0.724718i	0.972147	+	0.234372i	$0.0753034\pi$
$348$	1.73205	+	1.00000i	0.0928477	+	0.0536056i
$349$	12.5000	−	21.6506i	0.669110	−	1.15893i	−0.309044	−	0.951048i	$-0.600009\pi$
$349$	12.5000	−	21.6506i	0.669110	−	1.15893i	0.978153	−	0.207884i	$-0.0666577\pi$
$350$		0			0
$351$	2.50000	−	2.59808i	0.133440	−	0.138675i
$352$			3.00000i			0.159901i
$353$	12.1244	+	7.00000i	0.645314	+	0.372572i	0.786659	−	0.617388i	$-0.211809\pi$
$353$	12.1244	+	7.00000i	0.645314	+	0.372572i	−0.141344	+	0.989960i	$0.545142\pi$
$354$		0			0
$355$		0			0
$356$	−6.00000			−0.317999
$357$		0			0
$358$	−6.06218	+	3.50000i	−0.320396	+	0.184981i
$359$		0			0			−	1.00000i	$-0.5\pi$
$359$		0			0				1.00000i	$0.5\pi$
$360$		0			0
$361$	−8.50000	+	14.7224i	−0.447368	+	0.774865i
$362$	0.866025	+	0.500000i	0.0455173	+	0.0262794i
$363$			2.00000i			0.104973i
$364$		0			0
$365$		0			0
$366$	7.50000	−	12.9904i	0.392031	−	0.679018i
$367$	12.1244	+	7.00000i	0.632886	+	0.365397i	0.781869	−	0.623443i	$-0.214267\pi$
$367$	12.1244	+	7.00000i	0.632886	+	0.365397i	−0.148983	+	0.988840i	$0.547600\pi$
$368$	4.33013	−	2.50000i	0.225723	−	0.130322i
$369$	10.0000			0.520579
$370$		0			0
$371$		0			0
$372$		−	6.00000i		−	0.311086i
$373$	−9.52628	+	5.50000i	−0.493252	+	0.284779i	−0.725923	−	0.687776i	$-0.758587\pi$
$373$	−9.52628	+	5.50000i	−0.493252	+	0.284779i	0.232671	+	0.972556i	$0.425254\pi$
$374$	9.00000	−	15.5885i	0.465379	−	0.806060i
$375$		0			0
$376$	−12.0000			−0.618853
$377$	−6.92820	+	2.00000i	−0.356821	+	0.103005i
$378$		0			0
$379$	−3.00000	+	5.19615i	−0.154100	+	0.266908i	−0.932731	−	0.360573i	$-0.882581\pi$
$379$	−3.00000	+	5.19615i	−0.154100	+	0.266908i	0.778631	+	0.627482i	$0.215914\pi$
$380$		0			0
$381$	9.00000	+	15.5885i	0.461084	+	0.798621i
$382$		−	3.00000i		−	0.153493i
$383$	0.866025	−	0.500000i	0.0442518	−	0.0255488i	−0.477711	−	0.878517i	$-0.658533\pi$
$383$	0.866025	−	0.500000i	0.0442518	−	0.0255488i	0.521963	+	0.852968i	$0.325200\pi$
$384$	0.500000	+	0.866025i	0.0255155	+	0.0441942i
$385$		0			0
$386$	5.50000	+	9.52628i	0.279943	+	0.484875i
$387$	6.92820	+	4.00000i	0.352180	+	0.203331i
$388$	−4.33013	−	2.50000i	−0.219829	−	0.126918i
$389$	6.00000			0.304212			0.152106	−	0.988364i	$-0.451394\pi$
$389$	6.00000			0.304212			0.152106	+	0.988364i	$0.451394\pi$
$390$		0			0
$391$	−30.0000			−1.51717
$392$	6.06218	+	3.50000i	0.306186	+	0.176777i
$393$	10.3923	+	6.00000i	0.524222	+	0.302660i
$394$	5.00000	+	8.66025i	0.251896	+	0.436297i
$395$		0			0
$396$	−1.50000	−	2.59808i	−0.0753778	−	0.130558i
$397$	−19.0526	+	11.0000i	−0.956221	+	0.552074i	−0.895008	−	0.446051i	$-0.852830\pi$
$397$	−19.0526	+	11.0000i	−0.956221	+	0.552074i	−0.0612128	+	0.998125i	$0.519497\pi$
$398$			4.00000i			0.200502i
$399$		0			0
$400$		0			0
$401$	3.00000	−	5.19615i	0.149813	−	0.259483i	−0.781345	−	0.624099i	$-0.785466\pi$
$401$	3.00000	−	5.19615i	0.149813	−	0.259483i	0.931158	+	0.364615i	$0.118800\pi$
$402$		−	4.00000i		−	0.199502i
$403$	15.5885	+	15.0000i	0.776516	+	0.747203i
$404$		0			0
$405$		0			0
$406$		0			0
$407$	−23.3827	+	13.5000i	−1.15904	+	0.669170i
$408$		−	6.00000i		−	0.297044i
$409$	13.0000	+	22.5167i	0.642809	+	1.11338i	0.984803	+	0.173675i	$0.0555643\pi$
$409$	13.0000	+	22.5167i	0.642809	+	1.11338i	−0.341994	+	0.939702i	$0.611102\pi$
$410$		0			0
$411$		0			0
$412$	10.3923	−	6.00000i	0.511992	−	0.295599i
$413$		0			0
$414$	−2.50000	+	4.33013i	−0.122868	+	0.212814i
$415$		0			0
$416$	−3.50000	−	0.866025i	−0.171602	−	0.0424604i
$417$		−	20.0000i		−	0.979404i
$418$	−15.5885	−	9.00000i	−0.762456	−	0.440204i
$419$	−1.50000	+	2.59808i	−0.0732798	+	0.126924i	−0.900337	−	0.435194i	$-0.856680\pi$
$419$	−1.50000	+	2.59808i	−0.0732798	+	0.126924i	0.827057	+	0.562118i	$0.190013\pi$
$420$		0			0
$421$	11.0000			0.536107			0.268054	−	0.963404i	$-0.413620\pi$
$421$	11.0000			0.536107			0.268054	+	0.963404i	$0.413620\pi$
$422$	−10.3923	+	6.00000i	−0.505889	+	0.292075i
$423$	10.3923	−	6.00000i	0.505291	−	0.291730i
$424$	−12.0000			−0.582772
$425$		0			0
$426$	−3.50000	+	6.06218i	−0.169576	+	0.293713i
$427$		0			0
$428$			8.00000i			0.386695i
$429$	10.5000	+	2.59808i	0.506945	+	0.125436i
$430$		0			0
$431$	−7.50000	+	12.9904i	−0.361262	+	0.625725i	−0.988169	−	0.153370i	$-0.950987\pi$
$431$	−7.50000	+	12.9904i	−0.361262	+	0.625725i	0.626907	+	0.779094i	$0.284321\pi$
$432$	−0.866025	−	0.500000i	−0.0416667	−	0.0240563i
$433$	−32.0429	+	18.5000i	−1.53989	+	0.889053i	−0.541041	+	0.840996i	$0.681970\pi$
$433$	−32.0429	+	18.5000i	−1.53989	+	0.889053i	−0.998845	+	0.0480569i	$0.984697\pi$
$434$		0			0
$435$		0			0
$436$	2.50000	+	4.33013i	0.119728	+	0.207375i
$437$			30.0000i			1.43509i
$438$	0.866025	−	0.500000i	0.0413803	−	0.0238909i
$439$	−12.0000	+	20.7846i	−0.572729	+	0.991995i	0.423556	+	0.905870i	$0.360782\pi$
$439$	−12.0000	+	20.7846i	−0.572729	+	0.991995i	−0.996284	+	0.0861252i	$0.972552\pi$
$440$		0			0
$441$	−7.00000			−0.333333
$442$	15.5885	+	15.0000i	0.741467	+	0.713477i
$443$		−	1.00000i		−	0.0475114i	−0.999718	−	0.0237557i	$-0.992438\pi$
$443$		−	1.00000i		−	0.0475114i	0.999718	−	0.0237557i	$-0.00756239\pi$
$444$	−4.50000	+	7.79423i	−0.213561	+	0.369898i
$445$		0			0
$446$	8.00000	+	13.8564i	0.378811	+	0.656120i
$447$		−	14.0000i		−	0.662177i
$448$		0			0
$449$	11.0000	+	19.0526i	0.519122	+	0.899146i	0.999753	+	0.0222229i	$0.00707434\pi$
$449$	11.0000	+	19.0526i	0.519122	+	0.899146i	−0.480631	+	0.876923i	$0.659592\pi$
$450$		0			0
$451$	15.0000	+	25.9808i	0.706322	+	1.22339i
$452$	3.46410	+	2.00000i	0.162938	+	0.0940721i
$453$	1.73205	+	1.00000i	0.0813788	+	0.0469841i
$454$	23.0000			1.07944
$455$		0			0
$456$	−6.00000			−0.280976
$457$	28.5788	+	16.5000i	1.33686	+	0.771837i	0.986341	−	0.164717i	$-0.0526712\pi$
$457$	28.5788	+	16.5000i	1.33686	+	0.771837i	0.350521	+	0.936555i	$0.386005\pi$
$458$	19.9186	+	11.5000i	0.930734	+	0.537360i
$459$	3.00000	+	5.19615i	0.140028	+	0.242536i
$460$		0			0
$461$	1.00000	+	1.73205i	0.0465746	+	0.0806696i	0.888373	−	0.459123i	$-0.151836\pi$
$461$	1.00000	+	1.73205i	0.0465746	+	0.0806696i	−0.841798	+	0.539792i	$0.818503\pi$
$462$		0			0
$463$			18.0000i			0.836531i	0.908325	+	0.418265i	$0.137362\pi$
$463$			18.0000i			0.836531i	−0.908325	+	0.418265i	$0.862638\pi$
$464$	1.00000	+	1.73205i	0.0464238	+	0.0804084i
$465$		0			0
$466$		0			0
$467$			31.0000i			1.43451i	0.696811	+	0.717254i	$0.254601\pi$
$467$			31.0000i			1.43451i	−0.696811	+	0.717254i	$0.745399\pi$
$468$	3.46410	−	1.00000i	0.160128	−	0.0462250i
$469$		0			0
$470$		0			0
$471$	6.50000	−	11.2583i	0.299504	−	0.518756i
$472$		0			0
$473$			24.0000i			1.10352i
$474$	3.00000	+	5.19615i	0.137795	+	0.238667i
$475$		0			0
$476$		0			0
$477$	10.3923	−	6.00000i	0.475831	−	0.274721i
$478$	−9.52628	−	5.50000i	−0.435722	−	0.251564i
$479$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$479$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$480$		0			0
$481$	−9.00000	−	31.1769i	−0.410365	−	1.42154i
$482$		−	2.00000i		−	0.0910975i
$483$		0			0
$484$	−1.00000	+	1.73205i	−0.0454545	+	0.0787296i
$485$		0			0
$486$	1.00000			0.0453609
$487$	3.46410	−	2.00000i	0.156973	−	0.0906287i	−0.419456	−	0.907776i	$-0.637779\pi$
$487$	3.46410	−	2.00000i	0.156973	−	0.0906287i	0.576429	+	0.817147i	$0.304446\pi$
$488$	12.9904	−	7.50000i	0.588047	−	0.339509i
$489$	2.00000			0.0904431
$490$		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	$0.202656\pi$
$492$	8.66025	+	5.00000i	0.390434	+	0.225417i
$493$		−	12.0000i		−	0.540453i
$494$	15.0000	−	15.5885i	0.674882	−	0.701358i
$495$		0			0
$496$	3.00000	−	5.19615i	0.134704	−	0.233314i
$497$		0			0
$498$	−4.33013	+	2.50000i	−0.194038	+	0.112028i
$499$	34.0000			1.52205			0.761025	−	0.648723i	$-0.224697\pi$
$499$	34.0000			1.52205			0.761025	+	0.648723i	$0.224697\pi$
$500$		0			0
$501$	−10.5000	−	18.1865i	−0.469105	−	0.812514i
$502$			23.0000i			1.02654i
$503$	−7.79423	+	4.50000i	−0.347527	+	0.200645i	−0.663596	−	0.748091i	$-0.730970\pi$
$503$	−7.79423	+	4.50000i	−0.347527	+	0.200645i	0.316068	+	0.948736i	$0.397637\pi$
$504$		0			0
$505$		0			0
$506$	−15.0000			−0.666831
$507$	−6.06218	+	11.5000i	−0.269231	+	0.510733i
$508$			18.0000i			0.798621i
$509$	−16.0000	+	27.7128i	−0.709188	+	1.22835i	0.255971	+	0.966684i	$0.417605\pi$
$509$	−16.0000	+	27.7128i	−0.709188	+	1.22835i	−0.965159	+	0.261664i	$0.915729\pi$
$510$		0			0
$511$		0			0
$512$			1.00000i			0.0441942i
$513$	5.19615	−	3.00000i	0.229416	−	0.132453i
$514$		0			0
$515$		0			0
$516$	4.00000	+	6.92820i	0.176090	+	0.304997i
$517$	31.1769	+	18.0000i	1.37116	+	0.791639i
$518$		0			0
$519$	−8.00000			−0.351161
$520$		0			0
$521$	40.0000			1.75243			0.876216	−	0.481919i	$-0.160060\pi$
$521$	40.0000			1.75243			0.876216	+	0.481919i	$0.160060\pi$
$522$	−1.73205	−	1.00000i	−0.0758098	−	0.0437688i
$523$	22.5167	+	13.0000i	0.984585	+	0.568450i	0.903651	−	0.428269i	$-0.140876\pi$
$523$	22.5167	+	13.0000i	0.984585	+	0.568450i	0.0809336	+	0.996719i	$0.474210\pi$
$524$	6.00000	+	10.3923i	0.262111	+	0.453990i
$525$		0			0
$526$	−6.50000	−	11.2583i	−0.283413	−	0.490887i
$527$	−31.1769	+	18.0000i	−1.35809	+	0.784092i
$528$		−	3.00000i		−	0.130558i
$529$	1.00000	+	1.73205i	0.0434783	+	0.0753066i
$530$		0			0
$531$		0			0
$532$		0			0
$533$	−34.6410	+	10.0000i	−1.50047	+	0.433148i
$534$	6.00000			0.259645
$535$		0			0
$536$	2.00000	−	3.46410i	0.0863868	−	0.149626i
$537$	6.06218	−	3.50000i	0.261602	−	0.151036i
$538$		−	32.0000i		−	1.37962i
$539$	−10.5000	−	18.1865i	−0.452267	−	0.783349i
$540$		0			0
$541$	−13.0000			−0.558914			−0.279457	−	0.960158i	$-0.590154\pi$
$541$	−13.0000			−0.558914			−0.279457	+	0.960158i	$0.590154\pi$
$542$	15.5885	−	9.00000i	0.669582	−	0.386583i
$543$	−0.866025	−	0.500000i	−0.0371647	−	0.0214571i
$544$	3.00000	−	5.19615i	0.128624	−	0.222783i
$545$		0			0
$546$		0			0
$547$		−	34.0000i		−	1.45374i	−0.686778	−	0.726868i	$-0.740975\pi$
$547$		−	34.0000i		−	1.45374i	0.686778	−	0.726868i	$-0.259025\pi$
$548$		0			0
$549$	−7.50000	+	12.9904i	−0.320092	+	0.554416i
$550$		0			0
$551$	−12.0000			−0.511217
$552$	−4.33013	+	2.50000i	−0.184302	+	0.106407i
$553$		0			0
$554$	−13.0000			−0.552317
$555$		0			0
$556$	10.0000	−	17.3205i	0.424094	−	0.734553i
$557$	−20.7846	−	12.0000i	−0.880672	−	0.508456i	−0.00979220	−	0.999952i	$-0.503117\pi$
$557$	−20.7846	−	12.0000i	−0.880672	−	0.508456i	−0.870880	+	0.491496i	$0.836450\pi$
$558$			6.00000i			0.254000i
$559$	−28.0000	−	6.92820i	−1.18427	−	0.293032i
$560$		0			0
$561$	−9.00000	+	15.5885i	−0.379980	+	0.658145i
$562$	−25.9808	−	15.0000i	−1.09593	−	0.632737i
$563$	−32.0429	+	18.5000i	−1.35045	+	0.779682i	−0.988312	−	0.152443i	$-0.951286\pi$
$563$	−32.0429	+	18.5000i	−1.35045	+	0.779682i	−0.362137	+	0.932125i	$0.617953\pi$
$564$	12.0000			0.505291
$565$		0			0
$566$	12.0000	+	20.7846i	0.504398	+	0.873642i
$567$		0			0
$568$	−6.06218	+	3.50000i	−0.254363	+	0.146857i
$569$	−18.0000	+	31.1769i	−0.754599	+	1.30700i	0.190974	+	0.981595i	$0.438835\pi$
$569$	−18.0000	+	31.1769i	−0.754599	+	1.30700i	−0.945573	+	0.325409i	$0.894498\pi$
$570$		0			0
$571$	−10.0000			−0.418487			−0.209243	−	0.977864i	$-0.567100\pi$
$571$	−10.0000			−0.418487			−0.209243	+	0.977864i	$0.567100\pi$
$572$	7.79423	+	7.50000i	0.325893	+	0.313591i
$573$			3.00000i			0.125327i
$574$		0			0
$575$		0			0
$576$	−0.500000	−	0.866025i	−0.0208333	−	0.0360844i
$577$		−	43.0000i		−	1.79011i	−0.445952	−	0.895057i	$-0.647135\pi$
$577$		−	43.0000i		−	1.79011i	0.445952	−	0.895057i	$-0.352865\pi$
$578$	−16.4545	+	9.50000i	−0.684416	+	0.395148i
$579$	−5.50000	−	9.52628i	−0.228572	−	0.395899i
$580$		0			0
$581$		0			0
$582$	4.33013	+	2.50000i	0.179490	+	0.103628i
$583$	31.1769	+	18.0000i	1.29122	+	0.745484i
$584$	1.00000			0.0413803
$585$		0			0
$586$	28.0000			1.15667
$587$	−18.1865	−	10.5000i	−0.750639	−	0.433381i	0.0752860	−	0.997162i	$-0.476013\pi$
$587$	−18.1865	−	10.5000i	−0.750639	−	0.433381i	−0.825925	+	0.563781i	$0.809346\pi$
$588$	−6.06218	−	3.50000i	−0.250000	−	0.144338i
$589$	18.0000	+	31.1769i	0.741677	+	1.28462i
$590$		0			0
$591$	−5.00000	−	8.66025i	−0.205673	−	0.356235i
$592$	−7.79423	+	4.50000i	−0.320341	+	0.184949i
$593$		0			0		1.00000			$0$
$593$		0			0		−1.00000			$\pi$
$594$	1.50000	+	2.59808i	0.0615457	+	0.106600i
$595$		0			0
$596$	7.00000	−	12.1244i	0.286731	−	0.496633i
$597$		−	4.00000i		−	0.163709i
$598$	4.33013	−	17.5000i	0.177072	−	0.715628i
$599$	15.0000			0.612883			0.306442	−	0.951889i	$-0.400862\pi$
$599$	15.0000			0.612883			0.306442	+	0.951889i	$0.400862\pi$
$600$		0			0
$601$	−15.0000	+	25.9808i	−0.611863	+	1.05978i	0.379063	+	0.925371i	$0.376246\pi$
$601$	−15.0000	+	25.9808i	−0.611863	+	1.05978i	−0.990926	+	0.134407i	$0.957087\pi$
$602$		0			0
$603$			4.00000i			0.162893i
$604$	1.00000	+	1.73205i	0.0406894	+	0.0704761i
$605$		0			0
$606$		0			0
$607$	−15.5885	+	9.00000i	−0.632716	+	0.365299i	−0.781803	−	0.623525i	$-0.785700\pi$
$607$	−15.5885	+	9.00000i	−0.632716	+	0.365299i	0.149087	+	0.988824i	$0.452366\pi$
$608$	−5.19615	−	3.00000i	−0.210732	−	0.121666i
$609$		0			0
$610$		0			0
$611$	−30.0000	+	31.1769i	−1.21367	+	1.26128i
$612$			6.00000i			0.242536i
$613$	−12.1244	−	7.00000i	−0.489698	−	0.282727i	0.234751	−	0.972056i	$-0.424572\pi$
$613$	−12.1244	−	7.00000i	−0.489698	−	0.282727i	−0.724449	+	0.689328i	$0.757906\pi$
$614$	8.00000	−	13.8564i	0.322854	−	0.559199i
$615$		0			0
$616$		0			0
$617$	15.5885	−	9.00000i	0.627568	−	0.362326i	−0.152242	−	0.988343i	$-0.548649\pi$
$617$	15.5885	−	9.00000i	0.627568	−	0.362326i	0.779809	+	0.626017i	$0.215316\pi$
$618$	−10.3923	+	6.00000i	−0.418040	+	0.241355i
$619$	20.0000			0.803868			0.401934	−	0.915669i	$-0.368338\pi$
$619$	20.0000			0.803868			0.401934	+	0.915669i	$0.368338\pi$
$620$		0			0
$621$	2.50000	−	4.33013i	0.100322	−	0.173762i
$622$	−4.33013	−	2.50000i	−0.173622	−	0.100241i
$623$		0			0
$624$	3.50000	+	0.866025i	0.140112	+	0.0346688i
$625$		0			0
$626$	−0.500000	+	0.866025i	−0.0199840	+	0.0346133i
$627$	15.5885	+	9.00000i	0.622543	+	0.359425i
$628$	11.2583	−	6.50000i	0.449256	−	0.259378i
$629$	54.0000			2.15312
$630$		0			0
$631$	−9.00000	−	15.5885i	−0.358284	−	0.620567i	0.629390	−	0.777090i	$-0.283305\pi$
$631$	−9.00000	−	15.5885i	−0.358284	−	0.620567i	−0.987674	+	0.156523i	$0.949971\pi$
$632$			6.00000i			0.238667i
$633$	10.3923	−	6.00000i	0.413057	−	0.238479i
$634$	−16.0000	+	27.7128i	−0.635441	+	1.10062i
$635$		0			0
$636$	12.0000			0.475831
$637$	24.2487	−	7.00000i	0.960769	−	0.277350i
$638$		−	6.00000i		−	0.237542i
$639$	3.50000	−	6.06218i	0.138458	−	0.239816i
$640$		0			0
$641$	2.00000	+	3.46410i	0.0789953	+	0.136824i	0.902817	−	0.430026i	$-0.141495\pi$
$641$	2.00000	+	3.46410i	0.0789953	+	0.136824i	−0.823821	+	0.566849i	$0.808162\pi$
$642$		−	8.00000i		−	0.315735i
$643$	29.4449	−	17.0000i	1.16119	−	0.670415i	0.209603	−	0.977787i	$-0.432783\pi$
$643$	29.4449	−	17.0000i	1.16119	−	0.670415i	0.951589	+	0.307372i	$0.0994496\pi$
$644$		0			0
$645$		0			0
$646$	18.0000	+	31.1769i	0.708201	+	1.22664i
$647$	28.5788	+	16.5000i	1.12355	+	0.648682i	0.942305	−	0.334756i	$-0.108654\pi$
$647$	28.5788	+	16.5000i	1.12355	+	0.648682i	0.181245	+	0.983438i	$0.441987\pi$
$648$	0.866025	+	0.500000i	0.0340207	+	0.0196419i
$649$		0			0
$650$		0			0
$651$		0			0
$652$	1.73205	+	1.00000i	0.0678323	+	0.0391630i
$653$	10.3923	+	6.00000i	0.406682	+	0.234798i	0.689363	−	0.724416i	$-0.257890\pi$
$653$	10.3923	+	6.00000i	0.406682	+	0.234798i	−0.282681	+	0.959214i	$0.591224\pi$
$654$	−2.50000	−	4.33013i	−0.0977577	−	0.169321i
$655$		0			0
$656$	5.00000	+	8.66025i	0.195217	+	0.338126i
$657$	−0.866025	+	0.500000i	−0.0337869	+	0.0195069i
$658$		0			0
$659$	−17.5000	−	30.3109i	−0.681703	−	1.18074i	−0.974461	−	0.224558i	$-0.927906\pi$
$659$	−17.5000	−	30.3109i	−0.681703	−	1.18074i	0.292758	−	0.956187i	$-0.405427\pi$
$660$		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	$0.968376\pi$
$662$			26.0000i			1.01052i
$663$	−15.5885	−	15.0000i	−0.605406	−	0.582552i
$664$	−5.00000			−0.194038
$665$		0			0
$666$	4.50000	−	7.79423i	0.174371	−	0.302020i
$667$	−8.66025	+	5.00000i	−0.335326	+	0.193601i
$668$		−	21.0000i		−	0.812514i
$669$	−8.00000	−	13.8564i	−0.309298	−	0.535720i
$670$		0			0
$671$	−45.0000			−1.73721
$672$		0			0
$673$	28.5788	+	16.5000i	1.10163	+	0.636028i	0.936650	−	0.350268i	$-0.113909\pi$
$673$	28.5788	+	16.5000i	1.10163	+	0.636028i	0.164984	+	0.986296i	$0.447243\pi$
$674$	15.0000	−	25.9808i	0.577778	−	1.00074i
$675$		0			0
$676$	−11.0000	+	6.92820i	−0.423077	+	0.266469i
$677$		−	12.0000i		−	0.461197i	−0.973049	−	0.230599i	$-0.925932\pi$
$677$		−	12.0000i		−	0.461197i	0.973049	−	0.230599i	$-0.0740685\pi$
$678$	−3.46410	−	2.00000i	−0.133038	−	0.0768095i
$679$		0			0
$680$		0			0
$681$	−23.0000			−0.881362
$682$	−15.5885	+	9.00000i	−0.596913	+	0.344628i
$683$	33.7750	−	19.5000i	1.29236	−	0.746147i	0.313291	−	0.949657i	$-0.398568\pi$
$683$	33.7750	−	19.5000i	1.29236	−	0.746147i	0.979073	+	0.203510i	$0.0652350\pi$
$684$	6.00000			0.229416
$685$		0			0
$686$		0			0
$687$	−19.9186	−	11.5000i	−0.759941	−	0.438752i
$688$			8.00000i			0.304997i
$689$	−30.0000	+	31.1769i	−1.14291	+	1.18775i
$690$		0			0
$691$	−7.00000	+	12.1244i	−0.266293	+	0.461232i	−0.967901	−	0.251330i	$-0.919132\pi$
$691$	−7.00000	+	12.1244i	−0.266293	+	0.461232i	0.701609	+	0.712562i	$0.252465\pi$
$692$	−6.92820	−	4.00000i	−0.263371	−	0.152057i
$693$		0			0
$694$	−27.0000			−1.02491
$695$		0			0
$696$	−1.00000	−	1.73205i	−0.0379049	−	0.0656532i
$697$		−	60.0000i		−	2.27266i
$698$	−21.6506	+	12.5000i	−0.819489	+	0.473132i
$699$		0			0
$700$		0			0
$701$	42.0000			1.58632			0.793159	−	0.609015i	$-0.208435\pi$
$701$	42.0000			1.58632			0.793159	+	0.609015i	$0.208435\pi$
$702$	−3.46410	+	1.00000i	−0.130744	+	0.0377426i
$703$		−	54.0000i		−	2.03665i
$704$	1.50000	−	2.59808i	0.0565334	−	0.0979187i
$705$		0			0
$706$	−7.00000	−	12.1244i	−0.263448	−	0.456306i
$707$		0			0
$708$		0			0
$709$	−12.5000	−	21.6506i	−0.469447	−	0.813107i	0.529943	−	0.848034i	$-0.322213\pi$
$709$	−12.5000	−	21.6506i	−0.469447	−	0.813107i	−0.999390	+	0.0349269i	$0.988880\pi$
$710$		0			0
$711$	−3.00000	−	5.19615i	−0.112509	−	0.194871i
$712$	5.19615	+	3.00000i	0.194734	+	0.112430i
$713$	25.9808	+	15.0000i	0.972987	+	0.561754i
$714$		0			0
$715$		0			0
$716$	7.00000			0.261602
$717$	9.52628	+	5.50000i	0.355765	+	0.205401i
$718$		0			0
$719$	−1.50000	−	2.59808i	−0.0559406	−	0.0968919i	0.836699	−	0.547663i	$-0.184482\pi$
$719$	−1.50000	−	2.59808i	−0.0559406	−	0.0968919i	−0.892640	+	0.450771i	$0.851149\pi$
$720$		0			0
$721$		0			0
$722$	14.7224	−	8.50000i	0.547912	−	0.316337i
$723$			2.00000i			0.0743808i
$724$	−0.500000	−	0.866025i	−0.0185824	−	0.0321856i
$725$		0			0
$726$	1.00000	−	1.73205i	0.0371135	−	0.0642824i
$727$			18.0000i			0.667583i	0.942647	+	0.333792i	$0.108328\pi$
$727$			18.0000i			0.667583i	−0.942647	+	0.333792i	$0.891672\pi$
$728$		0			0
$729$	−1.00000			−0.0370370
$730$		0			0
$731$	24.0000	−	41.5692i	0.887672	−	1.53749i
$732$	−12.9904	+	7.50000i	−0.480138	+	0.277208i
$733$			35.0000i			1.29275i	0.763018	+	0.646377i	$0.223717\pi$
$733$			35.0000i			1.29275i	−0.763018	+	0.646377i	$0.776283\pi$
$734$	−7.00000	−	12.1244i	−0.258375	−	0.447518i
$735$		0			0
$736$	−5.00000			−0.184302
$737$	−10.3923	+	6.00000i	−0.382805	+	0.221013i
$738$	−8.66025	−	5.00000i	−0.318788	−	0.184053i
$739$	−17.0000	+	29.4449i	−0.625355	+	1.08315i	0.363117	+	0.931744i	$0.381713\pi$
$739$	−17.0000	+	29.4449i	−0.625355	+	1.08315i	−0.988472	+	0.151403i	$0.951621\pi$
$740$		0			0
$741$	−15.0000	+	15.5885i	−0.551039	+	0.572656i
$742$		0			0
$743$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$743$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$744$	−3.00000	+	5.19615i	−0.109985	+	0.190500i
$745$		0			0
$746$	11.0000			0.402739
$747$	4.33013	−	2.50000i	0.158431	−	0.0914702i
$748$	−15.5885	+	9.00000i	−0.569970	+	0.329073i
$749$		0			0
$750$		0			0
$751$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$751$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$752$	10.3923	+	6.00000i	0.378968	+	0.218797i
$753$		−	23.0000i		−	0.838167i
$754$	7.00000	+	1.73205i	0.254925	+	0.0630776i
$755$		0			0
$756$		0			0
$757$	−8.66025	−	5.00000i	−0.314762	−	0.181728i	0.334293	−	0.942469i	$-0.391502\pi$
$757$	−8.66025	−	5.00000i	−0.314762	−	0.181728i	−0.649056	+	0.760741i	$0.724836\pi$
$758$	5.19615	−	3.00000i	0.188733	−	0.108965i
$759$	15.0000			0.544466
$760$		0			0
$761$	14.0000	+	24.2487i	0.507500	+	0.879015i	0.999962	+	0.00868155i	$0.00276346\pi$
$761$	14.0000	+	24.2487i	0.507500	+	0.879015i	−0.492463	+	0.870334i	$0.663903\pi$
$762$		−	18.0000i		−	0.652071i
$763$		0			0
$764$	−1.50000	+	2.59808i	−0.0542681	+	0.0939951i
$765$		0			0
$766$	−1.00000			−0.0361315
$767$		0			0
$768$		−	1.00000i		−	0.0360844i
$769$	−1.00000	+	1.73205i	−0.0360609	+	0.0624593i	−0.883493	−	0.468445i	$-0.844814\pi$
$769$	−1.00000	+	1.73205i	−0.0360609	+	0.0624593i	0.847432	+	0.530904i	$0.178148\pi$
$770$		0			0
$771$		0			0
$772$		−	11.0000i		−	0.395899i
$773$	12.1244	−	7.00000i	0.436083	−	0.251773i	−0.265852	−	0.964014i	$-0.585653\pi$
$773$	12.1244	−	7.00000i	0.436083	−	0.251773i	0.701935	+	0.712241i	$0.252320\pi$
$774$	−4.00000	−	6.92820i	−0.143777	−	0.249029i
$775$		0			0
$776$	2.50000	+	4.33013i	0.0897448	+	0.155443i
$777$		0			0
$778$	−5.19615	−	3.00000i	−0.186291	−	0.107555i
$779$	−60.0000			−2.14972
$780$		0			0
$781$	21.0000			0.751439
$782$	25.9808	+	15.0000i	0.929070	+	0.536399i
$783$	1.73205	+	1.00000i	0.0618984	+	0.0357371i
$784$	−3.50000	−	6.06218i	−0.125000	−	0.216506i
$785$		0			0
$786$	−6.00000	−	10.3923i	−0.214013	−	0.370681i
$787$	−36.3731	+	21.0000i	−1.29656	+	0.748569i	−0.979808	−	0.199939i	$-0.935925\pi$
$787$	−36.3731	+	21.0000i	−1.29656	+	0.748569i	−0.316752	+	0.948509i	$0.602592\pi$
$788$		−	10.0000i		−	0.356235i
$789$	6.50000	+	11.2583i	0.231406	+	0.400807i
$790$		0			0
$791$		0			0
$792$			3.00000i			0.106600i
$793$	12.9904	−	52.5000i	0.461302	−	1.86433i
$794$	22.0000			0.780751
$795$		0			0
$796$	2.00000	−	3.46410i	0.0708881	−	0.122782i
$797$	10.3923	−	6.00000i	0.368114	−	0.212531i	−0.304520	−	0.952506i	$-0.598496\pi$
$797$	10.3923	−	6.00000i	0.368114	−	0.212531i	0.672634	+	0.739975i	$0.265163\pi$
$798$		0			0
$799$	−36.0000	−	62.3538i	−1.27359	−	2.20592i
$800$		0			0
$801$	−6.00000			−0.212000
$802$	−5.19615	+	3.00000i	−0.183483	+	0.105934i
$803$	−2.59808	−	1.50000i	−0.0916841	−	0.0529339i
$804$	−2.00000	+	3.46410i	−0.0705346	+	0.122169i
$805$		0			0
$806$	−6.00000	−	20.7846i	−0.211341	−	0.732107i
$807$			32.0000i			1.12645i
$808$		0			0
$809$	−5.00000	+	8.66025i	−0.175791	+	0.304478i	−0.940435	−	0.339975i	$-0.889582\pi$
$809$	−5.00000	+	8.66025i	−0.175791	+	0.304478i	0.764644	+	0.644453i	$0.222915\pi$
$810$		0			0
$811$	38.0000			1.33436			0.667180	−	0.744896i	$-0.267501\pi$
$811$	38.0000			1.33436			0.667180	+	0.744896i	$0.267501\pi$
$812$		0			0
$813$	−15.5885	+	9.00000i	−0.546711	+	0.315644i
$814$	27.0000			0.946350
$815$		0			0
$816$	−3.00000	+	5.19615i	−0.105021	+	0.181902i
$817$	−41.5692	−	24.0000i	−1.45432	−	0.839654i
$818$		−	26.0000i		−	0.909069i
$819$		0			0
$820$		0			0
$821$	5.00000	−	8.66025i	0.174501	−	0.302245i	−0.765487	−	0.643451i	$-0.777502\pi$
$821$	5.00000	−	8.66025i	0.174501	−	0.302245i	0.939989	+	0.341206i	$0.110835\pi$
$822$		0			0
$823$	13.8564	−	8.00000i	0.483004	−	0.278862i	−0.238664	−	0.971102i	$-0.576709\pi$
$823$	13.8564	−	8.00000i	0.483004	−	0.278862i	0.721668	+	0.692240i	$0.243376\pi$
$824$	−12.0000			−0.418040
$825$		0			0
$826$		0			0
$827$		−	27.0000i		−	0.938882i	−0.882964	−	0.469441i	$-0.844455\pi$
$827$		−	27.0000i		−	0.938882i	0.882964	−	0.469441i	$-0.155545\pi$
$828$	4.33013	−	2.50000i	0.150482	−	0.0868810i
$829$	21.0000	−	36.3731i	0.729360	−	1.26329i	−0.227794	−	0.973709i	$-0.573151\pi$
$829$	21.0000	−	36.3731i	0.729360	−	1.26329i	0.957154	−	0.289579i	$-0.0935154\pi$
$830$		0			0
$831$	13.0000			0.450965
$832$	2.59808	+	2.50000i	0.0900721	+	0.0866719i
$833$			42.0000i			1.45521i
$834$	−10.0000	+	17.3205i	−0.346272	+	0.599760i
$835$		0			0
$836$	9.00000	+	15.5885i	0.311272	+	0.539138i
$837$		−	6.00000i		−	0.207390i
$838$	2.59808	−	1.50000i	0.0897491	−	0.0518166i
$839$	10.5000	+	18.1865i	0.362500	+	0.627869i	0.988372	−	0.152057i	$-0.0485899\pi$
$839$	10.5000	+	18.1865i	0.362500	+	0.627869i	−0.625871	+	0.779926i	$0.715257\pi$
$840$		0			0
$841$	12.5000	+	21.6506i	0.431034	+	0.746574i
$842$	−9.52628	−	5.50000i	−0.328297	−	0.189543i
$843$	25.9808	+	15.0000i	0.894825	+	0.516627i
$844$	12.0000			0.413057
$845$		0			0
$846$	−12.0000			−0.412568
$847$		0			0
$848$	10.3923	+	6.00000i	0.356873	+	0.206041i
$849$	−12.0000	−	20.7846i	−0.411839	−	0.713326i
$850$		0			0
$851$	−22.5000	−	38.9711i	−0.771290	−	1.33591i
$852$	6.06218	−	3.50000i	0.207687	−	0.119908i
$853$			10.0000i			0.342393i	0.985237	+	0.171197i	$0.0547634\pi$
$853$			10.0000i			0.342393i	−0.985237	+	0.171197i	$0.945237\pi$
$854$		0			0
$855$		0			0
$856$	4.00000	−	6.92820i	0.136717	−	0.236801i
$857$		−	10.0000i		−	0.341593i	−0.985306	−	0.170797i	$-0.945366\pi$
$857$		−	10.0000i		−	0.341593i	0.985306	−	0.170797i	$-0.0546341\pi$
$858$	−7.79423	−	7.50000i	−0.266091	−	0.256046i
$859$	−10.0000			−0.341196			−0.170598	−	0.985341i	$-0.554570\pi$
$859$	−10.0000			−0.341196			−0.170598	+	0.985341i	$0.554570\pi$
$860$		0			0
$861$		0			0
$862$	12.9904	−	7.50000i	0.442454	−	0.255451i
$863$		−	39.0000i		−	1.32758i	−0.747921	−	0.663788i	$-0.768948\pi$
$863$		−	39.0000i		−	1.32758i	0.747921	−	0.663788i	$-0.231052\pi$
$864$	0.500000	+	0.866025i	0.0170103	+	0.0294628i
$865$		0			0
$866$	37.0000			1.25731
$867$	16.4545	−	9.50000i	0.558824	−	0.322637i
$868$		0			0
$869$	9.00000	−	15.5885i	0.305304	−	0.528802i
$870$		0			0
$871$	−4.00000	−	13.8564i	−0.135535	−	0.469506i
$872$		−	5.00000i		−	0.169321i
$873$	−4.33013	−	2.50000i	−0.146553	−	0.0846122i
$874$	15.0000	−	25.9808i	0.507383	−	0.878812i
$875$		0			0
$876$	−1.00000			−0.0337869
$877$	−11.2583	+	6.50000i	−0.380167	+	0.219489i	−0.677891	−	0.735163i	$-0.737106\pi$
$877$	−11.2583	+	6.50000i	−0.380167	+	0.219489i	0.297724	+	0.954652i	$0.403772\pi$
$878$	20.7846	−	12.0000i	0.701447	−	0.404980i
$879$	−28.0000			−0.944417
$880$		0			0
$881$	−20.0000	+	34.6410i	−0.673817	+	1.16709i	0.302996	+	0.952992i	$0.402013\pi$
$881$	−20.0000	+	34.6410i	−0.673817	+	1.16709i	−0.976813	+	0.214094i	$0.931320\pi$
$882$	6.06218	+	3.50000i	0.204124	+	0.117851i
$883$			40.0000i			1.34611i	0.739594	+	0.673054i	$0.235018\pi$
$883$			40.0000i			1.34611i	−0.739594	+	0.673054i	$0.764982\pi$
$884$	−6.00000	−	20.7846i	−0.201802	−	0.699062i
$885$		0			0
$886$	−0.500000	+	0.866025i	−0.0167978	+	0.0290947i
$887$	−41.5692	−	24.0000i	−1.39576	−	0.805841i	−0.401813	−	0.915722i	$-0.631620\pi$
$887$	−41.5692	−	24.0000i	−1.39576	−	0.805841i	−0.993945	+	0.109881i	$0.964953\pi$
$888$	7.79423	−	4.50000i	0.261557	−	0.151010i
$889$		0			0
$890$		0			0
$891$	−1.50000	−	2.59808i	−0.0502519	−	0.0870388i
$892$		−	16.0000i		−	0.535720i
$893$	−62.3538	+	36.0000i	−2.08659	+	1.20469i
$894$	−7.00000	+	12.1244i	−0.234115	+	0.405499i
$895$		0			0
$896$		0			0
$897$	−4.33013	+	17.5000i	−0.144579	+	0.584308i
$898$		−	22.0000i		−	0.734150i
$899$	−6.00000	+	10.3923i	−0.200111	+	0.346603i
$900$		0			0
$901$	−36.0000	−	62.3538i	−1.19933	−	2.07731i
$902$		−	30.0000i		−	0.998891i
$903$		0			0
$904$	−2.00000	−	3.46410i	−0.0665190	−	0.115214i
$905$		0			0
$906$	−1.00000	−	1.73205i	−0.0332228	−	0.0575435i
$907$	3.46410	+	2.00000i	0.115024	+	0.0664089i	0.556408	−	0.830909i	$-0.312179\pi$
$907$	3.46410	+	2.00000i	0.115024	+	0.0664089i	−0.441384	+	0.897318i	$0.645512\pi$
$908$	−19.9186	−	11.5000i	−0.661021	−	0.381641i
$909$		0			0
$910$		0			0
$911$	−41.0000			−1.35839			−0.679195	−	0.733958i	$-0.737671\pi$
$911$	−41.0000			−1.35839			−0.679195	+	0.733958i	$0.737671\pi$
$912$	5.19615	+	3.00000i	0.172062	+	0.0993399i
$913$	12.9904	+	7.50000i	0.429919	+	0.248214i
$914$	−16.5000	−	28.5788i	−0.545771	−	0.945304i
$915$		0			0
$916$	−11.5000	−	19.9186i	−0.379971	−	0.658129i
$917$		0			0
$918$		−	6.00000i		−	0.198030i
$919$	13.0000	+	22.5167i	0.428830	+	0.742756i	0.996770	−	0.0803145i	$-0.0255924\pi$
$919$	13.0000	+	22.5167i	0.428830	+	0.742756i	−0.567939	+	0.823071i	$0.692259\pi$
$920$		0			0
$921$	−8.00000	+	13.8564i	−0.263609	+	0.456584i
$922$		−	2.00000i		−	0.0658665i
$923$	−6.06218	+	24.5000i	−0.199539	+	0.806427i
$924$		0			0
$925$		0			0
$926$	9.00000	−	15.5885i	0.295758	−	0.512268i
$927$	10.3923	−	6.00000i	0.341328	−	0.197066i
$928$		−	2.00000i		−	0.0656532i
$929$	−8.00000	−	13.8564i	−0.262471	−	0.454614i	0.704427	−	0.709777i	$-0.251204\pi$
$929$	−8.00000	−	13.8564i	−0.262471	−	0.454614i	−0.966898	+	0.255163i	$0.917871\pi$
$930$		0			0
$931$	42.0000			1.37649
$932$		0			0
$933$	4.33013	+	2.50000i	0.141762	+	0.0818463i
$934$	15.5000	−	26.8468i	0.507175	−	0.878454i
$935$		0			0
$936$	−3.50000	−	0.866025i	−0.114401	−	0.0283069i
$937$		−	59.0000i		−	1.92745i	−0.266904	−	0.963723i	$-0.586001\pi$
$937$		−	59.0000i		−	1.92745i	0.266904	−	0.963723i	$-0.413999\pi$
$938$		0			0
$939$	0.500000	−	0.866025i	0.0163169	−	0.0282617i
$940$		0			0
$941$	−8.00000			−0.260793			−0.130396	−	0.991462i	$-0.541625\pi$
$941$	−8.00000			−0.260793			−0.130396	+	0.991462i	$0.541625\pi$
$942$	−11.2583	+	6.50000i	−0.366816	+	0.211781i
$943$	−43.3013	+	25.0000i	−1.41008	+	0.814112i
$944$		0			0
$945$		0			0
$946$	12.0000	−	20.7846i	0.390154	−	0.675766i
$947$	2.59808	+	1.50000i	0.0844261	+	0.0487435i	0.541619	−	0.840624i	$-0.317812\pi$
$947$	2.59808	+	1.50000i	0.0844261	+	0.0487435i	−0.457193	+	0.889368i	$0.651145\pi$
$948$		−	6.00000i		−	0.194871i
$949$	2.50000	−	2.59808i	0.0811534	−	0.0843371i
$950$		0			0
$951$	16.0000	−	27.7128i	0.518836	−	0.898650i
$952$		0			0
$953$	34.6410	−	20.0000i	1.12213	−	0.647864i	0.180188	−	0.983632i	$-0.442329\pi$
$953$	34.6410	−	20.0000i	1.12213	−	0.647864i	0.941944	+	0.335769i	$0.108996\pi$
$954$	−12.0000			−0.388514
$955$		0			0
$956$	5.50000	+	9.52628i	0.177883	+	0.308102i
$957$			6.00000i			0.193952i
$958$		0			0
$959$		0			0
$960$		0			0
$961$	5.00000			0.161290
$962$	−7.79423	+	31.5000i	−0.251296	+	1.01560i
$963$			8.00000i			0.257796i
$964$	−1.00000	+	1.73205i	−0.0322078	+	0.0557856i
$965$		0			0
$966$		0			0
$967$		−	22.0000i		−	0.707472i	−0.935345	−	0.353736i	$-0.884911\pi$
$967$		−	22.0000i		−	0.707472i	0.935345	−	0.353736i	$-0.115089\pi$
$968$	1.73205	−	1.00000i	0.0556702	−	0.0321412i
$969$	−18.0000	−	31.1769i	−0.578243	−	1.00155i
$970$		0			0
$971$	18.0000	+	31.1769i	0.577647	+	1.00051i	0.995748	+	0.0921142i	$0.0293625\pi$
$971$	18.0000	+	31.1769i	0.577647	+	1.00051i	−0.418101	+	0.908401i	$0.637304\pi$
$972$	−0.866025	−	0.500000i	−0.0277778	−	0.0160375i
$973$		0			0
$974$	−4.00000			−0.128168
$975$		0			0
$976$	−15.0000			−0.480138
$977$	24.2487	+	14.0000i	0.775785	+	0.447900i	0.834934	−	0.550349i	$-0.185506\pi$
$977$	24.2487	+	14.0000i	0.775785	+	0.447900i	−0.0591494	+	0.998249i	$0.518839\pi$
$978$	−1.73205	−	1.00000i	−0.0553849	−	0.0319765i
$979$	−9.00000	−	15.5885i	−0.287641	−	0.498209i
$980$		0			0
$981$	2.50000	+	4.33013i	0.0798189	+	0.138250i
$982$	4.33013	−	2.50000i	0.138180	−	0.0797782i
$983$		−	8.00000i		−	0.255160i	−0.991828	−	0.127580i	$-0.959279\pi$
$983$		−	8.00000i		−	0.255160i	0.991828	−	0.127580i	$-0.0407210\pi$
$984$	−5.00000	−	8.66025i	−0.159394	−	0.276079i
$985$		0			0
$986$	−6.00000	+	10.3923i	−0.191079	+	0.330958i
$987$		0			0
$988$	−20.7846	+	6.00000i	−0.661247	+	0.190885i
$989$	−40.0000			−1.27193
$990$		0			0
$991$	16.0000	−	27.7128i	0.508257	−	0.880327i	−0.491698	−	0.870766i	$-0.663623\pi$
$991$	16.0000	−	27.7128i	0.508257	−	0.880327i	0.999954	−	0.00956046i	$-0.00304324\pi$
$992$	−5.19615	+	3.00000i	−0.164978	+	0.0952501i
$993$		−	26.0000i		−	0.825085i
$994$		0			0
$995$		0			0
$996$	5.00000			0.158431
$997$	50.2295	−	29.0000i	1.59078	−	0.918439i	0.597611	−	0.801786i	$-0.296117\pi$
$997$	50.2295	−	29.0000i	1.59078	−	0.918439i	0.993173	−	0.116653i	$-0.0372165\pi$
$998$	−29.4449	−	17.0000i	−0.932061	−	0.538126i
$999$	−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.a.1699.1		4
5.2	odd	4		1950.2.i.v.451.1	yes	2
5.3	odd	4		1950.2.i.e.451.1	✓	2
5.4	even	2	inner	1950.2.z.a.1699.2		4
13.3	even	3	inner	1950.2.z.a.1849.2		4
65.3	odd	12		1950.2.i.e.601.1	yes	2
65.29	even	6	inner	1950.2.z.a.1849.1		4
65.42	odd	12		1950.2.i.v.601.1	yes	2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1950.2.i.e.451.1	✓	2	5.3	odd	4
1950.2.i.e.601.1	yes	2	65.3	odd	12
1950.2.i.v.451.1	yes	2	5.2	odd	4
1950.2.i.v.601.1	yes	2	65.42	odd	12
1950.2.z.a.1699.1		4	1.1	even	1	trivial
1950.2.z.a.1699.2		4	5.4	even	2	inner
1950.2.z.a.1849.1		4	65.29	even	6	inner
1950.2.z.a.1849.2		4	13.3	even	3	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

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)

\(f(q)\)	\(=\)	\(q+(-0.866025 - 0.500000i) q^{2} +(0.866025 + 0.500000i) q^{3} +(0.500000 + 0.866025i) q^{4} +(-0.500000 - 0.866025i) q^{6} -1.00000i q^{8} +(0.500000 + 0.866025i) q^{9} +O(q^{10})\)	\(q+(-0.866025 - 0.500000i) q^{2} +(0.866025 + 0.500000i) q^{3} +(0.500000 + 0.866025i) q^{4} +(-0.500000 - 0.866025i) q^{6} -1.00000i q^{8} +(0.500000 + 0.866025i) q^{9} +(-1.50000 + 2.59808i) q^{11} +1.00000i q^{12} +(-2.59808 - 2.50000i) q^{13} +(-0.500000 + 0.866025i) q^{16} +(5.19615 - 3.00000i) q^{17} -1.00000i q^{18} +(-3.00000 - 5.19615i) q^{19} +(2.59808 - 1.50000i) q^{22} +(-4.33013 - 2.50000i) q^{23} +(0.500000 - 0.866025i) q^{24} +(1.00000 + 3.46410i) q^{26} +1.00000i q^{27} +(1.00000 - 1.73205i) q^{29} -6.00000 q^{31} +(0.866025 - 0.500000i) q^{32} +(-2.59808 + 1.50000i) q^{33} -6.00000 q^{34} +(-0.500000 + 0.866025i) q^{36} +(7.79423 + 4.50000i) q^{37} +6.00000i q^{38} +(-1.00000 - 3.46410i) q^{39} +(5.00000 - 8.66025i) q^{41} +(6.92820 - 4.00000i) q^{43} -3.00000 q^{44} +(2.50000 + 4.33013i) q^{46} -12.0000i q^{47} +(-0.866025 + 0.500000i) q^{48} +(-3.50000 + 6.06218i) q^{49} +6.00000 q^{51} +(0.866025 - 3.50000i) q^{52} -12.0000i q^{53} +(0.500000 - 0.866025i) q^{54} -6.00000i q^{57} +(-1.73205 + 1.00000i) q^{58} +(7.50000 + 12.9904i) q^{61} +(5.19615 + 3.00000i) q^{62} -1.00000 q^{64} +3.00000 q^{66} +(3.46410 + 2.00000i) q^{67} +(5.19615 + 3.00000i) q^{68} +(-2.50000 - 4.33013i) q^{69} +(-3.50000 - 6.06218i) q^{71} +(0.866025 - 0.500000i) q^{72} +1.00000i q^{73} +(-4.50000 - 7.79423i) q^{74} +(3.00000 - 5.19615i) q^{76} +(-0.866025 + 3.50000i) q^{78} -6.00000 q^{79} +(-0.500000 + 0.866025i) q^{81} +(-8.66025 + 5.00000i) q^{82} -5.00000i q^{83} -8.00000 q^{86} +(1.73205 - 1.00000i) q^{87} +(2.59808 + 1.50000i) q^{88} +(-3.00000 + 5.19615i) q^{89} -5.00000i q^{92} +(-5.19615 - 3.00000i) q^{93} +(-6.00000 + 10.3923i) q^{94} +1.00000 q^{96} +(-4.33013 + 2.50000i) q^{97} +(6.06218 - 3.50000i) q^{98} -3.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 2 q^{4} - 2 q^{6} + 2 q^{9}+O(q^{10}) \) 4 * q + 2 * q^4 - 2 * q^6 + 2 * q^9	\( 4 q + 2 q^{4} - 2 q^{6} + 2 q^{9} - 6 q^{11} - 2 q^{16} - 12 q^{19} + 2 q^{24} + 4 q^{26} + 4 q^{29} - 24 q^{31} - 24 q^{34} - 2 q^{36} - 4 q^{39} + 20 q^{41} - 12 q^{44} + 10 q^{46} - 14 q^{49} + 24 q^{51} + 2 q^{54} + 30 q^{61} - 4 q^{64} + 12 q^{66} - 10 q^{69} - 14 q^{71} - 18 q^{74} + 12 q^{76} - 24 q^{79} - 2 q^{81} - 32 q^{86} - 12 q^{89} - 24 q^{94} + 4 q^{96} - 12 q^{99}+O(q^{100}) \) 4 * q + 2 * q^4 - 2 * q^6 + 2 * q^9 - 6 * q^11 - 2 * q^16 - 12 * q^19 + 2 * q^24 + 4 * q^26 + 4 * q^29 - 24 * q^31 - 24 * q^34 - 2 * q^36 - 4 * q^39 + 20 * q^41 - 12 * q^44 + 10 * q^46 - 14 * q^49 + 24 * q^51 + 2 * q^54 + 30 * q^61 - 4 * q^64 + 12 * q^66 - 10 * q^69 - 14 * q^71 - 18 * q^74 + 12 * q^76 - 24 * q^79 - 2 * q^81 - 32 * q^86 - 12 * q^89 - 24 * q^94 + 4 * q^96 - 12 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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